http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Sh68lee&feedformat=atom statwiki - User contributions [US] 2022-05-20T02:15:47Z User contributions MediaWiki 1.28.3 http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Efficient_kNN_Classification_with_Different_Numbers_of_Nearest_Neighbors&diff=49252 Efficient kNN Classification with Different Numbers of Nearest Neighbors 2020-12-05T20:25:53Z <p>Sh68lee: /* Reconstruction */</p> <hr /> <div>== Presented by == <br /> Cooper Brooke, Daniel Fagan, Maya Perelman<br /> <br /> == Introduction == <br /> Traditional model-based approaches for classification problem requires to train a model on training observations before predicting test samples. In contrast, the model-free k-Nearest Neighbors (KNNs) method classifies observations with a majority rule approach, labeling each piece of test data based on its k closest training observations (neighbors). This method has become very popular due to its relatively robust performance given how simple it is to implement.<br /> <br /> There are two main approaches to conduct kNN classification. The first is to use a fixed k value to classify all test samples, while the second is to use a different k value each time, for each test sample. The former, while easy to implement, has proven to be impractical in machine learning applications. Therefore, interest lies in developing an efficient way to apply a different optimal k value for each test sample. The authors of this paper presented the kTree and k*Tree methods to solve this research question.<br /> <br /> == Previous Work == <br /> <br /> Previous work on finding an optimal fixed k value for all test samples is well-studied. Zhang et al.  incorporated a certainty factor measure to solve for an optimal fixed k. This resulted in the conclusion that k should be &lt;math&gt;\sqrt{n}&lt;/math&gt; (where n is the number of training samples) when n &gt; 100. The method Song et al. explored involved selecting a subset of the most informative samples from neighbourhoods. Vincent and Bengio  took the unique approach of designing a k-local hyperplane distance to solve for k. Premachandran and Kakarala  had the solution of selecting a robust k using the consensus of multiple rounds of kNNs. These fixed k methods are valuable however are impractical for data mining and machine learning applications. <br /> <br /> Finding an efficient approach to assigning varied k values has also been previously studied. Tuning approaches such as the ones taken by Zhu et al. as well as Sahugara et al. have been popular. Zhu et al.  determined that optimal k values should be chosen using cross validation while Sahugara et al.  proposed using Monte Carlo validation to select varied k parameters. Other learning approaches such as those taken by Zheng et al. and Góra and Wojna also show promise. Zheng et al.  applied a reconstruction framework to learn suitable k values. Góra and Wojna  proposed using rule induction and instance-based learning to learn optimal k-values for each test sample. While all these methods are valid, their processes of either learning varied k values or scanning all training samples are time-consuming.<br /> <br /> == Motivation == <br /> <br /> Due to the previously mentioned drawbacks of fixed-k and current varied-k kNN classification, the paper’s authors sought to design a new approach to solve for different k values. The kTree and k*Tree approach seeks to calculate optimal values of k while avoiding computationally costly steps such as cross-validation.<br /> <br /> A secondary motivation of this research was to ensure that the kTree method would perform better than kNN using fixed values of k given that running costs would be similar in this instance.<br /> <br /> == Approach == <br /> <br /> <br /> === kTree Classification ===<br /> <br /> The proposed kTree method is illustrated by the following flow chart:<br /> <br /> [[File:Approach_Figure_1.png | center | 800x800px]]<br /> <br /> ==== Reconstruction ====<br /> <br /> The first step is to use the training samples to reconstruct themselves. The goal of this is to find the matrix of correlations between the training samples themselves, &lt;math&gt;\textbf{W}&lt;/math&gt;, such that the distance between an individual training sample and the corresponding correlation vector multiplied by the entire training set is minimized. This least square loss function where &lt;math&gt;\mathbf{X}\in \mathbb{R}^{d\times n} = [x_1,...,x_n]&lt;/math&gt; represents the training set which can be written as:<br /> <br /> \begin{aligned}<br /> \mathop{min}_{\textbf{W}} \sum_{i=1}^n ||Xw_i - x_i||^2<br /> \end{aligned}<br /> <br /> In addition, an &lt;math&gt;l_1&lt;/math&gt; regularization term multiplied by a tuning parameter, &lt;math&gt;\rho_1&lt;/math&gt;, is added to ensure that sparse results are generated as the objective is to minimize the number of training samples that will eventually be depended on by the test samples. <br /> <br /> \begin{aligned}<br /> \mathop{min}_{\textbf{W}} \sum_{i=1}^n ||Xw_i - x_i||^2 + \rho||\textbf{W}||^2_2<br /> \end{aligned}<br /> <br /> This is called ridge regression and it has a close solution where $$W = (X^TX+\rho I)^{-1}X^TX$$<br /> <br /> However, this objective function does not provide a sparse result, there we further employe a sparse objective function: <br /> <br /> $$W = (X^TX+\rho I)^{-1}X^TX, W &gt;= 0$$<br /> <br /> <br /> The least square loss function is then further modified to account for samples that have similar values for certain features yielding similar results. It is penalized with the function: <br /> <br /> $$\frac{1}{2} \sum^{d}_{i,j} ||x^iW-x^jW||^2_2$$<br /> <br /> with sij denotes the relation between feature vectors. It uses a radial basis function kernel to calculate Sij. After some transformations, this second regularization term that has tuning parameter &lt;math&gt;\rho_2&lt;/math&gt; is:<br /> <br /> \begin{aligned}<br /> R(W) = Tr(\textbf{W}^T \textbf{X}^T \textbf{LXW})<br /> \end{aligned}<br /> <br /> where &lt;math&gt;\mathbf{L}&lt;/math&gt; is a Laplacian matrix that indicates the relationship between features. The Laplacian matrix, also called the graph Laplacian, is a matrix representation of a graph. <br /> <br /> This gives a final objective function of:<br /> <br /> \begin{aligned}<br /> \mathop{min}_{\textbf{W}} \sum_{i=1}^n ||Xw_i - x_i||^2 + \rho_1||\textbf{W}|| + \rho_2R(\textbf{W})<br /> \end{aligned}<br /> <br /> Since this is a convex function, an iterative method can be used to find the optimal solution &lt;math&gt;\mathbf{W^*}&lt;/math&gt;.<br /> <br /> ==== Calculate ''k'' for training set ====<br /> <br /> Each element &lt;math&gt;w_{ij}&lt;/math&gt; in &lt;math&gt;\textbf{W*}&lt;/math&gt; represents the correlation between the ith and jth training sample so if a value is 0, it can be concluded that the jth training sample has no effect on the ith training sample which means that it should not be used in the prediction of the ith training sample. Consequently, all non-zero values in the &lt;math&gt;w_{.j}&lt;/math&gt; vector would be useful in predicting the ith training sample which gives the result that the number of these non-zero elements for each sample is equal to the optimal ''k'' value for each sample.<br /> <br /> For example, if there was a 4x4 training set where &lt;math&gt;\textbf{W*}&lt;/math&gt; had the form:<br /> <br /> [[File:Approach_Figure_2.png | center | 300x300px]]<br /> <br /> The optimal ''k'' value for training sample 1 would be 2 since the correlation between training sample 1 and both training samples 2 and 4 are non-zero.<br /> <br /> ==== Train a Decision Tree using ''k'' as the label ====<br /> <br /> A decision tree is trained using the traditional ID3 method;<br /> (1) calculate the entropy of every feature in your data set,<br /> (2) split the data-set based on the feature whose entropy is minimized after splitting (in the example below, this was feature a'),<br /> (3) make a decision tree node based on that feature,<br /> (4) repeat steps (1)-(3) recursively on the formed subsets using the remaining features, <br /> replacing the label by the previously learned optimal ''k'' value for each sample. More specifically, whereas in a normal decision tree, the target data are the labels themselves, in the kTree method, the target data is the optimal ''k'' value for each sample that was solved for in the previous step. As a result, the decision tree formed by the kTree method has the following form:<br /> <br /> [[File:Approach_Figure_3.png | center | 300x300px]]<br /> <br /> ==== Making Predictions for Test Data ====<br /> <br /> The optimal ''k'' values for each testing sample are easily obtainable using the kTree solved for in the previous step. The only remaining step is to predict the labels of the testing samples by finding the majority class of the optimal ''k'' nearest neighbors across '''all''' of the training data.<br /> <br /> === k*Tree Classification ===<br /> <br /> The proposed k*Tree method is illustrated by the following flow chart:<br /> <br /> [[File:Approach_Figure_4.png | center | 1000x1000px]]<br /> <br /> Clearly, this is a very similar approach to the kTree as the k*Tree method attempts to sacrifice very little in predictive power in return for a substantial decrease in complexity when actually implementing the traditional kNN on the testing data once the optimal ''k'' values have been found.<br /> <br /> While all steps previous are the exact same, the difference comes from additional data stored in the leaf nodes. k*Tree method not only stores the optimal ''k'' value but also the following information:<br /> <br /> * The training samples that have the same optimal ''k''<br /> * The ''k'' nearest neighbours of the previously identified training samples<br /> * The nearest neighbor of each of the previously identified ''k'' nearest neighbours<br /> <br /> The data stored in each node is summarized in the following figure:<br /> <br /> [[File:Approach_Figure_5.png | center | 800x800px]]<br /> <br /> When testing, the constructed k*Tree is searched for its optimal k values well as its nearest neighbours in the leaf node. It then selects a number of its nearest neighbours from the subset of training samples and assigns the test sample with the majority label of these nearest neighbours.<br /> <br /> In the kTree method, predictions were made based on all of the training data, whereas in the k*Tree method, predicting the test labels will only be done using the samples stored in the applicable node of the tree.<br /> <br /> == Experiments == <br /> <br /> In order to assess the performance of the proposed method against existing methods, a number of experiments were performed to measure classification accuracy and run time. The experiments were run on twenty public datasets provided by the UCI Repository of Machine Learning Data, and contained a mix of data types varying in size, in dimensionality, in the number of classes, and in imbalanced nature of the data. Ten-fold cross-validation was used to measure classification accuracy, and the following methods were compared against:<br /> <br /> # k-Nearest Neighbor: The classical kNN approach with k set to k=1,5,10,20 and square root of the sample size ; the best result was reported.<br /> # kNN-Based Applicability Domain Approach (AD-kNN) <br /> # kNN Method Based on Sparse Learning (S-kNN) <br /> # kNN Based on Graph Sparse Reconstruction (GS-kNN) <br /> # Filtered Attribute Subspace-based Bagging with Injected Randomness (FASBIR) , <br /> # Landmark-based Spectral Clustering kNN (LC-kNN) <br /> <br /> The experimental results were then assessed based on classification tasks that focused on different sample sizes, and tasks that focused on different numbers of features. <br /> <br /> <br /> '''A. Experimental Results on Different Sample Sizes'''<br /> <br /> The running cost and (cross-validation) classification accuracy based on experiments on ten UCI datasets can be seen in Table I below.<br /> <br /> [[File:Table_I_kNN.png | center | 1000x1000px]]<br /> <br /> The following key results are noted:<br /> * Regarding classification accuracy, the proposed methods (kTree and k*Tree) outperformed kNN, AD-KNN, FASBIR, and LC-kNN on all datasets by 1.5%-4.5%, but had no notable improvements compared to GS-kNN and S-kNN.<br /> * Classification methods which involved learning optimal k-values (for example the proposed kTree and k*Tree methods, or S-kNN, GS-kNN, AD-kNN) outperformed the methods with predefined k-values, such as traditional kNN.<br /> * The proposed k*Tree method had the lowest running cost of all methods. However, the k*Tree method was still outperformed in terms of classification accuracy by GS-kNN and S-kNN, but ran on average 15 000 times faster than either method. In addition, the kTree had the highest accuracy and it's running cost was lower than any other methods except the k*Tree method.<br /> <br /> <br /> '''B. Experimental Results on Different Feature Numbers'''<br /> <br /> The goal of this section was to evaluate the robustness of all methods under differing numbers of features; results can be seen in Table II below. The Fisher score, an algorithm that solves maximum likelihood equations numerically , was used to rank and select the most information features in the datasets. <br /> <br /> [[File:Table_II_kNN.png | center | 1000x1000px]]<br /> <br /> From Table II, the proposed kTree and k*Tree approaches outperformed kNN, AD-kNN, FASBIR and LC-KNN when tested for varying feature numbers. The S-kNN and GS-kNN approaches remained the best in terms of classification accuracy, but were greatly outperformed in terms of running cost by k*Tree. The cause for this is that k*Tree only scans a subsample of the training samples for kNN classification, while S-kNN and GS-kNN scan all training samples.<br /> <br /> == Conclusion == <br /> <br /> This paper introduced two novel approaches for kNN classification algorithms that can determine optimal k-values for each test sample. The proposed kTree and k*Tree methods can classify the test samples efficiently and effectively, by designing a training step that reduces the run time of the test stage and thus enhances the performance. Based on the experimental results for varying sample sizes and differing feature numbers, it was observed that the proposed methods outperformed existing ones in terms of running cost while still achieving similar or better classification accuracies. Future areas of investigation could focus on the improvement of kTree and k*Tree for data with large numbers of features.<br /> <br /> == Critiques == <br /> <br /> *The paper only assessed classification accuracy through cross-validation accuracy. However, it would be interesting to investigate how the proposed methods perform using different metrics, such as AUC, precision-recall curves, or in terms of holdout test data set accuracy. <br /> * The authors addressed that some of the UCI datasets contained imbalanced data (such as the Climate and German data sets) while others did not. However, the nature of the class imbalance was not extreme, and the effect of imbalanced data on algorithm performance was not discussed or assessed. Moreover, it would have been interesting to see how the proposed algorithms performed on highly imbalanced datasets in conjunction with common techniques to address imbalance (e.g. oversampling, undersampling, etc.). <br /> *While the authors contrast their kTree and k*Tree approach with different kNN methods, the paper could contrast their results with more of the approaches discussed in the Related Work section of their paper. For example, it would be interesting to see how the kTree and k*Tree results compared to Góra and Wojna varied optimal k method.<br /> <br /> * The paper conducted an experiment on kNN, AD-kNN, S-kNN, GS-kNN,FASBIR and LC-kNN with different sample sizes and feature numbers. It would be interesting to discuss why the running cost of FASBIR is between that of kTree and k*Tree in figure 21.<br /> <br /> * A different [https://iopscience.iop.org/article/10.1088/1757-899X/725/1/012133/pdf paper] also discusses optimizing the K value for the kNN algorithm in clustering. However, this paper suggests using the expectation-maximization algorithm as a means of finding the optimal k value.<br /> <br /> * It would be really helpful if kTrees method can be explained at the very beginning. The transition from KNN to kTrees is not very smooth.<br /> <br /> * It would be nice to have a comparison of the running costs of different methods to see how much faster kTree and k*Tree performed<br /> <br /> * It would be better to show the key result only on a summary rather than stacking up all results without screening.<br /> <br /> * In the results section, it was mentioned that in the experiment on data sets with different numbers of features, the kTree and k*Tree model did not achieve GS-kNN or S-kNN's accuracies, but was faster in terms of running cost. It might be helpful here if the authors add some more supporting arguments about the benefit of this tradeoff, which appears to be a minor decrease in accuracy for a large improvement in speed. This could further showcase the advantages of the kTree and k*Tree models. More quantitative analysis or real-life scenario examples could be some choices here.<br /> <br /> * An interesting thing to notice while solving for the optimal matrix &lt;math&gt;W^*&lt;/math&gt; that minimizes the loss function is that &lt;math&gt;W^*&lt;/math&gt; is not necessarily a symmetric matrix. That is, the correlation between the &lt;math&gt;i^{th}&lt;/math&gt; entry and the &lt;math&gt;j^{th}&lt;/math&gt; entry is different from that between the &lt;math&gt;j^{th}&lt;/math&gt; entry and the &lt;math&gt;i^{th}&lt;/math&gt; entry, which makes the resulting W* not really semantically meaningful. Therefore, it would be interesting if we may set a threshold on the allowing difference between the &lt;math&gt;ij^{th}&lt;/math&gt; entry and the &lt;math&gt;ji^{th}&lt;/math&gt; entry in &lt;math&gt;W^*&lt;/math&gt; and see if this new configuration will give better or worse results compared to current ones, which will provide better insights of the algorithm.<br /> <br /> * It would be interesting to see how the proposed model works with highly non-linear datasets. In the event it does not work well, it would pose the question: would replacing the k*Tree with a SVM or a neural network improve the accuracy? There could be experiments to show if this variant would prove superior over the original models.<br /> <br /> * The key results are a little misleading - for example they claim &quot;the kTree had the highest accuracy and it's running cost was lower than any other methods except the k*Tree method&quot; is false. The kTree method had slightly lower accuracy than both GS-kNN and S-kNN and kTree was also slower than LC-kNN<br /> <br /> * I want to point to the discussion on k*Tree's structure. In order for k*Tree to work effectively, its leaf nodes needs to store additional information. In addition to the optimal k value, it also needs to store things like the training samples that have the optimal k, and the k nearest neighbours of the previously identified training samples. How big of am impact does this structure have on storage cost? Since the number of leaf nodes can be large, the storage cost may be large as well. This can potentially make k*tree ineffective to use in practice, especially for very large datasets.<br /> <br /> * It would be better if the author can explain more on KTree method and the similarity of KTree method and KNN method.<br /> <br /> * Even though we are given a table with averages on the accuracy and mean running cost, it would have been nice to see a direct visual comparison in the figures followed below. In addition to comparing to other algorithms, it would be helpful to see the average expected cost of these algorithms to show as control or rather a standard to accuracy and compute cost to assess the overall general expected cost of running such classification algorithm to fully assess its efficacy.<br /> <br /> * It doesn't clearly mention what's the definition/similarity/difference between Ktree and KNN methods. If the authors could put some detailed explanations in the beginning, the flow of this paper would have been much better.<br /> <br /> == References == <br /> <br />  C. Zhang, Y. Qin, X. Zhu, and J. Zhang, “Clustering-based missing value imputation for data preprocessing,” in Proc. IEEE Int. Conf., Aug. 2006, pp. 1081–1086.<br /> <br />  Y. Song, J. Huang, D. Zhou, H. Zha, and C. L. Giles, “IKNN: Informative K-nearest neighbor pattern classification,” in Knowledge Discovery in Databases. Berlin, Germany: Springer, 2007, pp. 248–264.<br /> <br />  P. Vincent and Y. Bengio, “K-local hyperplane and convex distance nearest neighbor algorithms,” in Proc. NIPS, 2001, pp. 985–992.<br /> <br />  V. Premachandran and R. Kakarala, “Consensus of k-NNs for robust neighborhood selection on graph-based manifolds,” in Proc. CVPR, Jun. 2013, pp. 1594–1601.<br /> <br />  X. Zhu, S. Zhang, Z. Jin, Z. Zhang, and Z. Xu, “Missing value estimation for mixed-attribute data sets,” IEEE Trans. Knowl. Data Eng., vol. 23, no. 1, pp. 110–121, Jan. 2011.<br /> <br />  F. Sahigara, D. Ballabio, R. Todeschini, and V. Consonni, “Assessing the validity of QSARS for ready biodegradability of chemicals: An applicability domain perspective,” Current Comput.-Aided Drug Design, vol. 10, no. 2, pp. 137–147, 2013.<br /> <br />  S. Zhang, M. Zong, K. Sun, Y. Liu, and D. Cheng, “Efficient kNN algorithm based on graph sparse reconstruction,” in Proc. ADMA, 2014, pp. 356–369.<br /> <br />  X. Zhu, L. Zhang, and Z. Huang, “A sparse embedding and least variance encoding approach to hashing,” IEEE Trans. Image Process., vol. 23, no. 9, pp. 3737–3750, Sep. 2014.<br /> <br />  U. Lall and A. Sharma, “A nearest neighbor bootstrap for resampling hydrologic time series,” Water Resour. Res., vol. 32, no. 3, pp. 679–693, 1996.<br /> <br />  D. Cheng, S. Zhang, Z. Deng, Y. Zhu, and M. Zong, “KNN algorithm with data-driven k value,” in Proc. ADMA, 2014, pp. 499–512.<br /> <br />  F. Sahigara, D. Ballabio, R. Todeschini, and V. Consonni, “Assessing the validity of QSARS for ready biodegradability of chemicals: An applicability domain perspective,” Current Comput.-Aided Drug Design, vol. 10, no. 2, pp. 137–147, 2013. <br /> <br />  Z. H. Zhou and Y. Yu, “Ensembling local learners throughmultimodal perturbation,” IEEE Trans. Syst. Man, B, vol. 35, no. 4, pp. 725–735, Apr. 2005.<br /> <br />  Z. H. Zhou, Ensemble Methods: Foundations and Algorithms. London, U.K.: Chapman &amp; Hall, 2012.<br /> <br />  Z. Deng, X. Zhu, D. Cheng, M. Zong, and S. Zhang, “Efficient kNN classification algorithm for big data,” Neurocomputing, vol. 195, pp. 143–148, Jun. 2016.<br /> <br />  K. Tsuda, M. Kawanabe, and K.-R. Müller, “Clustering with the fisher score,” in Proc. NIPS, 2002, pp. 729–736.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=49251 User:Cvmustat 2020-12-05T20:05:52Z <p>Sh68lee: /* Critiques */</p> <hr /> <div><br /> == Combine Convolution with Recurrent Networks for Text Classification == <br /> '''Team Members''': Bushra Haque, Hayden Jones, Michael Leung, Cristian Mustatea<br /> <br /> '''Date''': Week of Nov 23 <br /> <br /> == Introduction ==<br /> <br /> <br /> Text classification is the task of assigning a set of predefined categories to natural language texts. It involves learning an embedding layer which allows context-dependent classification. It is a fundamental task in Natural Language Processing (NLP) with various applications such as sentiment analysis, and topic classification. A classic example involving text classification is given a set of News articles, is it possible to classify the genre or subject of each article? Text classification is useful as text data is a rich source of information, but extracting insights from it directly can be difficult and time-consuming as most text data is unstructured. NLP text classification can help automatically structure and analyze text quickly and cost-effectively, allowing for individuals to extract important features from the text easier than before. <br /> <br /> Text classification work mainly focuses on three topics: feature engineering, feature selection, and the use of different types of machine learning algorithms.<br /> :1. Feature engineering, the most widely used feature is the bag of words feature. Some more complex functions are also designed, such as part-of-speech tags, noun phrases, and tree kernels.<br /> :2. Feature selection aims to remove noisy features and improve classification performance. The most common feature selection method is to delete stop words.<br /> :3. Machine learning algorithms usually use classifiers, such as Logistic Regression (LR), Naive Bayes (NB), and Support Vector Machine (SVM).<br /> <br /> In practice, pre-trained word embeddings and deep neural networks are used together for NLP text classification. Word embeddings are used to map the raw text data to an implicit space where the semantic relationships of the words are preserved; words with similar meaning have a similar representation. One can then feed these embeddings into deep neural networks to learn different features of the text. Convolutional neural networks can be used to determine the semantic composition of the text(the meaning), as it treats texts as a 2D matrix by concatenating the embedding of words together. It uses a 1D convolution operator to perform the feature mapping and then conducts a 1D pooling operation over the time domain for obtaining a fixed-length output feature vector, and it can capture both local and position invariant features of the text. Alternatively, Recurrent Neural Networks can be used to determine the contextual meaning of each word in the text (how each word relates to one another) by treating the text as sequential data and then analyzing each word separately.  Previous approaches to attempt to combine these two neural networks to incorporate the advantages of both models involve streamlining the two networks, which might decrease their performance. Besides, most methods incorporating a bi-directional Recurrent Neural Network usually concatenate the forward and backward hidden states at each time step, which results in a vector that does not have the interaction information between the forward and backward hidden states. The hidden state in one direction contains only the contextual meaning in that particular direction, however a word's contextual representation, intuitively, is more accurate when collected and viewed from both directions. This paper argues that the failure to observe the meaning of a word in both directions causes the loss of the true meaning of the word, especially for polysemic words (words with more than one meaning) that are context-sensitive.<br /> <br /> == Paper Key Contributions ==<br /> <br /> This paper suggests an enhanced method of text classification by proposing a new way of combining Convolutional and Recurrent Neural Networks (CRNN) involving the addition of a neural tensor layer. The proposed method maintains each network's respective strengths that are normally lost in previous combination methods. The new suggested architecture is called CRNN, which utilizes both a CNN and RNN that run in parallel on the same input sentence. CNN uses weight matrix learning and produces a 2D matrix that shows the importance of each word based on local and position-invariant features. The bidirectional RNN produces a matrix that learns each word's contextual representation; the words' importance about to with concerning the rest of the sentence. <br /> <br /> A possible limitation of traditional convolutional layers is that they extract features from the data using a non-linearity applied on affine functions. The extracted feature is calculated by multiplying the weight matrix with the input data, summing up the products, adding a scalar, then employing a non-linear function. The purpose of the function is to achieve a better representation of the input data by using more layers. However, this cannot be achieved by stacking more convolutional layers because a consequent layer will not be able to extract more complex features using the output from the previous layer. <br /> <br /> Unlike CNN, CRNN introduces a neural tensor layer on top of the RNN to obtain the fusion of bi-directional contextual information surrounding a particular word. This method combines the weight matrix and the word representations together as well as classifies the text according to certain criteria, providing the important information of each word for prediction, which helps to explain the results. The model also uses dropout and L2 regularization to prevent overfitting, which in our case means only updating parts of the filters while the other features (columns in the matrix) remain zero.<br /> <br /> == CRNN Results vs Benchmarks ==<br /> <br /> In order to benchmark the performance of the CRNN model, as well as compare it to other previous efforts, multiple datasets and classification problems were used. All of these datasets are publicly available and can be easily downloaded by any user for testing.<br /> <br /> - '''Movie Reviews:''' a sentiment analysis dataset, with two classes (positive and negative).<br /> <br /> - '''Yelp:''' a sentiment analysis dataset, with five classes. For this test, a subset of 120,000 reviews was randomly chosen from each class for a total of 600,000 reviews.<br /> <br /> - '''AG's News:''' a news categorization dataset, using only the 4 largest classes from the dataset. There are 30000 training samples and 1900 test samples.<br /> <br /> - '''20 Newsgroups:''' a news categorization dataset, again using only 4 large classes (comp, politics, rec, and religion) from the dataset.<br /> <br /> - '''Sogou News:''' a Chinese news categorization dataset, using 10 major classes as a multi-class classification and include 6500 samples randomly from each class.<br /> <br /> - '''Yahoo! Answers:''' a topic classification dataset, with 10 classes and each class contains 140000 training samples and 5000 testing samples.<br /> <br /> For the English language datasets, the initial word representations were created using the publicly available ''word2vec'' [https://code.google.com/p/word2vec/] from Google news. For the Chinese language dataset, ''jieba'' [https://github.com/fxsjy/jieba] was used to segment sentences, and then 50-dimensional word vectors were trained on Chinese ''wikipedia'' using ''word2vec''.<br /> <br /> A number of other models are run against the same data after preprocessing. Some of these models include:<br /> <br /> - '''Self-attentive LSTM:''' an LSTM model with multi-hop attention for sentence embedding.<br /> <br /> - '''RCNN:''' the RCNN's recurrent structure allows for increased depth of capture for contextual information. Less noise is introduced on account of the model's holistic structure (compared to local features).<br /> <br /> The following results are obtained:<br /> <br /> [[File:table of results.png|550px|center]]<br /> <br /> The bold results represent the best performing model for a given dataset. These results show that the CRNN model is the best model for 4 of the 6 datasets, with the Self-attentive LSTM beating the CRNN by 0.03 and 0.12 on the news categorization problems. Considering that the CRNN model has better performance than the Self-attentive LSTM on the other 4 datasets, this suggests that the CRNN model is a better performer overall in the conditions of this benchmark.<br /> <br /> It should be noted that including the neural tensor layer in the CRNN model leads to a significant performance boost compared to the CRNN models without it. The performance boost can be attributed to the fact that the neural tensor layer captures the surrounding contextual information for each word, and brings this information between the forward and backward RNN in a direct method. As seen in the table, this leads to a better classification accuracy across all datasets.<br /> <br /> Another important result was that the CRNN model filter size impacted performance only in the sentiment analysis datasets, as seen in the following table, where the results for the AG's news, Yelp, and Yahoo! Answer datasets are displayed:<br /> <br /> [[File:filter_effects.png|550px|center]]<br /> <br /> == CRNN Model Architecture ==<br /> <br /> The CRNN model is a combination of RNN and CNN. It uses a CNN to compute the importance of each word in the text and utilizes a neural tensor layer to fuse forward and backward hidden states of bi-directional RNN.<br /> <br /> The input of the network is a text, which is a sequence of words. The output of the network is the text representation that is subsequently used as input of a fully-connected layer to obtain the class prediction.<br /> <br /> '''RNN Pipeline:'''<br /> <br /> The goal of the RNN pipeline is to input each word in a text, and retrieve the contextual information surrounding the word and compute the contextual representation of the word itself. This is accomplished by the use of a bi-directional RNN, such that a Neural Tensor Layer (NTL) can combine the results of the RNN to obtain the final output. RNNs are well-suited to NLP tasks because of their ability to sequentially process data such as ordered text.<br /> <br /> A RNN is similar to a feed-forward neural network, but it relies on the use of hidden states. Hidden states are layers in the neural net that produce two outputs: &lt;math&gt; \hat{y}_{t} &lt;/math&gt; and &lt;math&gt; h_t &lt;/math&gt;. For a time step &lt;math&gt; t &lt;/math&gt;, &lt;math&gt; h_t &lt;/math&gt; is fed back into the layer to compute &lt;math&gt; \hat{y}_{t+1} &lt;/math&gt; and &lt;math&gt; h_{t+1} &lt;/math&gt;. <br /> <br /> The pipeline will actually use a variant of RNN called GRU, short for Gated Recurrent Units. This is done to address the vanishing gradient problem which causes the network to struggle to memorize words that came earlier in the sequence. Traditional RNNs are only able to remember the most recent words in a sequence, which may be problematic since words that came at the beginning of the sequence that is important to the classification problem may be forgotten. A GRU attempts to solve this by controlling the flow of information through the network using update and reset gates. <br /> <br /> Let &lt;math&gt;h_{t-1} \in \mathbb{R}^m, x_t \in \mathbb{R}^d &lt;/math&gt; be the inputs, and let &lt;math&gt;\mathbf{W}_z, \mathbf{W}_r, \mathbf{W}_h \in \mathbb{R}^{m \times d}, \mathbf{U}_z, \mathbf{U}_r, \mathbf{U}_h \in \mathbb{R}^{m \times m}&lt;/math&gt; be trainable weight matrices. Then the following equations describe the update and reset gates:<br /> <br /> <br /> &lt;math&gt;<br /> z_t = \sigma(\mathbf{W}_zx_t + \mathbf{U}_zh_{t-1}) \text{update gate} \\<br /> r_t = \sigma(\mathbf{W}_rx_t + \mathbf{U}_rh_{t-1}) \text{reset gate} \\<br /> \tilde{h}_t = \text{tanh}(\mathbf{W}_hx_t + r_t \circ \mathbf{U}_hh_{t-1}) \text{new memory} \\<br /> h_t = (1-z_t)\circ \tilde{h}_t + z_t\circ h_{t-1}<br /> &lt;/math&gt;<br /> <br /> <br /> Note that &lt;math&gt; \sigma, \text{tanh}, \circ &lt;/math&gt; are all element-wise functions. The above equations do the following:<br /> <br /> &lt;ol&gt;<br /> &lt;li&gt; &lt;math&gt;h_{t-1}&lt;/math&gt; carries information from the previous iteration and &lt;math&gt;x_t&lt;/math&gt; is the current input &lt;/li&gt;<br /> &lt;li&gt; the update gate &lt;math&gt;z_t&lt;/math&gt; controls how much past information should be forwarded to the next hidden state &lt;/li&gt;<br /> &lt;li&gt; the rest gate &lt;math&gt;r_t&lt;/math&gt; controls how much past information is forgotten or reset &lt;/li&gt;<br /> &lt;li&gt; new memory &lt;math&gt;\tilde{h}_t&lt;/math&gt; contains the relevant past memory as instructed by &lt;math&gt;r_t&lt;/math&gt; and current information from the input &lt;math&gt;x_t&lt;/math&gt; &lt;/li&gt;<br /> &lt;li&gt; then &lt;math&gt;z_t&lt;/math&gt; is used to control what is passed on from &lt;math&gt;h_{t-1}&lt;/math&gt; and &lt;math&gt;(1-z_t)&lt;/math&gt; controls the new memory that is passed on<br /> &lt;/ol&gt;<br /> <br /> We treat &lt;math&gt;h_0&lt;/math&gt; and &lt;math&gt; h_{n+1} &lt;/math&gt; as zero vectors in the method. Thus, each &lt;math&gt;h_t&lt;/math&gt; can be computed as above to yield results for the bi-directional RNN. The resulting hidden states &lt;math&gt;\overrightarrow{h_t}&lt;/math&gt; and &lt;math&gt;\overleftarrow{h_t}&lt;/math&gt; contain contextual information around the &lt;math&gt; t&lt;/math&gt;-th word in forward and backward directions respectively. Contrary to convention, instead of concatenating these two vectors, it is argued that the word's contextual representation is more precise when the context information from different directions is collected and fused using a neural tensor layer as it permits greater interactions among each element of hidden states. Using these two vectors as input to the neural tensor layer, &lt;math&gt;V^i &lt;/math&gt;, we compute a new representation that aggregates meanings from the forward and backward hidden states more accurately as follows:<br /> <br /> &lt;math&gt; <br /> [\hat{h_t}]_i = tanh(\overrightarrow{h_t}V^i\overleftarrow{h_t} + b_i) <br /> &lt;/math&gt;<br /> <br /> Where &lt;math&gt;V^i \in \mathbb{R}^{m \times m} &lt;/math&gt; is the learned tensor layer, and &lt;math&gt; b_i \in \mathbb{R} &lt;/math&gt; is the bias.We repeat this &lt;math&gt; m &lt;/math&gt; times with different &lt;math&gt;V^i &lt;/math&gt; matrices and &lt;math&gt; b_i &lt;/math&gt; vectors. Through the neural tensor layer, each element in &lt;math&gt; [\hat{h_t}]_i &lt;/math&gt; can be viewed as a different type of intersection between the forward and backward hidden states. In the model, &lt;math&gt; [\hat{h_t}]_i &lt;/math&gt; will have the same size as the forward and backward hidden states. We then concatenate the three hidden states vectors to form a new vector that summarizes the context information :<br /> &lt;math&gt;<br /> \overleftrightarrow{h_t} = [\overrightarrow{h_t}^T,\overleftarrow{h_t}^T,\hat{h_t}]^T <br /> &lt;/math&gt;<br /> <br /> We calculate this vector for every word in the text and then stack them all into matrix &lt;math&gt; H &lt;/math&gt; with shape &lt;math&gt;n&lt;/math&gt;-by-&lt;math&gt;3m&lt;/math&gt;.<br /> <br /> &lt;math&gt;<br /> H = [\overleftrightarrow{h_1};...\overleftrightarrow{h_n}]<br /> &lt;/math&gt;<br /> <br /> This &lt;math&gt;H&lt;/math&gt; matrix is then forwarded as the results from the Recurrent Neural Network.<br /> <br /> <br /> '''CNN Pipeline:'''<br /> <br /> The goal of the CNN pipeline is to learn the relative importance of words in an input sequence based on different aspects. The process of this CNN pipeline is summarized as the following steps:<br /> <br /> &lt;ol&gt;<br /> &lt;li&gt; Given a sequence of words, each word is converted into a word vector using the word2vec algorithm which gives matrix X. <br /> &lt;/li&gt;<br /> <br /> &lt;li&gt; Word vectors are then convolved through the temporal dimension with filters of various sizes (ie. different K) with learnable weights to capture various numerical K-gram representations. These K-gram representations are stored in matrix C.<br /> &lt;/li&gt;<br /> <br /> &lt;ul&gt;<br /> &lt;li&gt; The convolution makes this process capture local and position-invariant features. Local means the K words are contiguous. Position-invariant means K contiguous words at any position are detected in this case via convolution.<br /> <br /> &lt;li&gt; Temporal dimension example: convolve words from 1 to K, then convolve words 2 to K+1, etc<br /> &lt;/li&gt;<br /> &lt;/ul&gt;<br /> <br /> &lt;li&gt; Since not all K-gram representations are equally meaningful, there is a learnable matrix W which takes the linear combination of K-gram representations to more heavily weigh the more important K-gram representations for the classification task.<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt; Each linear combination of the K-gram representations gives the relative word importance based on the aspect that the linear combination encodes.<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt; The relative word importance vs aspect gives rise to an interpretable attention matrix A, where each element says the relative importance of a specific word for a specific aspect.<br /> &lt;/li&gt;<br /> <br /> &lt;/ol&gt;<br /> <br /> [[File:Group12_Figure1.png |center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: The architecture of CRNN.&lt;/div&gt;<br /> <br /> == Merging RNN &amp; CNN Pipeline Outputs ==<br /> <br /> The results from both the RNN and CNN pipeline can be merged by simply multiplying the output matrices. That is, we compute &lt;math&gt;S=A^TH&lt;/math&gt; which has shape &lt;math&gt;z \times 3m&lt;/math&gt; and is essentially a linear combination of the hidden states. The concatenated rows of S results in a vector in &lt;math&gt;\mathbb{R}^{3zm}&lt;/math&gt; and can be passed to a fully connected Softmax layer to output a vector of probabilities for our classification task. <br /> <br /> To train the model, we make the following decisions:<br /> &lt;ul&gt;<br /> &lt;li&gt; Use cross-entropy loss as the loss function (A cross-entropy loss function usually takes in two distributions, a true distribution p and an estimated distribution q, and measures the average number of bits need to identify an event. This calculation is independent of the kind of layers used in the network as well as the kind of activation being implemented.) &lt;/li&gt;<br /> &lt;li&gt; Perform dropout on random columns in matrix C in the CNN pipeline &lt;/li&gt;<br /> &lt;li&gt; Perform L2 regularization on all parameters &lt;/li&gt;<br /> &lt;li&gt; Use stochastic gradient descent with a learning rate of 0.001 &lt;/li&gt;<br /> &lt;/ul&gt;<br /> <br /> == Interpreting Learned CRNN Weights ==<br /> <br /> Recall that attention matrix A essentially stores the relative importance of every word in the input sequence for every aspect chosen. Naturally, this means that A is an n-by-z matrix, with n being the number of words in the input sequence and z being the number of aspects considered in the classification task. <br /> <br /> Furthermore, for any specific aspect, words with higher attention values are more important relative to other words in the same input sequence. likewise, for any specific word, aspects with higher attention values prioritize the specific word more than other aspects.<br /> <br /> For example, in this paper, a sentence is sampled from the Movie Reviews dataset, and the transpose of attention matrix A is visualized. Each word represents an element in matrix A, the intensity of red represents the magnitude of an attention value in A, and each sentence is the relative importance of each word for a specific context. In the first row, the words are weighted in terms of a positive aspect, in the last row, the words are weighted in terms of a negative aspect, and in the middle row, the words are weighted in terms of a positive and negative aspect. Notice how the relative importance of words is a function of the aspect.<br /> <br /> [[File:Interpretation example.png|800px|center]]<br /> <br /> From the above sample, it is interesting that the word &quot;but&quot; is viewed as a negative aspect. From a linguistic perspective, the semantic of &quot;but&quot; is incredibly difficult to capture because of the degree of contextual information it needs. In this case, &quot;but&quot; is in the middle of a transition from a negative to a positive so the first row should also have given attention to that word. Also, it seems that the model has learned to give very high attention to the two words directly adjacent to the word of high attention: &quot;is&quot; and &quot;and&quot; beside &quot;powerful&quot;, and &quot;an&quot; and &quot;cast&quot; beside &quot;unwieldy&quot;.<br /> <br /> The paper also shows that the model can determine important words in the news. The authors take Ag's news dataset and randomly select 10 important words for each class. The table (shown below) contains eye-catching words which fit their classes well.<br /> <br /> [[File:news_words.png|480px|center]]<br /> <br /> == Conclusion &amp; Summary ==<br /> <br /> This paper proposed a new architecture, the Convolutional Recurrent Neural Network, for text classification. The Convolutional Neural Network is used to learn the relative importance of each word from their different aspects and stores this information into a weight matrix. The Recurrent Neural Network learns each word's contextual representation through the combination of the forward and backward context information that is fused using a neural tensor layer and is stored as a matrix. These two matrices are then combined to get the text representation used for classification. Although the specifics of the performed tests are lacking, the experiment's results indicate that the proposed method performed well in comparison to most previous methods. In addition to performing well, the proposed method also provides insight into which words contribute greatly to the classification decision as to the learned matrix from the Convolutional Neural Network stores the relative importance of each word. This information can then be used in other applications or analyses. In the future, one can explore the features extracted from the model and use them to potentially learn new methods such as model space. <br /> <br /> == Critiques ==<br /> <br /> 1. In the '''Method''' section of the paper, some explanations used the same notation for multiple different elements of the model. This made the paper harder to follow and understand since they were referring to different elements by identical notation. Additionally, the decision to use sigmoid and hyperbolic tangent functions as nonlinearities for representation learning is not supported with evidence that these are optimal.<br /> <br /> 2. In '''Comparison of Methods''', the authors discuss the range of hyperparameter settings that they search through. While some of the hyperparameters have a large range of search values, three parameters are fixed without much explanation as to why for all experiments, size of the hidden state of GRU, number of layers, and dropout. These parameters have a lot to do with the complexity of the model and this paper could be improved by providing relevant reasoning behind these values, or by providing additional experimental results over different values of these parameters.<br /> <br /> 3. In the '''Results''' section of the paper, they tried to show that the classification results from the CRNN model can be better interpreted than other models. In these explanations, the details were lacking and the authors did not adequately demonstrate how their model is better than others.<br /> <br /> 4. Finally, in the '''Results''' section again, the paper compares the CRNN model to several models which they did not implement and reproduce results with. This can be seen in the chart of results above, where several models do not have entries in the table for all six datasets. Since the authors used a subset of the datasets, these other models which were not reproduced could have different accuracy scores if they had been tested on the same data as the CRNN model. This difference in training and testing data is not mentioned in the paper, and the conclusion that the CRNN model is better in all cases may not be valid.<br /> <br /> 5. Considering the general methodology, the author in the paper chose to fuse CNN with Gated recurrent unit (GRU), which is only one version of RNN. However, it has been shown that LSTM generally performs better than GRU, and the author should discuss their choice of using GRU in CRNN instead of LSTM in more detail. Looking at the authors' experimental results, LSTM even outperforms CRNN (with GRU) in some cases, which further motivates the idea of adopting LSTM for RNN to combine with CNN. Whether combining LSTM with CNN will lead to a better performance will of course need further verification, but in principle author should at least address the issue. <br /> <br /> 6. This is an interesting method, I would be curious to see if this can be combined or compared with Quasi-Recurrent Neural Networks (https://arxiv.org/abs/1611.01576). In my experience, QRNNs perform similarly to LSTMs while running significantly faster using convolutions with a special temporal pooling. This seems compatible with the neural tensor layer proposed in this paper, which may be combined to yield stronger performance with faster runtimes.<br /> <br /> 7. It would be interesting to see how the attention matrix is being constructed and how attention values are being determined in each matrix. For instance, does every different subject have its own attention matrix? If so, how will the situation be handled when the same attention matrix is used in different settings?<br /> <br /> 8. The paper shows the CRNN model not performing the best with Ag's news and 20newsgroups. It would be interesting to investigate this in detail and see the difference in the way the data is handled in the model compared to the best performing model(self-attentive LSTM in both datasets).<br /> <br /> 9. From the Interpreting Learned CRNN Weights part, the samples are labeled as positive and negative, and their words all have opposite emotional polarities. It can be observed that regardless of whether the polarity of the example is positive or negative, the keyword can be extracted by this method, reflecting that it can capture multiple semantically meaningful components. At the same time, it will be very interesting to see if this method is applicable to other specific categories.<br /> <br /> 10. The authors of this paper provide 2 examples of what topic classification is, but do not provide any explicit examples of &quot;polysemic words whose meanings are context-sensitive&quot;, one of their main critiques of current methods. This is an opportunity to promote the use of their method and engage and inform the reader, simply by listing examples of these words.<br /> <br /> 11. In the &quot;Interpreting Learned CRNN Weights&quot; parts, authors gave a figure but did not explain whether this is an example of positive case or negative case. I suggest the author to label the figure. Also, in the paper, we can see there are 2 figures and both of the figures have been labelled as positive or negative but there is only one figure without labelled in the summary.<br /> <br /> 12. In the CRNN Results vs Benchmarks, it would be better to provide more details and comparison of other methods other than CRNN. It would be clear and more intuitive for the readers why the author will choose CRNN rather than the others.<br /> <br /> 13. The author should explore more on why labeling from certain data source is much more accurate than other data source.<br /> <br /> 14. Nice visual illustration for explaining the whole process. More explanations can be done on how two neural networks are combined. Would the result be different if two neural networks were modelled sequentially?<br /> <br /> == Comments ==<br /> <br /> - Could this be applied to ancient languages such as hieroglyphs to decipher/better understand them?<br /> <br /> - Another application for CRNN might be classifying spoken language as well as any form of audio.<br /> <br /> -I think it will be better to show more results by using this method. Maybe it will be better to put the result part after the architecture part? Writing a motivation will be better since it will catch readers' &quot;eyes&quot;. I think it will be interesting to ask: whether can we apply this to ancient Chinese poetry? Since there are lots of types of ancient Chinese poetry, doing a classification for them will be interesting.<br /> <br /> - In another [https://www.aclweb.org/anthology/W99-0908/ paper] written by Andrew McCallum and Kamal Nigam, they introduce a different method of text classification. Namely, instead of a combination of recurrent and convolutional neural networks, they instead utilized bootstrapping with keywords, Expectation-Maximization algorithm, and shrinkage.<br /> <br /> == References ==<br /> ----<br /> <br />  Grimes, Seth. “Unstructured Data and the 80 Percent Rule.” Breakthrough Analysis, 1 Aug. 2008, breakthroughanalysis.com/2008/08/01/unstructured-data-and-the-80-percent-rule/.<br /> <br />  N. Kalchbrenner, E. Grefenstette, and P. Blunsom, “A convolutional neural network for modeling sentences,”<br /> arXiv preprint arXiv:1404.2188, 2014.<br /> <br />  K. Cho, B. V. Merri¨enboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning<br /> phrase representations using RNN encoder-decoder for statistical machine translation,” arXiv preprint<br /> arXiv:1406.1078, 2014.<br /> <br />  Keren, G., &amp;amp; Schuller, B. (2016, February 18). Convolutional RNN: An Enhanced Model for Extracting Features from Sequential Data. Retrieved November 30, 2020, from https://arxiv.org/pdf/1602.05875.pdf.<br /> <br />  S. Lai, L. Xu, K. Liu, and J. Zhao, “Recurrent convolutional neural networks for text classification,” in Proceedings<br /> of AAAI, 2015, pp. 2267–2273.<br /> <br />  H. Chen, P. Tio, A. Rodan, and X. Yao, “Learning in the model space for cognitive fault diagnosis,” IEEE<br /> Transactions on Neural Networks and Learning Systems, vol. 25, no. 1, pp. 124–136, 2014.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN&diff=49249 Music Recommender System Based using CRNN 2020-12-05T19:45:53Z <p>Sh68lee: /* Critiques/ Insights: */</p> <hr /> <div>==Introduction and Objective:==<br /> <br /> In the digital era of music streaming, companies, such as Spotify and Pandora, are faced with the following challenge: can they provide users with relevant and personalized music recommendations amidst the ever-growing abundance of music and user data?<br /> <br /> The objective of this paper is to implement a personalized music recommender system that takes user listening history as input and continually finds new music that captures individual user preferences.<br /> <br /> This paper argues that a music recommendation system should vary from the general recommendation system used in practice since it should combine music feature recognition and audio processing technologies to extract music features, and combine them with data on user preferences.<br /> <br /> The authors of this paper took a content-based music approach to build the recommendation system - specifically, comparing the similarity of features based on the audio signal.<br /> <br /> The following two-method approach for building the recommendation system was followed:<br /> #Make recommendations including genre information extracted from classification algorithms.<br /> #Make recommendations without genre information.<br /> <br /> The authors used convolutional recurrent neural networks (CRNN), which is a combination of convolutional neural networks (CNN) and recurrent neural network(RNN), as their main classification model.<br /> <br /> ==Methods and Techniques:==<br /> Generally, a music recommender can be divided into three main parts: (i) users, (ii) items, and (iii) user-item matching algorithms. Firstly, a model for a users music taste is generated based on their profiles. Secondly, item profiling based on editorial, cultural, and acoustic metadata is exploited to increase listener satisfaction. Thirdly, a matching algorithm is employed to recommend personalized music to the listener. Two main approaches are currently available;<br /> <br /> (1) Collaborative filtering<br /> <br /> It is based on users' historical listening data and depends on user ratings. Nearest neighbour is the standard method used for collaborative filtering and can be broken into two classes of methods: (i) user-based neighbourhood methods and (ii) item-based neighbourhood methods. <br /> <br /> User-based neighbourhood methods calculate the similarity between the target user and other users, and selects the k most similar. A weighted average of the most similar users' song ratings is then computed to predict how the target user would rate those songs. Songs that have a high predicted rating are then recommended to the user. In contrast, methods that use item-based neighbourhoods calculate similarities between songs that the target user has rated well and songs they have not listened to in order to recommend songs.<br /> <br /> That being said, collaborative filtering faces many challenges. For example, given that each user sees only a small portion of all music libraries, sparsity and scalability become an issue. However, this can be dealt with using matrix factorization. A more difficult challenge to overcome is the fact that users often don't rate songs when they are listening to music. <br /> <br /> (2) Content-based filtering<br /> <br /> Content based recommendation systems base their recommendations on the similarity of an items features and features that the user has enjoyed. It has two-steps; (i) Extract audio content features and (ii) predict user preferences.<br /> <br /> In this work, the authors take a content-based approach, as they compare the similarity of audio signal features to make recommendations. To classify music, the original music’s audio signal is converted into a spectrogram image. Using the image and the Short Time Fourier Transform (STFT), we convert the data into the Mel scale which is used in the CNN and CRNN models. <br /> === Mel Scale: === <br /> The scale of pitches that are heard by listeners, which translates to equal pitch increments.<br /> <br /> [[File:Mel.png|frame|none|Mel Scale on Spectrogram]]<br /> <br /> === Short Time Fourier Transform (STFT): ===<br /> The transformation that determines the sinusoidal frequency of the audio, with a Hanning smoothing function. In the continuous case this is written as: &lt;math&gt;\mathbf{STFT}\{x(t)\}(\tau,\omega) \equiv X(\tau, \omega) = \int_{-\infty}^{\infty} x(t) w(t-\tau) e^{-i \omega t} \, d t &lt;/math&gt;<br /> <br /> where: &lt;math&gt;w(\tau)&lt;/math&gt; is the Hanning smoothing function. The STFT is applied over a specified window length at a certain time allowing the frequency to represented for that given window rather than the entire signal as a typical Fourier Transform would.<br /> <br /> === Convolutional Neural Network (CNN): ===<br /> A Convolutional Neural Network is a Neural Network that uses convolution in place of matrix multiplication for some layer calculations. By training the data, weights for inputs are updated to find the most significant data relevant to classification. These convolutional layers gather small groups of data with kernels and try to find patterns that can help find features in the overall data. The features are then used for classification. Padding is another technique used to extend the pixels on the edge of the original image to allow the kernel to more accurately capture the borderline pixels. Padding is also used if one wishes the convolved output image to have a certain size. The image on the left represents the mathematical expression of a convolution operation, while the right image demonstrates an application of a kernel on the data.<br /> <br /> [[File:Convolution.png|thumb|400px|left|Convolution Operation]]<br /> [[File:PaddingKernels.png|thumb|400px|center|Example of Padding (white 0s) and Kernels (blue square)]]<br /> <br /> === Convolutional Recurrent Neural Network (CRNN): === <br /> The CRNN is similar to the architecture of a CNN, but with the addition of a GRU, which is a Recurrent Neural Network (RNN). An RNN is used to treat sequential data, by reusing the activation function of previous nodes to update the output. A Gated Recurrent Unit (GRU) is used to store more long-term memory and will help train the early hidden layers. GRUs can be thought of as LSTMs but with a forget gate, and has fewer parameters than an LSTM. These gates are used to determine how much information from the past should be passed along onto the future. They are originally aimed to prevent the vanishing gradient problem, since deeper networks will result in smaller and smaller gradients at each layer. The GRU can choose to copy over all the information in the past, thus eliminating the risk of vanishing gradients.<br /> <br /> [[File:GRU441.png|thumb|400px|left|Gated Recurrent Unit (GRU)]]<br /> [[File:Recurrent441.png|thumb|400px|center|Diagram of General Recurrent Neural Network]]<br /> <br /> ==Data Screening:==<br /> <br /> The authors of this paper used a publicly available music dataset made up of 25,000 30-second songs from the Free Music Archives which contains 16 different genres. The data is cleaned up by removing low audio quality songs, wrongly labelled genres and those that have multiple genres. To ensure a balanced dataset, only 1000 songs each from the genres of classical, electronic, folk, hip-hop, instrumental, jazz and rock were used in the final model. <br /> <br /> [[File:Data441.png|thumb|200px|none|Data sorted by music genre]]<br /> <br /> ==Implementation:==<br /> <br /> === Modeling Neural Networks ===<br /> <br /> As noted previously, both CNNs and CRNNs were used to model the data. The advantage of CRNNs is that they are able to model time sequence patterns in addition to frequency features from the spectrogram, allowing for greater identification of important features. Furthermore, feature vectors produced before the classification stage could be used to improve accuracy. <br /> <br /> In implementing the neural networks, the Mel-spectrogram data was split up into training, validation, and test sets at a ratio of 8:1:1 respectively and labelled via one-hot encoding. This made it possible for the categorical data to be labelled correctly for binary classification. As opposed to classical stochastic gradient descent, the authors opted to use binary classier and ADAM optimization to update weights in the training phase, and parameters of &lt;math&gt;\alpha = 0.001, \beta_1 = 0.9, \beta_2 = 0.999&lt;\math&gt;. Binary cross-entropy was used as the loss function. <br /> Input spectrogram image are 96x1366. In both the CNN and CRNN models, the data was trained over 100 epochs and batch size of 50 (limited computing power) with a binary cross-entropy loss function. Notable model specific details are below:<br /> <br /> '''CNN'''<br /> * Five convolutional layers with 3x3 kernel, stride 1, padding, batch normalization, and ReLU activation<br /> * Max pooling layers <br /> * The sigmoid function was used as the output layer<br /> <br /> '''CRNN'''<br /> * Four convolutional layers with 3x3 kernel (which construct a 2D temporal pattern - two layers of RNNs with Gated Recurrent Units), stride 1, padding, batch normalization, ReLU activation, and dropout rate 0.1<br /> * Feature maps are N x1x15 (N = number of features maps, 68 feature maps in this case) is used for RNNs.<br /> * 4 Max pooling layers for four convolutional layers with kernel ((2x2)-(3x3)-(4x4)-(4x4)) and same stride<br /> * The sigmoid function was used as the output layer<br /> <br /> The CNN and CRNN architecture is also given in the charts below.<br /> <br /> [[File:CNN441.png|thumb|800px|none|Implementation of CNN Model]]<br /> [[File:CRNN441.png|thumb|800px|none|Implementation of CRNN Model]]<br /> <br /> === Music Recommendation System ===<br /> <br /> The recommendation system is computed by the cosine similarity of the extraction features from the neural network. Each genre will have a song act as a centre point for each class. The final inputs of the trained neural networks will be the feature variables. The featured variables will be used in the cosine similarity to find the best recommendations. <br /> <br /> The values are between [-1,1], where larger values are songs that have similar features. When the user inputs five songs, those songs become the new inputs in the neural networks and the features are used by the cosine similarity with other music. The largest five cosine similarities are used as recommendations.<br /> [[File:Cosine441.png|frame|100px|none|Cosine Similarity]]<br /> <br /> == Evaluation Metrics ==<br /> === Precision: ===<br /> * The proportion of True Positives with respect to the '''predicted''' positive cases (true positives and false positives)<br /> * For example, out of all the songs that the classifier '''predicted''' as Classical, how many are actually Classical?<br /> * Describes the rate at which the classifier predicts the true genre of songs among those predicted to be of that certain genre<br /> <br /> === Recall: ===<br /> * The proportion of True Positives with respect to the '''actual''' positive cases (true positives and false negatives)<br /> * For example, out of all the songs that are '''actually''' Classical, how many are correctly predicted to be Classical?<br /> * Describes the rate at which the classifier predicts the true genre of songs among the correct instances of that genre<br /> <br /> === F1-Score: ===<br /> An accuracy metric that combines the classifier’s precision and recall scores by taking the harmonic mean between the two metrics:<br /> <br /> [[File:F1441.png|frame|100px|none|F1-Score]]<br /> <br /> === Receiver operating characteristics (ROC): ===<br /> * A graphical metric that is used to assess a classification model at different classification thresholds <br /> * In the case of a classification threshold of 0.5, this means that if &lt;math&gt;P(Y = k | X = x) &gt; 0.5&lt;/math&gt; then we classify this instance as class k<br /> * Plots the true positive rate versus false positive rate as the classification threshold is varied<br /> <br /> [[File:ROCGraph.jpg|thumb|400px|none|ROC Graph. Comparison of True Positive Rate and False Positive Rate]]<br /> <br /> === Area Under the Curve (AUC) ===<br /> AUC is the area under the ROC in doing so, the ROC provides an aggregate measure across all possible classification thresholds.<br /> <br /> In the context of the paper: When scoring all songs as &lt;math&gt;Prob(Classical | X=x)&lt;/math&gt;, it is the probability that the model ranks a random Classical song at a higher probability than a random non-Classical song.<br /> <br /> [[File:AUCGraph.jpg|thumb|400px|none|Area under the ROC curve.]]<br /> <br /> == Results ==<br /> === Accuracy Metrics ===<br /> The table below is the accuracy metrics with the classification threshold of 0.5.<br /> <br /> [[File:TruePositiveChart.jpg|thumb|none|True Positive / False Positive Chart]]<br /> On average, CRNN outperforms CNN in true positive and false positive cases. In addition, it is very apparent that false positives are much more frequent for songs in the Instrumental genre, perhaps indicating that more pre-processing needs to be done for songs in this genre or that it should be excluded from analysis completely given how most music has instrumental components.<br /> <br /> <br /> [[File:F1Chart441.jpg|thumb|400px|none|F1 Chart]]<br /> On average, CRNN outperforms CNN in F1-score. <br /> <br /> <br /> [[File:AUCChart.jpg|thumb|400px|none|AUC Chart]]<br /> On average, CRNN also outperforms CNN in AUC metric.<br /> <br /> <br /> CRNN models that consider the frequency features and time sequence patterns of songs have a better classification performance through metrics such as F1 score and AUC when comparing to CNN classifier.<br /> <br /> === Evaluation of Music Recommendation System: ===<br /> <br /> * A listening experiment was performed with 30 participants to access user responses to given music recommendations.<br /> * Participants choose 5 pieces of music they enjoyed and the recommender system generated 5 new recommendations. The participants then evaluated the music recommendation by recording whether the song was liked or disliked.<br /> * The recommendation system takes two approaches to the recommendation:<br /> ** Method one uses only the value of cosine similarity.<br /> ** Method two uses the value of cosine similarity and information on music genre.<br /> *Perform test of significance of differences in average user likes between the two methods using a t-statistic:<br /> [[File:H0441.png|frame|100px|none|Hypothesis test between method 1 and method 2]]<br /> <br /> Comparing the two methods, &lt;math&gt; H_0: u_1 - u_2 = 0&lt;/math&gt;, we have &lt;math&gt; t_{stat} = -4.743 &lt; -2.037 &lt;/math&gt;, which demonstrates that the increase in average user likes with the addition of music genre information is statistically significant.<br /> <br /> == Conclusion: ==<br /> <br /> The two two main conclusions obtained from this paper:<br /> <br /> - The music genre should be a key feature to increase the predictive capabilities of the music recommendation system.<br /> <br /> - To extract the song genre from a song’s audio signals and get overall better performance, CRNN’s are superior to CNN’s as they consider frequency in features and time sequence patterns of audio signals. <br /> <br /> According to the paper, the authors suggested adding other music features like tempo gram for capturing local tempo as a way to improve the accuracy of the recommender system.<br /> <br /> == Critiques/ Insights: ==<br /> # The authors fail to give reference to the performance of current recommendation algorithms used in the industry; my critique would be for the authors to bench-mark their novel approach with other recommendation algorithms such as collaborative filtering to see if there is a lift in predictive capabilities.<br /> # The listening experiment used to evaluate the recommendation system only includes songs that are outputted by the model. Users may be biased if they believe all songs have come from a recommendation system. To remove bias, we suggest having 15 songs where 5 songs are recommended and 10 songs are set. With this in the user’s mind, it may remove some bias in response and give more accurate predictive capabilities. <br /> # They could go into more details about how CRNN makes it perform better than CNN, in terms of attributes of each network.<br /> # The methodology introduced in this paper is probably also suitable for movie recommendations. As music is presented as spectrograms (images) in a time sequence, and it is very similar to a movie. <br /> # The way of evaluation is a very interesting approach. Since it's usually not easy to evaluate the testing result when it's subjective. By listing all these evaluations' performance, the result would be more comprehensive. A practice that might reduce bias is by coming back to the participants after a couple of days and asking whether they liked the music that was recommended. Often times music &quot;grows&quot; on people and their opinion of a new song may change after some time has passed. <br /> # The paper lacks the comparison between the proposed algorithm and the music recommendation algorithms being used now. It will be clearer to show the superiority of this algorithm.<br /> # The GAN neural network has been proposed to enhance the performance of the neural network, so an improved result may appear after considering using GAN.<br /> # The limitation of CNN and CRNN could be that they are only able to process the spectrograms with single labels rather than multiple labels. This is far from enough for the music recommender systems in today's music industry since the edges between various genres are blurred.<br /> # Is it possible for CNN and CRNN to identify different songs? The model would be harder to train, based on my experience, the efficiency of CNN in R is not very high, which can be improved for future work.<br /> # according to the author, the recommender system is done by calculating the cosine similarity of extraction features from one music to another music. Is possible to represent it by Euclidean distance or p-norm distances?<br /> # In real-life application, most of the music software will have the ability to recommend music to the listener and ask do they like the music that was recommended. It would be a nice application by involving some new information from the listener.<br /> # This paper is very similar to another [https://link.springer.com/chapter/10.1007/978-3-319-46131-1_29 paper], written by Bruce Fewerda and Markus Schedl. Both papers are suggesting methods of building music recommendation systems. However, this paper recommends music based on genre, but the paper written by Fewerda and Schedl suggests a personality-based user modeling for music recommender systems.<br /> # Actual music listeners do not listen to one genre of music, and in fact listening to the same track or the same genre would be somewhat unusual. Could this method be used to make recommendations not on genre, but based on other categories? (Such as the theme of the lyrics, the pitch of the singer, or the date published). Would this model be able to differentiate between tracks of varying &quot;lyric vocabulation difficulty&quot;? Or would NLP algorithms be needed to consider lyrics?<br /> # This model can be applied to many other fields such as recommending the news in the news app, recommending things to buy in the amazon, recommending videos to watch in YOUTUBE and so on based on the user information.<br /> # Looks like for the most genres, CRNN outperforms CNN, but CNN did do better on a few genres (like Jazz), so it might be better to mix them together or might use CNN for some genres and CRNN for the rest.<br /> # Cosine similarity is used to find songs with similar patterns as the input ones from users. That is, feature variables are extracted from the trained neural network model before the classification layer, and used as the basis to find similar songs. One potential problem of this approach is that if the neural network classifies an input song incorrectly, the extracted feature vector will not be a good representation of the input song. Thus, a song that is in fact really similar to the input song may have a small cosine similarity value, i.e. not be recommended. In conclusion, if the first classification is wrong, future inferences based on that is going to make it deviate further from the true answer. A possible future improvement will be how to offset this inference error.<br /> # In the tables when comparing performance and accuracies of the CNN and CRNN models on different genres of music, the researchers claimed that CRNN had superior performance to CNN models. This seemed intuitive, especially in the cases when the differences in accuracies were large. However, maybe the researchers should consider including some hypothesis testing statistics in such tables, which would support such claims in a more rigorous manner.<br /> # A music recommender system that doesn't use the song's meta data such as artist and genre and rather tries to classify genre itself seems unproductive. I also believe that the specific artist matters much more than the genre since within a genre you have many different styles. It just seems like the authors hamstring their recommender system by excluding other relevant data.<br /> # The genres that are posed in the paper are very broad and may not be specific enough to distinguish a listeners actual tastes (ie, I like rock and roll, but not punk rock, which could both be in the &quot;rock&quot; category). It would be interesting to run similar experiments with more concrete and specific genres to study the possibility of improving accuracy in the model.<br /> # This summary is well organized with detailed explanation to the music recommendation algorithm. However, since the data used in this paper is cleaned to buffer the efficiency of the recommendation, there should be a section evaluating the impact of noise on the performance this algorithm and how to minimize the impact.<br /> # This method will be better if the user choose some certain music genres that they like while doing the sign-up process. This is similar to recommending articles on twitter.<br /> # I have some feedback for the &quot;Evaluation of Music Recommendation System&quot; section. Firstly, there can be a brief mention of the participants' background information. Secondly, the summary mentions that &quot;participants choose 5 pieces of music they enjoyed&quot;. Are they free to choose any music they like, or are they choosing from a pool of selections? What are the lengths of these music pieces? Lastly, method one and method two are compared against each other. It's intuitive that method two will outperform method one, since method two makes use of both cosine similarity and information on music genre, whereas method one only makes use of cosine similarity. Thus, saying method two outperforms method one is not necessarily surprising. I would like to see more explanation on why these methods are chosen, and why comparing them directly is considered to be fair.<br /> # In the Collecting Music Data section, the author has indicated that for maintaining the balance of data for each genre that they are choosing to omit some genres and a portion of the dataset. However, how this was done was not explained explicitly which can be a concern for results replication. It would be better to describe the steps and measures taken to ensure the actions taken by the teams are reproducible. <br /> # For cleaning data, for training purposes, the team is choosing to omit the ones with lower music quality. While this is a sound option, it can be adjusted that the ratings for the music are deducted to adjust the balance. This could be important since a poor music quality could mean either equipment failure or corrupt server storage or it was a recording of a live performance that often does not have a perfect studio quality yet it would be loved by many real-life users. This omission is not entirely justified and feels like a deliberate adjustment for later results.<br /> # It would be more convincing if the author could provide more comparison between CRNN and CNN.<br /> # How is the result used to recommend songs within genres? It looks like it only predicts what genre the user likes to listen and recommends one of the songs from that genre. How can this recommender system be used to recommend songs within the same genre?<br /> <br /> == References: ==<br /> Nilashi, M., et.al. ''Collaborative Filtering Recommender Systems''. Research Journal of Applied Sciences, Engineering and Technology 5(16):4168-4182, 2013.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=A_universal_SNP_and_small-indel_variant_caller_using_deep_neural_networks&diff=49247 A universal SNP and small-indel variant caller using deep neural networks 2020-12-05T19:37:53Z <p>Sh68lee: /* Critique and Discussion */</p> <hr /> <div>== Background ==<br /> <br /> Genes determine Biological functions, and mutants or alleles(one of two or more alternative forms of a gene that arise by mutation and are found at the same place on a chromosome) of those genes determine differences within a function. Determining novel alleles is very important in understanding the genetic variation within a species. For example, different alleles of the gene OCA2 determine eyes' color. All animals receive one copy of each gene from each of their parents. Mutations of a gene are classified as either homozygous (both copies are the same) or heterozygous (the two copies are different).<br /> <br /> Next-generation sequencing is a prevalent technique for sequencing or reading DNA. Since all genes are encoded as DNA, sequencing is an essential tool for understanding genes. Next-generation sequencing works by reading short sections of DNA of length k, called k-means, and then piecing them together or aligning them to a reference genome. Next-generation sequencing is relatively fast and inexpensive, although it can randomly misidentify some nucleotides, introducing errors. However, NGS reading is errorful and arises from a complex error process depending on various factors.<br /> <br /> The process of variant calling is determining novel alleles from sequencing data (typically next-generation sequencing data). Some significant alleles only differ from the &quot;standard&quot; version of a gene by only a single base pair, such as the mutation which causes multiple sclerosis. Therefore it is crucial to accurately call single nucleotide swaps/polymorphisms (SNPs), insertions, and deletions (indels). Calling SNPs and small indels are technically challenging since it requires a program to distinguish between genuinely novel mutations and errors in the sequencing data.<br /> <br /> Previous approaches usually involved using various statistical techniques. A widely used one is GATK. GATK uses a combination of logistic regression, hidden Markov models, naive Bayes classification, and Gaussian mixture models to perform the process . However, these methods have their weaknesses as some assumptions do not hold (i.e., independence assumptions). In addition, given that GATK testing has focused primarily on human whole-genome data sequenced using Illumina technology, it is not easily generalizable to different types of data, organisms, and experimental designs/sequencing technologies [[https://gatk.broadinstitute.org/hc/en-us/articles/360035894711-About-the-GATK-Best-Practices 3]]. <br /> <br /> This paper aims to solve the problem of calling SNPs and small indels using a convolutional neural net by casting the reads as images and classifying whether they contain a mutation. It introduces a variant caller called &quot;DeepVariant&quot;, which requires no specialized knowledge, but performs better than previous state-of-art methods.<br /> <br /> == Overview ==<br /> <br /> In Figure 1, the DeepVariant workflow overview is illustrated.<br /> <br /> [[File:figure 111.JPG|Figure 1. In all panels, blue boxes represent data and red boxes are processes]]<br /> <br /> <br /> Initially, the NGS reads aligned to a reference genome are scanned for candidate variants which are different sites from the reference genome. The read and reference data are encoded as an image for each candidate variant site. Then, trained CNN can compute the genotype likelihoods, (heterozygous or homozygous) for each of the candidate variants (figure1, left box). <br /> To train the CNN for image classification purposes, the DeepVariant machinery makes pileup images for a labeled sample with known genotypes. These labeled images and known genotypes are provided to CNN for training, and a stochastic gradient descent algorithm is used to optimize the CNN parameters to maximize genotype prediction accuracy. After the convergence of the model, the final model is frozen to use for calling mutations for other image classification tests (figure1, middle box).<br /> For example, in figure 1 (right box), the reference and read bases are encoded into a pileup image at a candidate variant site. CNN using this encoded image computes the genotype likelihoods for the three diploid genotype states of homozygous reference (hom-ref), heterozygous (het) or homozygous alternate (hom-alt). In this example, a heterozygous variant call is emitted, as the most probable genotype here is “het”.<br /> <br /> == Preprocessing ==<br /> <br /> Before the sequencing reads can be fed into the classifier, they must be pre-processed. There are many pre-processing steps that are necessary for this algorithm. These steps represent the real novelty in this technique by transforming the data to allow us to use more common neural network architectures for classification. The pre-processing of the data can be broken into three phases: the realignment of reads, finding candidate variants and creating the candidate variants' images.<br /> <br /> The realignment of the pre-processing reads phase is essential to ensure the sequences can be adequately compared to the reference sequences. First, the sequences are aligned to a reference sequence. Reads that align poorly are grouped with other reads around them to build that section, or haplotype, from scratch. If there is strong evidence that the new version of the haplotype fits the reads well, the reads are re-aligned. This process updates the CIGAR (Compact Idiosyncratic Gapped Alignment Report) string to represent a sequence's alignment to a reference for each read.<br /> <br /> Once the reads are correctly aligned, the algorithm then proceeds to find candidate variants, regions in the DNA sequence containing variants. It is these candidate variants that will eventually be passed as input to the neural network. To find these, we need to consider each position in the reference sequence independently. Any unusable reads are filtered at this point. This includes reads that are not appropriately aligned, marked as duplicates, those that fail vendor quality checks, or whose mapping quality is less than ten. For each site in the genome, we collect all the remaining reads that overlap that site. The corresponding allele aligned to that site is then determined by decoding the CIGAR string, which was updated in each read's realignment phase. The alleles are then classified into one of four categories: reference-matching base, reference-mismatching base, insertion with a specific sequence, or deletion with a specific length, and the number of occurrences of each distinct allele across all reads is counted. Read bases are only included as potential alleles if each base in the allele has a quality score of at least 10.<br /> <br /> The last phase of pre-processing is to convert these candidate variants into images representing the data with candidate variants identified. This allows for the use of well established convolutional neural networks for image classification for this technical problem. Each color channel is used to store a different piece of information about a candidate variant. The red channel encodes which base we have (A, G, C, or T) by mapping each base to a particular value. The quality of the read is mapped to the green color channel.<br /> <br /> Moreover, the blue channel encodes whether or not the reference is on the positive strand of the DNA. Each row of the image represents a read, and each column represents a particular base in that read. The reference strand is repeated for the first five rows of the encoded image to maintain its information after a 5x5 convolution is applied. With the data pre-processing complete, the images can then be passed into the neural network for classification.<br /> <br /> == Neural Network ==<br /> <br /> The neural network used is a convolutional neural network. Although the full network architecture is not revealed in the paper, there are several details which we can discuss. The architecture of the network is an input layer attached to an adapted Inception v2 ImageNet model with nine partitions. The inception v2 model in particular uses a series of CNNs. One interesting aspect about the Inception model is that rather than optimizing a series of hyperparameters in order to determine the most optimal parameter configuration, Inception instead concatenates a series of different sizes of filters on the same layer, which acts to learn the best architecture out of these concatenated filters. The input layer takes as input the images representing the candidate variants and rescales them to 299x299 pixels. The output layer is a three-class Softmax layer initialized with Gaussian random weights with a standard deviation of 0.001. This final layer is fully connected to the previous layer. The three classes are the homozygous reference (meaning it is not a variant), heterozygous variant, and homozygous variant. The candidate variant is classified into the class with the highest probability. The model is trained using stochastic gradient descent with a weight decay of 0.00004. The training was done in mini-batches, each with 32 images, using a root mean squared (RMS) decay of 0.9. For the multiple sequencing technologies experiments, a single model was trained with a learning rate of 0.0015 and momentum 0.8 for 250,000 update steps. For all other experiments, multiple models were trained, and the one with the highest accuracy on the training set was chosen as the final model. The multiple models stem from using each combination of the possible parameter values for the learning rate (0.00095, 0.001, 0.0015) and momentum (0.8, 0.85, 0.9). These models were trained for 80 hours, or until the training accuracy converged.<br /> <br /> == Results ==<br /> <br /> DeepVariant was trained using data available from the CEPH (Centre d’Etude du Polymorphism Humain) female sample NA12878 and was evaluated on the unseen Ashkenazi male sample NA24385. The results were compared with other most commonly used bioinformatics methods, such as the GATK, FreeBayes22, SAMtools23, 16GT24 and Strelka25 (Table 1). For better comparison, the overall accuracy (F1), recall, precision, and numbers of true positives (TP), false negatives (FN) and false positives (FP) are illustrated over the whole genome.<br /> <br /> [[File:table 11.JPG]]<br /> <br /> DeepVariant showed the highest accuracy and more than 50% fewer errors per genome compared to the next best algorithm. <br /> <br /> They also evaluated the same set of algorithms using the synthetic diploid sample CHM1-CHM1326 (Table 2).<br /> <br /> [[File:Table 333.JPG]]<br /> <br /> Results illustrated that the DeepVariant method outperformed all other algorithms for variant calling (SNP and indel) and showed the highest accuracy in terms of F1, Recall, precision and TP.<br /> <br /> == Conclusion ==<br /> <br /> This endeavor to further advance a data-centric approach to understanding the gene sequence illustrates the advantages of deep learning over humans. With billions of DNA base pairs, no humans can digest that amount of gene expressions. In the past, computational techniques are unfeasible due to the lack of computing power, but in the 21st century, it seems that machine learning is the way to go for molecular biology.<br /> <br /> DeepVariant’s strong performance on human data proves that deep learning is a promising technique for variant calling. Perhaps the most exciting feature of DeepVariant is its simplicity. Unlike other states of the art variant callers, DeepVariant does not know the sequencing technologies that create the reads or even the biological processes that introduce mutations. It simplifies the problem of variant calling to preprocessing the reads and training a generic deep learning model. It also suggests that DeepVariant could be significantly improved by tailoring the preprocessing to specific sequencing technologies and developing a dedicated CNN architecture for the reads, rather than casting them as images.<br /> <br /> == Critique and Discussion==<br /> <br /> The paper presents an attractive method for solving a significant problem. Building &quot;images&quot; of reads and running them through a generic image classification CNN seems like a strange approach, and, interestingly, it works well. The most significant issues with the paper are the lack of specific information about how the methods. Some extra information is included in the supplementary material, but there are still some significant gaps. In particular:<br /> <br /> 1. What is the structure of the neural net? How many layers, and what sizes? The paper for ConvNet does not have this information. We suspect that this might be a trade secret that Google is protecting.<br /> <br /> 2. How is the realignment step implemented? The paper mentions that it uses a &quot;De-Bruijn-graph-based read assembly procedure&quot; to realign reads to a new haplotype. It is a non-standard step in most genomics workflows, yet the paper does not describe how they do the realignment or build the haplotypes.<br /> <br /> 3. How did they settle on the image construction algorithm? The authors provide pseudocode for the construction of pileup images, but they do not describe how to make decisions. For instance, the color values for different base pairs are not evenly spaced. Also, the image begins with five rows of the reference genome.<br /> <br /> One thing we appreciated about the paper was their commentary on future developments. The authors clarify that this approach can be improved on and provide specific ideas for the next steps.<br /> <br /> Overall, the paper presents an interesting idea with strong results but lacks detail in some vital implementation pieces.<br /> <br /> The topic of this project is good, but we need more details on the algorithm. In the neural network part, the details are not enough; authors should provide a figure to explain better how the model works and the model's structure. Otherwise, we cannot understand how the model works. When we preprocess the data if different data have different lengths, shall we add more information or drop some information to match?<br /> <br /> 5 Particularly, which package did the researchers use to perform this analysis? Different packages of deep learning can have different accuracy and efficiency while making predictions on this data set. <br /> <br /> Further studies on DeepVariant [https://www.nature.com/articles/s41598-018-36177-7 have shown] that it is a framework with great potential and sets the medical standard genetics field.<br /> <br /> 6. It was mentioned that part of the network used is an &quot;adapted Inception v2 ImageNet model&quot; - does this mean that it used an Inception v2 model that was trained on ImageNet? This is not clear, but if this is the case, then why is this useful? Why would the features that are extracted for an image be useful for genomics? Did they try using a model that was not trained? Also, they describe the preprocessing method used but were there any alternatives that they considered?<br /> <br /> 7. A more extensive discussion on the &quot;Neural Network&quot; section can be given. For example, the paragraph's last sentence says that &quot;Models are trained for 80 hours, or until the training accuracy converged.&quot; This sentence implies that if the training accuracy does converge, it usually takes less than 80 hours. More exciting data can thus be presented about the training accuracy converging time. How often do the models converge? How long does it take for the models to converge on average? Moreover, why is the number 80 chosen here? Is it a random upper bound set by people to bound the runtime of the model training, or is the number 80 carefully chosen so that it is twice/three times/ten times the average training accuracy converging time?<br /> <br /> 8. It would be more convincing if the author could provide more detail on the structure of the neural network.<br /> <br /> 9. It is clear that this is a very thoroughly written paper with substantial comparison results and computation numbers to back up the testing. However, simply because the implementation link is given in the paper, there still lacks information regarding the structure of the model. It is also structurally missing a conclusion section to complete a summary on the overall conclusion and results comparison to give a final conclusion to the efficacy of the proposed model.<br /> <br /> 10. It would be interesting to see how the model would behave if we incorporate transformers to the model, this has been on reason Alpha Fold 2 was so successful.<br /> <br /> 11. The result illustration is hard to interpret, it would be nicer if explanations can be added. Lacking details on neural networks used. How was mathematical calculations done on prediction?<br /> <br /> == References ==<br />  Hartwell, L.H. ''et. al.'' ''Genetics: From Genes to Genomes''. (McGraw-Hill Ryerson, 2014).<br /> <br />  Poplin, R. ''et. al''. A universal SNP and small-indel variant caller using deep neural networks. ''Nature Biotechnology'' '''36''', 983-987 (2018).</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&diff=49245 Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms 2020-12-05T19:23:26Z <p>Sh68lee: /* Critiques */</p> <hr /> <div><br /> == Presented by ==<br /> <br /> Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee<br /> <br /> == Introduction ==<br /> <br /> This paper presents ConvNetQuake, an approach on detecting heart disease from ECG signals by fine-tuning the deep learning neural network. For context, ConvNetQuake is a convolutional neural network, used by Perol, Gharbi, and Denolle , for Earthquake detection and location from a single waveform. A deep learning approach was used due to the model's ability to be trained using multiple GPUs and terabyte-sized datasets. This, in turn, creates a model that is robust against noise. The purpose of this paper is to provide detailed analyses of the contributions of the ECG leads on identifying heart disease, to show the use of multiple channels in ConvNetQuake enhances prediction accuracy, and to show that feature engineering is not necessary for any of the training, validation, or testing processes. In this area, the combination of data fusion and machine learning techniques exhibits great promise to healthcare innovation, and the analyses in this paper help further this realization. The benefits of translating knowledge between deep learning and its real-world applications in health are also illustrated.<br /> <br /> == Previous Work and Motivation ==<br /> <br /> The database used in previous works is the Physikalisch-Technische Bundesanstalt (PTB) database, which consists of ECG records. Previous papers used techniques, such as CNN, SVM, K-nearest neighbors, naïve Bayes classification, and ANN. From these instances, the paper observes several shortcomings in the previous papers. The first being the issue that most papers use feature selection on the raw ECG data before training the model. Dabanloo and Attarodi  used various techniques such as ANN, K-nearest neighbors, and Naïve Bayes. However, they extracted two features, the T-wave integral and the total integral, to aid in localizing and detecting heart disease. Sharma and Sunkaria  used SVM and K-nearest neighbors as their classifier, but extracted various features using stationary wavelet transforms to decompose the ECG signal into sub-bands. The second issue is that papers that do not use feature selection would arbitrarily pick ECG leads for classification without rationale. For example, Liu et al.  used a deep CNN that uses 3 seconds of ECG signal from lead II at a time as input. The decision for using lead II compared to the other leads was not explained. <br /> <br /> The issue with feature selection is that it can be time-consuming and impractical with large volumes of data. The second issue with the arbitrary selection of leads is that it does not offer insight into why the lead was chosen and the contributions of each lead in the identification of heart disease. Thus, this paper addresses these two issues through implementing a deep learning model that does not rely on feature selection of ECG data and to quantify the contributions of each ECG and Frank lead in identifying heart disease.<br /> <br /> == Model Architecture ==<br /> <br /> The dataset, which was used to train, validate, and test the neural network models, consists of 549 ECG records taken from 290 unique patients. Each ECG record has a mean length of over 100 seconds.<br /> <br /> This Deep Neural Network model was created by modifying the ConvNetQuake model by adding 1D batch normalization layers; this addition helps to combat overfitting. A second modification that was made was to introduce the use of label smoothing, which can help by discouraging the model from making overconfident predictions. Label smoothing refers to the method of relaxing the confidence on the model's prediction labels. The authors' experiments demonstrated that both of these modifications helped to increase model accuracy. <br /> <br /> During the training stage, a 10-second long two-channel input was fed into the neural network. In order to ensure that the two channels were weighted equally, both channels were normalized. Besides, time invariance was incorporated by selecting the 10-second long segment randomly from the entire signal. <br /> <br /> The input layer is a 10-second long ECG signal. There are 8 hidden layers in this model, each of which consists of a 1D convolution layer with the ReLu activation function followed by a batch normalization layer. The output layer is a one-dimensional layer that uses the Sigmoid activation function.<br /> <br /> This model is trained by using batches of size 10. The learning rate is &lt;math&gt;10^{-4}&lt;/math&gt;. The ADAM optimizer is used. The ADAM (adaptive moment estimation) optimizer is a stochastic gradient optimization method that uses adaptive learning rates for the parameters used in the estimating the gradient's first and second moments . In training the model, the dataset is split into a train set, validation set, and test set with ratios 80-10-10.<br /> <br /> During the training process, the model was trained from scratch numerous times to avoid inserting unintended variation into the model by randomly initializing weights.<br /> <br /> The following images gives a visual representation of the model.<br /> <br /> [[File:architecture.png | thumb | center | 1000px | Model Architecture (Gupta et al., 2019)]]<br /> <br /> ==Results== <br /> <br /> The paper first uses quantification of accuracies for single channels with 20-fold cross-validation, resulting in the highest individual accuracies: v5, v6, vx, vz, and ii. The researchers further investigated the accuracies for pairs of the top 5 highest individual channels using 20-fold cross-validation. They arrived at the conclusion of highest pairs accuracies to fed into a neural network is lead v6 and lead vz. They then use 100-fold cross validation on v6 and vz pair of channels, then compare outliers based on top 20, top 50 and total 100 performing models, finding that standard deviation is non-trivial and there are few models performed very poorly. <br /> <br /> Next, they discussed 2 factors affecting model performance evaluation: 1） Random train-val-test split might have effects on the performance of the model, but it can be improved by access with a larger data set and further discussion; and 2） random initialization of the weights of the neural network shows little effects on the performance of the model performance evaluation, because of showing high average results with a fixed train-val-test split. <br /> <br /> Comparing with other models in the other 12 papers, the model in this article has the highest accuracy, specificity, and precision. With concerns of patients' records affecting the training accuracy, they used 290 fold patient-wise split, resulting in the same highest accuracy of the pair v6 and vz same as record-wise split. The second best pair was ii and vz, which also contains the vz channel. Combining the two best pair channels into v6, vz, vii ultimately gave the best results over 10 trials which has an average of 97.83% in patient-wise split. Even though the patient-wise split might result in lower accuracy evaluation, however, it still maintains a very high average.<br /> <br /> ==Conclusion &amp; Discussion== <br /> <br /> The paper introduced a new architecture for heart condition classification based on raw ECG signals using multiple leads. It outperformed the state-of-art model by a large margin of 1 percent. This study finds that out of the 15 ECG channels(12 conventional ECG leads and 3 Frank Leads), channel v6, vz, and ii contain the most meaningful information for detecting myocardial infarction. Also, recent advances in machine learning can be leveraged to produce a model capable of classifying myocardial infraction with a cardiologist-level success rate. To further improve the performance of the models, access to a larger labeled data set is needed. The PTB database is small. It is difficult to test the true robustness of the model with a relatively small test set. If a larger data set can be found to help correctly identify other heart conditions beyond myocardial infraction, the research group plans to share the deep learning models and develop an open-source, computationally efficient app that can be readily used by cardiologists.<br /> <br /> A detailed analysis of the relative importance of each of the 15 ECG channels indicates that deep learning can identify myocardial infraction by processing only ten seconds of raw ECG data from the v6, vz, and ii leads and reaches a cardiologist-level success rate. Deep learning algorithms may be readily used as commodity software. The neural network model that was originally designed to identify earthquakes may be re-designed and tuned to identify myocardial infarction. Feature engineering of ECG data is not required to identify myocardial infraction in the PTB database. This model only required ten seconds of raw ECG data to identify this heart condition with cardiologist-level performance. Access to a larger database should be provided to deep learning researchers so they can work on detecting different types of heart conditions. Deep learning researchers and the cardiology community can work together to develop deep learning algorithms that provide trustworthy, real-time information regarding heart conditions with minimal computational resources.<br /> <br /> Fourier Transform (such as FFT) can be helpful when dealing with ECG signals. It transforms signals from the time domain to the frequency domain, which means some hidden features in frequency may be discovered.<br /> <br /> A limitation specified by the authors is the lack of labeled data. The use of a small dataset such as PTB makes it difficult to determine the robustness of the model due to the small size of the test set. Given a larger dataset, the model could be tested to see if it generalizes to identify heart conditions other than myocardial infarction.<br /> <br /> ==Critiques==<br /> - The lack of large, labelled data sets is often a common problem in most applied deep learning studies. Since the PTB database is as small as you describe it to be, the robustness of the model which may be hard to gauge. There are very likely various other physical factors that may play a role in the study which the deep neural network may not be able to adjust for as well, since health data can be somewhat subjective at times and/or may be somewhat inaccurate, especially if machines are used to measurement. This might mean error was propagated forward in the study.<br /> <br /> - Additionally, there is a risk of confirmation bias, which may occur when a model is self-training, especially given the fact that the training set is small.<br /> <br /> - I feel that the results of deep learning models in medical settings where the consequences of misclassification can be severe should be evaluated by assigning weights to classification. In case if the misclassification can lead to severe consequences, then the network should be trained in such a way that it errs towards safety. For example, in case if heart disease, the consequences will be very high if the system says that there is no heart disease when in fact there is. So, the evaluation metric must be selected carefully.<br /> <br /> - This is a useful and meaningful application topic in machine learning. Using Deep Learning to detect heart disease can be very helpful if it is difficult to detect disease by looking at ECG by humans eys. This model also useful for doing statistics, such as calculating the percentage of people get heart disease. But I think the doctor should not 100% trust the result from the model, it is almost impossible to get 100% accuracy from a model. So, I think double-checking by human eyes is necessary if the result is weird. What is more, I think it will be interesting to discuss more applications in mediccal by using this method, such as detecting the Brainwave diagram to predict a person's mood and to diagnose mental diseases.<br /> <br /> - Compared to the dataset for other topics such as object recognition, the PTB database is pretty small with only 549 ECG records. And these are highly unbiased (Table 1) with 4 records for myocarditis and 148 for myocardial infarction. Medical datasets can only be labeled by specialists. This is why these datasets are related small. It would be great if there will be a larger, more comprehensive dataset.<br /> <br /> - Only results using 20-fold cross validation were presented. It should be shown that the results could be reproduced using a more common number of folds like 5 or 10<br /> <br /> - There are potential issues with the inclusion of Frank leads. From a practitioner standpoint, ECGs taken with Frank leads are less common. This could prevent the use of this technique. Additionally, Frank leads are expressible as a linear combinations of the 12 traditional leads. The authors are not adding any fundamentally new information by including them and their inclusion could be viewed as a form of feature selection (going against the authors' original intentions).<br /> <br /> - It will better if we can see how the model in this paper outperformed those methods that used feature selections. The details of the results are not enough.<br /> <br /> - A new extended dataset for PTB dubbed [https://www.nature.com/articles/s41597-020-0495-6 PTB-XL], has 21837 records. Using this dataset could yield a more accurate result, since the original PTB's small dataset posed limitations on the deep learning model.<br /> <br /> - The paper mentions that it has better results, but by how much? what accuracy did the methods you compared to have? Also, what methods did you compare to? (Authors mentioned feature engineering methods but this is vague) Also how much were the labels smoothed? (i.e. 1 -&gt; 0.99 or 1-&gt; 0.95 for example) How much of a difference did the label smoothing make?<br /> <br /> - It is nice to see that the authors also considered training and testing the model on data via a patient-wise split, which gives more insights towards the cases when a patient has multiple records of diagnosis. Obviously and similar to what other critiques suggested, using a patient-wise split might disadvantage from the lack of training data, given that there are only 290 unique patients in the PTB database. Also, acquiring prior knowledge from professionals about correlations, such as causal relationships, between different diagnoses might be helpful for improving the model.<br /> <br /> - As mentioned above, the dataset is comparably small in the context of machine learning. While on the other hand, each record has a length of roughly 100 seconds, which is significantly large as a single input. Therefore, it might be helpful to apply data augmentation algorithms during data preprocessing sections so that there will be a more reasonable dataset than what we currently have so far, which has a high chance of being biased or overfitted.<br /> <br /> - There are several points from the Model Architecture section that can be improved. It mentions that both 1d batch normalization layers and label smoothing are used to improve the accuracy of the models, based on empirical experiment results. Yet, there's no breakdown of how each of these two method improves the accuracy. So it's left unclear whether each method is significant on its own, or the model simultaneously requires both methods in order to achieve improved accuracy. Some more data can be provided about this. It's mentioned that &quot;models are trained from scratch numerous times.&quot; How many times is numerous times? Can we get the exact number? Training time about the models should also be provided. This is because if these models take a long time to train, then training them from scratch every time may cause issues with respect to runtime.<br /> <br /> - The authors should have indicated how much the accuracy has been improved by what method. It is a little unclear that how can we define &quot;better results&quot;. Also, this paper could be more clear if they included the details about the Model Architecture such as how it was performed and how long was the training time for the model.<br /> <br /> - The summary is lacking several components such as explanation of model, data-preprocessing, result visualization and such. It is hard to understand how the result improved since there is no comparison. Information about dataset is unclear too, it is not explained well what they are and how they are populated.<br /> <br /> == References ==<br /> <br />  Na Liu et al. &quot;A Simple and Effective Method for Detecting Myocardial Infarction Based on Deep Convolutional Neural Network&quot;. In: Journal of Medical Imaging and Health Informatics (Sept. 2018). doi: 10.1166/jmihi.2018.2463.<br /> <br />  Naser Safdarian, N.J. Dabanloo, and Gholamreza Attarodi. &quot;A New Pattern Recognition Method for Detection and Localization of Myocardial Infarction Using T-Wave Integral and Total Integral as Extracted Features from One Cycle of ECG Signal&quot;. In: J. Biomedical Science and Engineering (Aug. 2014). doi: http://dx.doi.org/10.4236/jbise.2014.710081.<br /> <br />  L.D. Sharma and R.K. Sunkaria. &quot;Inferior myocardial infarction detection using stationary wavelet transform and machine learning approach.&quot; In: Signal, Image and Video Processing (July 2017). doi: https://doi.org/10.1007/s11760-017-1146-z.<br /> <br />  Perol Thibaut, Gharbi Michaël, and Denolle Marin. &quot;Convolutional neural network for earthquake detection and location&quot;. In: Science Advances (Feb. 2018). doi: 10.1126/sciadv.1700578<br /> <br />  Kingma, D. and Ba, J., 2015. Adam: A Method for Stochastic Optimization. In: International Conference for Learning Representations. [online] San Diego: 3rd International Conference for Learning Representations, p.1. Available at: &lt;https://arxiv.org/pdf/1412.6980.pdf&gt; [Accessed 3 December 2020].</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&diff=49244 Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms 2020-12-05T19:20:51Z <p>Sh68lee: /* Model Architecture */</p> <hr /> <div><br /> == Presented by ==<br /> <br /> Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee<br /> <br /> == Introduction ==<br /> <br /> This paper presents ConvNetQuake, an approach on detecting heart disease from ECG signals by fine-tuning the deep learning neural network. For context, ConvNetQuake is a convolutional neural network, used by Perol, Gharbi, and Denolle , for Earthquake detection and location from a single waveform. A deep learning approach was used due to the model's ability to be trained using multiple GPUs and terabyte-sized datasets. This, in turn, creates a model that is robust against noise. The purpose of this paper is to provide detailed analyses of the contributions of the ECG leads on identifying heart disease, to show the use of multiple channels in ConvNetQuake enhances prediction accuracy, and to show that feature engineering is not necessary for any of the training, validation, or testing processes. In this area, the combination of data fusion and machine learning techniques exhibits great promise to healthcare innovation, and the analyses in this paper help further this realization. The benefits of translating knowledge between deep learning and its real-world applications in health are also illustrated.<br /> <br /> == Previous Work and Motivation ==<br /> <br /> The database used in previous works is the Physikalisch-Technische Bundesanstalt (PTB) database, which consists of ECG records. Previous papers used techniques, such as CNN, SVM, K-nearest neighbors, naïve Bayes classification, and ANN. From these instances, the paper observes several shortcomings in the previous papers. The first being the issue that most papers use feature selection on the raw ECG data before training the model. Dabanloo and Attarodi  used various techniques such as ANN, K-nearest neighbors, and Naïve Bayes. However, they extracted two features, the T-wave integral and the total integral, to aid in localizing and detecting heart disease. Sharma and Sunkaria  used SVM and K-nearest neighbors as their classifier, but extracted various features using stationary wavelet transforms to decompose the ECG signal into sub-bands. The second issue is that papers that do not use feature selection would arbitrarily pick ECG leads for classification without rationale. For example, Liu et al.  used a deep CNN that uses 3 seconds of ECG signal from lead II at a time as input. The decision for using lead II compared to the other leads was not explained. <br /> <br /> The issue with feature selection is that it can be time-consuming and impractical with large volumes of data. The second issue with the arbitrary selection of leads is that it does not offer insight into why the lead was chosen and the contributions of each lead in the identification of heart disease. Thus, this paper addresses these two issues through implementing a deep learning model that does not rely on feature selection of ECG data and to quantify the contributions of each ECG and Frank lead in identifying heart disease.<br /> <br /> == Model Architecture ==<br /> <br /> The dataset, which was used to train, validate, and test the neural network models, consists of 549 ECG records taken from 290 unique patients. Each ECG record has a mean length of over 100 seconds.<br /> <br /> This Deep Neural Network model was created by modifying the ConvNetQuake model by adding 1D batch normalization layers; this addition helps to combat overfitting. A second modification that was made was to introduce the use of label smoothing, which can help by discouraging the model from making overconfident predictions. Label smoothing refers to the method of relaxing the confidence on the model's prediction labels. The authors' experiments demonstrated that both of these modifications helped to increase model accuracy. <br /> <br /> During the training stage, a 10-second long two-channel input was fed into the neural network. In order to ensure that the two channels were weighted equally, both channels were normalized. Besides, time invariance was incorporated by selecting the 10-second long segment randomly from the entire signal. <br /> <br /> The input layer is a 10-second long ECG signal. There are 8 hidden layers in this model, each of which consists of a 1D convolution layer with the ReLu activation function followed by a batch normalization layer. The output layer is a one-dimensional layer that uses the Sigmoid activation function.<br /> <br /> This model is trained by using batches of size 10. The learning rate is &lt;math&gt;10^{-4}&lt;/math&gt;. The ADAM optimizer is used. The ADAM (adaptive moment estimation) optimizer is a stochastic gradient optimization method that uses adaptive learning rates for the parameters used in the estimating the gradient's first and second moments . In training the model, the dataset is split into a train set, validation set, and test set with ratios 80-10-10.<br /> <br /> During the training process, the model was trained from scratch numerous times to avoid inserting unintended variation into the model by randomly initializing weights.<br /> <br /> The following images gives a visual representation of the model.<br /> <br /> [[File:architecture.png | thumb | center | 1000px | Model Architecture (Gupta et al., 2019)]]<br /> <br /> ==Results== <br /> <br /> The paper first uses quantification of accuracies for single channels with 20-fold cross-validation, resulting in the highest individual accuracies: v5, v6, vx, vz, and ii. The researchers further investigated the accuracies for pairs of the top 5 highest individual channels using 20-fold cross-validation. They arrived at the conclusion of highest pairs accuracies to fed into a neural network is lead v6 and lead vz. They then use 100-fold cross validation on v6 and vz pair of channels, then compare outliers based on top 20, top 50 and total 100 performing models, finding that standard deviation is non-trivial and there are few models performed very poorly. <br /> <br /> Next, they discussed 2 factors affecting model performance evaluation: 1） Random train-val-test split might have effects on the performance of the model, but it can be improved by access with a larger data set and further discussion; and 2） random initialization of the weights of the neural network shows little effects on the performance of the model performance evaluation, because of showing high average results with a fixed train-val-test split. <br /> <br /> Comparing with other models in the other 12 papers, the model in this article has the highest accuracy, specificity, and precision. With concerns of patients' records affecting the training accuracy, they used 290 fold patient-wise split, resulting in the same highest accuracy of the pair v6 and vz same as record-wise split. The second best pair was ii and vz, which also contains the vz channel. Combining the two best pair channels into v6, vz, vii ultimately gave the best results over 10 trials which has an average of 97.83% in patient-wise split. Even though the patient-wise split might result in lower accuracy evaluation, however, it still maintains a very high average.<br /> <br /> ==Conclusion &amp; Discussion== <br /> <br /> The paper introduced a new architecture for heart condition classification based on raw ECG signals using multiple leads. It outperformed the state-of-art model by a large margin of 1 percent. This study finds that out of the 15 ECG channels(12 conventional ECG leads and 3 Frank Leads), channel v6, vz, and ii contain the most meaningful information for detecting myocardial infarction. Also, recent advances in machine learning can be leveraged to produce a model capable of classifying myocardial infraction with a cardiologist-level success rate. To further improve the performance of the models, access to a larger labeled data set is needed. The PTB database is small. It is difficult to test the true robustness of the model with a relatively small test set. If a larger data set can be found to help correctly identify other heart conditions beyond myocardial infraction, the research group plans to share the deep learning models and develop an open-source, computationally efficient app that can be readily used by cardiologists.<br /> <br /> A detailed analysis of the relative importance of each of the 15 ECG channels indicates that deep learning can identify myocardial infraction by processing only ten seconds of raw ECG data from the v6, vz, and ii leads and reaches a cardiologist-level success rate. Deep learning algorithms may be readily used as commodity software. The neural network model that was originally designed to identify earthquakes may be re-designed and tuned to identify myocardial infarction. Feature engineering of ECG data is not required to identify myocardial infraction in the PTB database. This model only required ten seconds of raw ECG data to identify this heart condition with cardiologist-level performance. Access to a larger database should be provided to deep learning researchers so they can work on detecting different types of heart conditions. Deep learning researchers and the cardiology community can work together to develop deep learning algorithms that provide trustworthy, real-time information regarding heart conditions with minimal computational resources.<br /> <br /> Fourier Transform (such as FFT) can be helpful when dealing with ECG signals. It transforms signals from the time domain to the frequency domain, which means some hidden features in frequency may be discovered.<br /> <br /> A limitation specified by the authors is the lack of labeled data. The use of a small dataset such as PTB makes it difficult to determine the robustness of the model due to the small size of the test set. Given a larger dataset, the model could be tested to see if it generalizes to identify heart conditions other than myocardial infarction.<br /> <br /> ==Critiques==<br /> - The lack of large, labelled data sets is often a common problem in most applied deep learning studies. Since the PTB database is as small as you describe it to be, the robustness of the model which may be hard to gauge. There are very likely various other physical factors that may play a role in the study which the deep neural network may not be able to adjust for as well, since health data can be somewhat subjective at times and/or may be somewhat inaccurate, especially if machines are used to measurement. This might mean error was propagated forward in the study.<br /> <br /> - Additionally, there is a risk of confirmation bias, which may occur when a model is self-training, especially given the fact that the training set is small.<br /> <br /> - I feel that the results of deep learning models in medical settings where the consequences of misclassification can be severe should be evaluated by assigning weights to classification. In case if the misclassification can lead to severe consequences, then the network should be trained in such a way that it errs towards safety. For example, in case if heart disease, the consequences will be very high if the system says that there is no heart disease when in fact there is. So, the evaluation metric must be selected carefully.<br /> <br /> - This is a useful and meaningful application topic in machine learning. Using Deep Learning to detect heart disease can be very helpful if it is difficult to detect disease by looking at ECG by humans eys. This model also useful for doing statistics, such as calculating the percentage of people get heart disease. But I think the doctor should not 100% trust the result from the model, it is almost impossible to get 100% accuracy from a model. So, I think double-checking by human eyes is necessary if the result is weird. What is more, I think it will be interesting to discuss more applications in mediccal by using this method, such as detecting the Brainwave diagram to predict a person's mood and to diagnose mental diseases.<br /> <br /> - Compared to the dataset for other topics such as object recognition, the PTB database is pretty small with only 549 ECG records. And these are highly unbiased (Table 1) with 4 records for myocarditis and 148 for myocardial infarction. Medical datasets can only be labeled by specialists. This is why these datasets are related small. It would be great if there will be a larger, more comprehensive dataset.<br /> <br /> - Only results using 20-fold cross validation were presented. It should be shown that the results could be reproduced using a more common number of folds like 5 or 10<br /> <br /> - There are potential issues with the inclusion of Frank leads. From a practitioner standpoint, ECGs taken with Frank leads are less common. This could prevent the use of this technique. Additionally, Frank leads are expressible as a linear combinations of the 12 traditional leads. The authors are not adding any fundamentally new information by including them and their inclusion could be viewed as a form of feature selection (going against the authors' original intentions).<br /> <br /> - It will better if we can see how the model in this paper outperformed those methods that used feature selections. The details of the results are not enough.<br /> <br /> - A new extended dataset for PTB dubbed [https://www.nature.com/articles/s41597-020-0495-6 PTB-XL], has 21837 records. Using this dataset could yield a more accurate result, since the original PTB's small dataset posed limitations on the deep learning model.<br /> <br /> - The paper mentions that it has better results, but by how much? what accuracy did the methods you compared to have? Also, what methods did you compare to? (Authors mentioned feature engineering methods but this is vague) Also how much were the labels smoothed? (i.e. 1 -&gt; 0.99 or 1-&gt; 0.95 for example) How much of a difference did the label smoothing make?<br /> <br /> - It is nice to see that the authors also considered training and testing the model on data via a patient-wise split, which gives more insights towards the cases when a patient has multiple records of diagnosis. Obviously and similar to what other critiques suggested, using a patient-wise split might disadvantage from the lack of training data, given that there are only 290 unique patients in the PTB database. Also, acquiring prior knowledge from professionals about correlations, such as causal relationships, between different diagnoses might be helpful for improving the model.<br /> <br /> - As mentioned above, the dataset is comparably small in the context of machine learning. While on the other hand, each record has a length of roughly 100 seconds, which is significantly large as a single input. Therefore, it might be helpful to apply data augmentation algorithms during data preprocessing sections so that there will be a more reasonable dataset than what we currently have so far, which has a high chance of being biased or overfitted.<br /> <br /> - There are several points from the Model Architecture section that can be improved. It mentions that both 1d batch normalization layers and label smoothing are used to improve the accuracy of the models, based on empirical experiment results. Yet, there's no breakdown of how each of these two method improves the accuracy. So it's left unclear whether each method is significant on its own, or the model simultaneously requires both methods in order to achieve improved accuracy. Some more data can be provided about this. It's mentioned that &quot;models are trained from scratch numerous times.&quot; How many times is numerous times? Can we get the exact number? Training time about the models should also be provided. This is because if these models take a long time to train, then training them from scratch every time may cause issues with respect to runtime.<br /> <br /> - The authors should have indicated how much the accuracy has been improved by what method. It is a little unclear that how can we define &quot;better results&quot;. Also, this paper could be more clear if they included the details about the Model Architecture such as how it was performed and how long was the training time for the model.<br /> <br /> == References ==<br /> <br />  Na Liu et al. &quot;A Simple and Effective Method for Detecting Myocardial Infarction Based on Deep Convolutional Neural Network&quot;. In: Journal of Medical Imaging and Health Informatics (Sept. 2018). doi: 10.1166/jmihi.2018.2463.<br /> <br />  Naser Safdarian, N.J. Dabanloo, and Gholamreza Attarodi. &quot;A New Pattern Recognition Method for Detection and Localization of Myocardial Infarction Using T-Wave Integral and Total Integral as Extracted Features from One Cycle of ECG Signal&quot;. In: J. Biomedical Science and Engineering (Aug. 2014). doi: http://dx.doi.org/10.4236/jbise.2014.710081.<br /> <br />  L.D. Sharma and R.K. Sunkaria. &quot;Inferior myocardial infarction detection using stationary wavelet transform and machine learning approach.&quot; In: Signal, Image and Video Processing (July 2017). doi: https://doi.org/10.1007/s11760-017-1146-z.<br /> <br />  Perol Thibaut, Gharbi Michaël, and Denolle Marin. &quot;Convolutional neural network for earthquake detection and location&quot;. In: Science Advances (Feb. 2018). doi: 10.1126/sciadv.1700578<br /> <br />  Kingma, D. and Ba, J., 2015. Adam: A Method for Stochastic Optimization. In: International Conference for Learning Representations. [online] San Diego: 3rd International Conference for Learning Representations, p.1. Available at: &lt;https://arxiv.org/pdf/1412.6980.pdf&gt; [Accessed 3 December 2020].</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=49242 Loss Function Search for Face Recognition 2020-12-05T19:18:16Z <p>Sh68lee: /* Critiques */</p> <hr /> <div>== Presented by ==<br /> Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br /> <br /> == Introduction ==<br /> Face recognition is a technology that can label a face to a specific identity. The field of study involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face image and another face image map to the same identity. Loss functions play an important role in evaluating how well the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. However, traditional softmax loss lacks the power of feature discrimination. To solve this problem, a center loss was developed to learn centers for each identity to enhance the intra-class compactness. Hence, the paper introduced a new loss function using a scale parameter to produce higher gradients to well-separated samples which can reduce the softmax probability. <br /> <br /> Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much efforts such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective . It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space.<br /> <br /> '''Soft Max'''<br /> Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br /> <br /> &lt;center&gt;&lt;math&gt;L_1=-\log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}&lt;/math&gt;  &lt;/center&gt;<br /> <br /> <br /> Specifically for face recognition, &lt;math&gt;L_1&lt;/math&gt; is modified such that &lt;math&gt;w^T_yx&lt;/math&gt; is normalized and &lt;math&gt;s&lt;/math&gt; represents the magnitude of &lt;math&gt;w^T_yx&lt;/math&gt;:<br /> <br /> &lt;center&gt;&lt;math&gt;L_2=-\log\frac{e^{s \cos{(\theta_{{w_y},x})}}}{e^{s \cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s \cos{(\theta_{{w_y},x})}}}}&lt;/math&gt;  &lt;/center&gt;<br /> <br /> Where &lt;math&gt; \cos{(\theta_{{w_k},x})} = w^T_y &lt;/math&gt; is cosine similarity and &lt;math&gt;\theta_{{w_k},x}&lt;/math&gt; is angle between &lt;math&gt; w_k&lt;/math&gt; and x. The learnt features with this soft max loss are prone to be separable (as desired).<br /> <br /> '''Margin-based Softmax'''<br /> <br /> This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above.<br /> <br /> The margin-based softmax function is:<br /> <br /> &lt;center&gt;&lt;math&gt;L_3=-\log\frac{e^{s f{(m,\theta_{{w_y},x})}}}{e^{s f{(m,\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s \cos{(\theta_{{w_y},x})}}}} &lt;/math&gt; &lt;/center&gt;<br /> <br /> Here, &lt;math&gt;f{(m,\theta_{{w_y},x})} \leq \cos (\theta_{w_y,x})&lt;/math&gt; is a carefully chosen margin function.<br /> <br /> Some other variations of chosen functions:<br /> <br /> '''A-Softmax Loss:''' &lt;math&gt;f{(m_1,\theta_{{w_y},x})} = \cos (m_1\theta_{w_y,x})&lt;/math&gt; , where m1 &gt;= 1 and a integer.<br /> <br /> '''Arc-Softmax Loss:'''&lt;math&gt;f{(m_1,\theta_{{w_y},x})} = \cos (\theta_{w_y,x} + m_2)&lt;/math&gt;, where m2 &gt; 0<br /> <br /> '''AM-Softmax Loss:'''&lt;math&gt;f{(m,\theta_{{w_y},x})} = \cos (m_1\theta_{w_y,x} + m_2) - m_3&lt;/math&gt;, where m1 &gt;= 1 and a integer; m2,m3 &gt; 0<br /> <br /> <br /> <br /> In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br /> <br /> == Motivation ==<br /> Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions is high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine-tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br /> <br /> To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one required parameter and an improved search space using a reward-based method was determined by the authors to be the best option for their loss function.<br /> <br /> == Problem Formulation ==<br /> === Analysis of Margin-based Softmax Loss ===<br /> Based on the softmax probability and the margin-based softmax probability, the following function can be developed :<br /> <br /> &lt;center&gt;&lt;math&gt;p_m=\frac{1}{ap+(1-a)}*p&lt;/math&gt;&lt;/center&gt;<br /> &lt;center&gt; where &lt;math&gt;a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}&lt;/math&gt; and &lt;math&gt;a≤0&lt;/math&gt;&lt;/center&gt;<br /> <br /> &lt;math&gt;a&lt;/math&gt; is considered as a modulating factor and &lt;math&gt;h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]&lt;/math&gt; is a modulating function . Therefore, regardless of the margin function (&lt;math&gt;f&lt;/math&gt;), the minimization of the softmax probability will ensure success.<br /> <br /> Compared to AM-LFS, this method involves only one parameter (&lt;math&gt;a&lt;/math&gt;) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (&lt;math&gt;p_m={a_i}p+b_i&lt;/math&gt;) may not be discriminative because it could be larger than the softmax probability.<br /> <br /> === Random Search ===<br /> Unified formulation &lt;math&gt;L_5&lt;/math&gt; is generated by inserting a simple modulating function &lt;math&gt;h{(a,p)}=\frac{1}{ap+(1-a)}&lt;/math&gt; into the original softmax loss. It can be written as below :<br /> <br /> &lt;center&gt;&lt;math&gt;L_5=-log{(h{(a,p)}*p)}&lt;/math&gt; where &lt;math&gt;h \in (0,1]&lt;/math&gt; and &lt;math&gt;a≤0&lt;/math&gt;&lt;/center&gt;<br /> <br /> This encourages the feature margin between different classes and has the capability of feature discrimination. This leads to defining the search space as the choice of &lt;math&gt;h{(a,p)}&lt;/math&gt; whose impacts on the training procedure are decided by the modulating factor &lt;math&gt;a&lt;/math&gt;. In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br /> <br /> === Reward-Guided Search ===<br /> Random search has no guidance for training. To solve this, the authors use reinforcement learning. Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward . The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br /> <br /> &lt;center&gt;&lt;math&gt;G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T&lt;/math&gt;&lt;/center&gt;<br /> <br /> where &lt;math&gt;G_t&lt;/math&gt; = cumulative reward, &lt;math&gt;R_t&lt;/math&gt; = immediate reward, and &lt;math&gt;R_T&lt;/math&gt; = end of episode.<br /> <br /> &lt;math&gt;G_t&lt;/math&gt; is the sum of immediate rewards from arbitrary time &lt;math&gt;t&lt;/math&gt;. It is a random variable because it depends on the immediate reward which depends on the agent action and the environment's reaction to this action.<br /> <br /> &lt;center&gt;[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]&lt;/center&gt;<br /> &lt;center&gt;Figure 1: Reinforcement Learning scenario &lt;/center&gt;<br /> <br /> The reward function is what guides the agent to move in a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed . <br /> <br /> In this paper, RL is being used to generate a distribution of the hyperparameter &lt;math&gt;\mu&lt;/math&gt; for the SoftMax equation using the reward function. At each epoch, &lt;math&gt;B&lt;/math&gt; hyper-parameters &lt;math&gt;{a_1, a_2, ..., a_B }&lt;/math&gt; are sampled as &lt;math&gt;a \sim \mathcal{N}(\mu, \sigma)&lt;/math&gt;. In each epoch, &lt;math&gt;B&lt;/math&gt; models are generated with rewards &lt;math&gt;R(a_i), i \in [1, B]&lt;/math&gt;. &lt;math&gt;\mu&lt;/math&gt; updates after each epoch from the reward function. <br /> <br /> &lt;center&gt;&lt;math&gt;\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}&lt;/math&gt;&lt;/center&gt;<br /> <br /> Where &lt;math&gt;{g(a_i; \mu, \sigma})&lt;/math&gt; is the PDF of a Gaussian distribution. The distributions of &lt;math&gt;{a}&lt;/math&gt; are updated and the best model if found from the &lt;math&gt;{B}&lt;/math&gt; candidates for the next epoch.<br /> <br /> === Optimization ===<br /> Calculating the reward involves a standard bi-level optimization problem. A standard bi-level optimization problem is a hierarchy of two optimization tasks, an upper-level or leader and lower-level or follower problems, which involves a hyperparameter ({&lt;math&gt;a_1,a_2,…,a_B&lt;/math&gt;}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br /> <br /> &lt;center&gt;&lt;math&gt;max_a R(a)=r(M_{w^*(a)},S_v)&lt;/math&gt;&lt;/center&gt;<br /> &lt;center&gt;&lt;math&gt;w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)&lt;/math&gt;&lt;/center&gt;<br /> <br /> In this case, the loss function takes the training set &lt;math&gt;S_t&lt;/math&gt; and the reward function takes the validation set &lt;math&gt;S_v&lt;/math&gt;. The weights &lt;math&gt;w&lt;/math&gt; are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({&lt;math&gt;M_{we1},M_{we2},…,M_{weB}&lt;/math&gt;}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. In the end, the algorithm takes the model with the highest score without retraining.<br /> <br /> == Results and Discussion ==<br /> === Data Preprocessing ===<br /> The training datasets consisted of cleaned versions of CASIA-WebFace and MS-Celeb-1M-v1c to remove the impact of noisy labels in the original sets.<br /> Furthermore, it is important to perform open-set evaluation for face recognition problem. That is, there shall be no overlapping identities between training and testing sets. As a result, there were a total of 15,414 identities removed from the testing sets. For fairness during comparison, all summarized results will be based on refined datasets.<br /> <br /> === Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br /> For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms, however, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br /> <br /> Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. The following table gives a summary of the performance of each model.<br /> <br /> &lt;center&gt;Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> <br /> &lt;center&gt;[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> === Results on RFW ===<br /> The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br /> <br /> &lt;center&gt;Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> <br /> &lt;center&gt;Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> === Results on MegaFace and Trillion-Pairs ===<br /> The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at &lt;math&gt;1e^{-3}&lt;/math&gt; on MegaFace, the identification TPR@FAR = &lt;math&gt;1e^{-6}&lt;/math&gt; and the verification TPR@FAR = &lt;math&gt;1e^{-9}&lt;/math&gt; on Trillion-Pairs are reported on Table 4 and 5.<br /> <br /> On the test sets MegaFace and Trillion-Pairs, Search-Softmax achieves the best performance over all other alternative methods. On MegaFace, Search-Softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br /> <br /> &lt;center&gt;Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> <br /> &lt;center&gt;Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a similar trend with Trillion-Pairs where Search-Softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br /> <br /> &lt;center&gt;[[Image:G25_Figure2_left.png|800px |alt=Alt text|Title text]] [[Image:G25_Figure2_right.png|800px |alt=Alt text|Title text]]&lt;/center&gt;<br /> &lt;center&gt;Figure 2. From Left to Right: CMC curves and ROC curves on MegaFace Set with training set CASIA-WebFace-R, CMC curves and ROC curves on MegaFace Set with training set MS-Celeb-1M-v1c-R .&lt;/center&gt;<br /> <br /> == Conclusion ==<br /> In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. While these developed methods were generally more effective in increasing accuracy versus previous methods, there is very little difference between the two. It can be seen that Search-Softmax performs slightly better than Random-Softmax most of the time.<br /> <br /> == Critiques ==<br /> * Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument​.<br /> * Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would​.<br /> * AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate​.<br /> * The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show many advantages since they produce very similar results. A more complicated data set needs to be tested to prove the method's reliability.<br /> * There is another paper Large-Margin Softmax Loss for Convolutional Neural Networks[https://arxiv.org/pdf/1612.02295.pdf] that provides a more detailed explanation about how to reduce margin-based softmax loss.<br /> * It is questionable when it comes to the accuracy of testing sets, as they only used the clean version of CASIA-WebFace and MS-Celeb-1M-vlc for training instead of these two training sets with noisy labels.<br /> * In a similar [https://arxiv.org/pdf/1905.09773.pdf?utm_source=thenewstack&amp;utm_medium=website&amp;utm_campaign=platform paper], written by Tae-Hyun Oh et al., they also discuss an optimal loss function for face recognition. However, since in the other paper, they were doing face recognition from voice audio, the loss function used was slightly different than the ones discussed in this paper.<br /> * This model has many applications such as identifying disguised prisoners for police. But we need to do a good data preprocessing otherwise we might not get a good predicted result. But authors did not mention about the data preprocessing which is a key part of this model.<br /> * It will be better if we can know what kind of noises was removed in the clean version. Also, simply removing the overlapping data is wasteful. It would be better to just put them into one of the train and test samples.<br /> * This paper indicate that the new searching method and loss function have induced more effective face recognition result than other six methods. But there is no mention of the increase or decrease in computational efficiency since only very little difference exist between those methods and the real time evaluation is often required at the face recognition application level.<br /> * There are some loss functions that receives more than 2 inputs. For example, the ''triplet loss'' function, developed by Google, takes 3 inputs: positive input, negative input and anchor input. This makes sense because for face recognition, we want to model to learn not only what it is supposed to predict but also what it is not supposed to predict. Typically, triplet loss handles false positives much better. This paper can extend its scope to such loss function that takes more than 2 inputs.<br /> * It would be good to also know what the training time is like for the method, specifically the &quot;Reward-Guided Search&quot; which uses RL. Also the authors mention some data preprocessing that was performed, was this same preprocessing also performed for the methods they compared against?<br /> * Sections on Data Processing and Results can be improved. About the datasets, I have some questions about why they are divided in the current fashion. It is mentioned that &quot;CASIA-WebFace and MS-Celeb-1M-v1c&quot; are used as training datasets. But the comparison of algorithms are divided into three groups: Megaface and TrillionPairs, RFW, and a group of other datasets. In general, when we are comparing algorithms, we want to have a holistic view of how each algorithm compare. So I have some concerns about dividing the results into three section. More explanation can be provided. It also seems like Random-Softmax and Search Softmax outperform all other algorithms across all datasets. So it would make even more sense to have a big table including all the results. About data preprocessing, I believe that giving more information about which noisy data are removed would be nice.<br /> * Despite thorough comparison between each method against the proposed method, it does not give a reason to why it was the case that it was either better or worse, and it does not necessarily need to be a mathematical explanation but an intuitive one to demonstrate how it can be replicated and whether the results require a certain condition to achieve. <br /> * Though we have a graph demonstrating the training loss with Random-Softmax and Search-Softmax with regards to the number of Epochs as an independent variable which we may deduce the number of epochs used in later graphs but since one of the main features is that &quot;Meanwhile, our optimization strategy enables that the dynamic loss can guide<br /> * Did the paper address why the average model performs worse on African faces, would it be a lack of data points?<br /> the model training of different epochs, which helps further boost the discrimination power.&quot; it is imperative that the results are comparable along the same scale (for example, for 20 epochs, then take the average of the losses).<br /> * The result summary is overwhelming with numbers and representation of result is lacking. It would be great if the result can be explained. Introduction of model and its component is lacking and could be explained more.<br /> <br /> == References ==<br />  X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, &quot;Loss Function Search for Face Recognition&quot;, in International Conference on Machine Learning, 2020, pp. 1-10.<br /> <br />  Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br /> 2020].<br /> <br />  S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br /> <br />  “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br /> <br />  B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition&diff=49240 Loss Function Search for Face Recognition 2020-12-05T19:15:55Z <p>Sh68lee: /* Results on MegaFace and Trillion-Pairs */</p> <hr /> <div>== Presented by ==<br /> Jan Lau, Anas Mahdi, Will Thibault, Jiwon Yang<br /> <br /> == Introduction ==<br /> Face recognition is a technology that can label a face to a specific identity. The field of study involves two tasks: 1. Identifying and classifying a face to a certain identity and 2. Verifying if this face image and another face image map to the same identity. Loss functions play an important role in evaluating how well the prediction models the given data. In the application of face recognition, they are used for training convolutional neural networks (CNNs) with discriminative features. However, traditional softmax loss lacks the power of feature discrimination. To solve this problem, a center loss was developed to learn centers for each identity to enhance the intra-class compactness. Hence, the paper introduced a new loss function using a scale parameter to produce higher gradients to well-separated samples which can reduce the softmax probability. <br /> <br /> Margin-based (angular, additive, additive angular margins) soft-max loss functions are important in learning discriminative features in face recognition. There have been hand-crafted methods previously developed that require much efforts such as A-softmax, V-softmax, AM-Softmax, and Arc-softmax. Li et al. proposed an AutoML for loss function search method also known as AM-LFS from a hyper-parameter optimization perspective . It automatically determines the search space by leveraging reinforcement learning to the search loss functions during the training process, though the drawback is the complex and unstable search space.<br /> <br /> '''Soft Max'''<br /> Softmax probability is the probability for each class. It contains a vector of values that add up to 1 while ranging between 0 and 1. Cross-entropy loss is the negative log of the probabilities. When softmax probability is combined with cross-entropy loss in the last fully connected layer of the CNN, it yields the softmax loss function:<br /> <br /> &lt;center&gt;&lt;math&gt;L_1=-\log\frac{e^{w^T_yx}}{e^{w^T_yx} + \sum_{k≠y}^K{e^{w^T_yx}}}&lt;/math&gt;  &lt;/center&gt;<br /> <br /> <br /> Specifically for face recognition, &lt;math&gt;L_1&lt;/math&gt; is modified such that &lt;math&gt;w^T_yx&lt;/math&gt; is normalized and &lt;math&gt;s&lt;/math&gt; represents the magnitude of &lt;math&gt;w^T_yx&lt;/math&gt;:<br /> <br /> &lt;center&gt;&lt;math&gt;L_2=-\log\frac{e^{s \cos{(\theta_{{w_y},x})}}}{e^{s \cos{(\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s \cos{(\theta_{{w_y},x})}}}}&lt;/math&gt;  &lt;/center&gt;<br /> <br /> Where &lt;math&gt; \cos{(\theta_{{w_k},x})} = w^T_y &lt;/math&gt; is cosine similarity and &lt;math&gt;\theta_{{w_k},x}&lt;/math&gt; is angle between &lt;math&gt; w_k&lt;/math&gt; and x. The learnt features with this soft max loss are prone to be separable (as desired).<br /> <br /> '''Margin-based Softmax'''<br /> <br /> This function is crucial in face recognition because it is used for enhancing feature discrimination. While there are different variations of the softmax loss function, they build upon the same structure as the equation above.<br /> <br /> The margin-based softmax function is:<br /> <br /> &lt;center&gt;&lt;math&gt;L_3=-\log\frac{e^{s f{(m,\theta_{{w_y},x})}}}{e^{s f{(m,\theta_{{w_y},x})}} + \sum_{k≠y}^K{e^{s \cos{(\theta_{{w_y},x})}}}} &lt;/math&gt; &lt;/center&gt;<br /> <br /> Here, &lt;math&gt;f{(m,\theta_{{w_y},x})} \leq \cos (\theta_{w_y,x})&lt;/math&gt; is a carefully chosen margin function.<br /> <br /> Some other variations of chosen functions:<br /> <br /> '''A-Softmax Loss:''' &lt;math&gt;f{(m_1,\theta_{{w_y},x})} = \cos (m_1\theta_{w_y,x})&lt;/math&gt; , where m1 &gt;= 1 and a integer.<br /> <br /> '''Arc-Softmax Loss:'''&lt;math&gt;f{(m_1,\theta_{{w_y},x})} = \cos (\theta_{w_y,x} + m_2)&lt;/math&gt;, where m2 &gt; 0<br /> <br /> '''AM-Softmax Loss:'''&lt;math&gt;f{(m,\theta_{{w_y},x})} = \cos (m_1\theta_{w_y,x} + m_2) - m_3&lt;/math&gt;, where m1 &gt;= 1 and a integer; m2,m3 &gt; 0<br /> <br /> <br /> <br /> In this paper, the authors first identified that reducing the softmax probability is a key contribution to feature discrimination and designed two design search spaces (random and reward-guided method). They then evaluated their Random-Softmax and Search-Softmax approaches by comparing the results against other face recognition algorithms using nine popular face recognition benchmarks.<br /> <br /> == Motivation ==<br /> Previous algorithms for facial recognition frequently rely on CNNs that may include metric learning loss functions such as contrastive loss or triplet loss. Without sensitive sample mining strategies, the computational cost for these functions is high. This drawback prompts the redesign of classical softmax loss that cannot discriminate features. Multiple softmax loss functions have since been developed, and including margin-based formulations, they often require fine-tuning of parameters and are susceptible to instability. Therefore, researchers need to put in a lot of effort in creating their method in the large design space. AM-LFS takes an optimization approach for selecting hyperparameters for the margin-based softmax functions, but its aforementioned drawbacks are caused by the lack of direction in designing the search space.<br /> <br /> To solve the issues associated with hand-tuned softmax loss functions and AM-LFS, the authors attempt to reduce the softmax probability to improve feature discrimination when using margin-based softmax loss functions. The development of margin-based softmax loss with only one required parameter and an improved search space using a reward-based method was determined by the authors to be the best option for their loss function.<br /> <br /> == Problem Formulation ==<br /> === Analysis of Margin-based Softmax Loss ===<br /> Based on the softmax probability and the margin-based softmax probability, the following function can be developed :<br /> <br /> &lt;center&gt;&lt;math&gt;p_m=\frac{1}{ap+(1-a)}*p&lt;/math&gt;&lt;/center&gt;<br /> &lt;center&gt; where &lt;math&gt;a=1-e^{s{cos{(\theta_{w_y},x)}-f{(m,\theta_{w_y},x)}}}&lt;/math&gt; and &lt;math&gt;a≤0&lt;/math&gt;&lt;/center&gt;<br /> <br /> &lt;math&gt;a&lt;/math&gt; is considered as a modulating factor and &lt;math&gt;h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]&lt;/math&gt; is a modulating function . Therefore, regardless of the margin function (&lt;math&gt;f&lt;/math&gt;), the minimization of the softmax probability will ensure success.<br /> <br /> Compared to AM-LFS, this method involves only one parameter (&lt;math&gt;a&lt;/math&gt;) that is also constrained, versus AM-LFS which has 2M parameters without constraints that specify the piecewise linear functions the method requires. Also, the piecewise linear functions of AM-LFS (&lt;math&gt;p_m={a_i}p+b_i&lt;/math&gt;) may not be discriminative because it could be larger than the softmax probability.<br /> <br /> === Random Search ===<br /> Unified formulation &lt;math&gt;L_5&lt;/math&gt; is generated by inserting a simple modulating function &lt;math&gt;h{(a,p)}=\frac{1}{ap+(1-a)}&lt;/math&gt; into the original softmax loss. It can be written as below :<br /> <br /> &lt;center&gt;&lt;math&gt;L_5=-log{(h{(a,p)}*p)}&lt;/math&gt; where &lt;math&gt;h \in (0,1]&lt;/math&gt; and &lt;math&gt;a≤0&lt;/math&gt;&lt;/center&gt;<br /> <br /> This encourages the feature margin between different classes and has the capability of feature discrimination. This leads to defining the search space as the choice of &lt;math&gt;h{(a,p)}&lt;/math&gt; whose impacts on the training procedure are decided by the modulating factor &lt;math&gt;a&lt;/math&gt;. In order to validate the unified formulation, a modulating factor is randomly set at each training epoch. This is noted as Random-Softmax in this paper.<br /> <br /> === Reward-Guided Search ===<br /> Random search has no guidance for training. To solve this, the authors use reinforcement learning. Unlike supervised learning, reinforcement learning (RL) is a behavioral learning model. It does not need to have input/output labelled and it does not need a sub-optimal action to be explicitly corrected. The algorithm receives feedback from the data to achieve the best outcome. The system has an agent that guides the process by taking an action that maximizes the notion of cumulative reward . The process of RL is shown in figure 1. The equation of the cumulative reward function is: <br /> <br /> &lt;center&gt;&lt;math&gt;G_t \overset{\Delta}{=} R_t+R_{t+1}+R_{t+2}+⋯+R_T&lt;/math&gt;&lt;/center&gt;<br /> <br /> where &lt;math&gt;G_t&lt;/math&gt; = cumulative reward, &lt;math&gt;R_t&lt;/math&gt; = immediate reward, and &lt;math&gt;R_T&lt;/math&gt; = end of episode.<br /> <br /> &lt;math&gt;G_t&lt;/math&gt; is the sum of immediate rewards from arbitrary time &lt;math&gt;t&lt;/math&gt;. It is a random variable because it depends on the immediate reward which depends on the agent action and the environment's reaction to this action.<br /> <br /> &lt;center&gt;[[Image:G25_Figure1.png|300px |link=https://en.wikipedia.org/wiki/Reinforcement_learning#/media/File:Reinforcement_learning_diagram.svg |alt=Alt text|Title text]]&lt;/center&gt;<br /> &lt;center&gt;Figure 1: Reinforcement Learning scenario &lt;/center&gt;<br /> <br /> The reward function is what guides the agent to move in a certain direction. As mentioned above, the system receives feedback from the data to achieve the best outcome. This is caused by the reward being edited based on the feedback it receives when a task is completed . <br /> <br /> In this paper, RL is being used to generate a distribution of the hyperparameter &lt;math&gt;\mu&lt;/math&gt; for the SoftMax equation using the reward function. At each epoch, &lt;math&gt;B&lt;/math&gt; hyper-parameters &lt;math&gt;{a_1, a_2, ..., a_B }&lt;/math&gt; are sampled as &lt;math&gt;a \sim \mathcal{N}(\mu, \sigma)&lt;/math&gt;. In each epoch, &lt;math&gt;B&lt;/math&gt; models are generated with rewards &lt;math&gt;R(a_i), i \in [1, B]&lt;/math&gt;. &lt;math&gt;\mu&lt;/math&gt; updates after each epoch from the reward function. <br /> <br /> &lt;center&gt;&lt;math&gt;\mu_{e+1}=\mu_e + \eta \frac{1}{B} \sum_{i=1}^B R{(a_i)}{\nabla_a}log{(g(a_i;\mu,\sigma))}&lt;/math&gt;&lt;/center&gt;<br /> <br /> Where &lt;math&gt;{g(a_i; \mu, \sigma})&lt;/math&gt; is the PDF of a Gaussian distribution. The distributions of &lt;math&gt;{a}&lt;/math&gt; are updated and the best model if found from the &lt;math&gt;{B}&lt;/math&gt; candidates for the next epoch.<br /> <br /> === Optimization ===<br /> Calculating the reward involves a standard bi-level optimization problem. A standard bi-level optimization problem is a hierarchy of two optimization tasks, an upper-level or leader and lower-level or follower problems, which involves a hyperparameter ({&lt;math&gt;a_1,a_2,…,a_B&lt;/math&gt;}) that can be used for minimizing one objective function while maximizing another objective function simultaneously:<br /> <br /> &lt;center&gt;&lt;math&gt;max_a R(a)=r(M_{w^*(a)},S_v)&lt;/math&gt;&lt;/center&gt;<br /> &lt;center&gt;&lt;math&gt;w^*(a)=_w \sum_{(x,y) \in S_t} L^a (M_w(x),y)&lt;/math&gt;&lt;/center&gt;<br /> <br /> In this case, the loss function takes the training set &lt;math&gt;S_t&lt;/math&gt; and the reward function takes the validation set &lt;math&gt;S_v&lt;/math&gt;. The weights &lt;math&gt;w&lt;/math&gt; are trained such that the loss function is minimized while the reward function is maximized. The calculated reward for each model ({&lt;math&gt;M_{we1},M_{we2},…,M_{weB}&lt;/math&gt;}) yields the corresponding score, then the algorithm chooses the one with the highest score for model index selection. With the model containing the highest score being used in the next epoch, this process is repeated until the training reaches convergence. In the end, the algorithm takes the model with the highest score without retraining.<br /> <br /> == Results and Discussion ==<br /> === Data Preprocessing ===<br /> The training datasets consisted of cleaned versions of CASIA-WebFace and MS-Celeb-1M-v1c to remove the impact of noisy labels in the original sets.<br /> Furthermore, it is important to perform open-set evaluation for face recognition problem. That is, there shall be no overlapping identities between training and testing sets. As a result, there were a total of 15,414 identities removed from the testing sets. For fairness during comparison, all summarized results will be based on refined datasets.<br /> <br /> === Results on LFW, SLLFW, CALFW, CPLFW, AgeDB, DFP ===<br /> For LFW, there is not a noticeable difference between the algorithms proposed in this paper and the other algorithms, however, AM-Softmax achieved higher results than Search-Softmax. Random-Softmax achieved the highest results by 0.03%.<br /> <br /> Random-Softmax outperforms baseline Soft-max and is comparable to most of the margin-based softmax. Search-Softmax boost the performance and better most methods specifically when training CASIA-WebFace-R data set, it achieves 0.72% average improvement over AM-Softmax. The reason the model proposed by the paper gives better results is because of their optimization strategy which helps boost the discimination power. Also the sampled candidate from the paper’s proposed search space can well approximate the margin-based loss functions. More tests need to happen to more complicated protocols to test the performance further. Not a lot of improvement has been shown on those test sets, since they are relatively simple and the performance of all the methods on these test sets are near saturation. The following table gives a summary of the performance of each model.<br /> <br /> &lt;center&gt;Table 1.Verification performance (%) of different methods on the test sets LFW, SLLFW, CALFW, CPLFW, AgeDB and CFP. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> <br /> &lt;center&gt;[[Image:G25_Table1.png|900px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> === Results on RFW ===<br /> The RFW dataset measures racial bias which consists of Caucasian, Indian, Asian, and African. Using this as the test set, Random-softmax and Search-softmax performed better than the other methods. Random-softmax outperforms the baseline softmax by a large margin which means reducing the softmax probability will enhance the feature discrimination for face recognition. It is also observed that the reward guided search-softmax method is more likely to enhance the discriminative feature learning resulting in higher performance as shown in Table 2 and Table 3. <br /> <br /> &lt;center&gt;Table 2. Verification performance (%) of different methods on the test set RFW. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table2.png|500px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> <br /> &lt;center&gt;Table 3. Verification performance (%) of different methods on the test set RFW. The training set is '''MS-Celeb-1M-v1c-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table3.png|500px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> === Results on MegaFace and Trillion-Pairs ===<br /> The different loss functions are tested again with more complicated protocols. The identification (Id.) Rank-1 and the verification (Veri.) with the true positive rate (TPR) at low false acceptance rate (FAR) at &lt;math&gt;1e^{-3}&lt;/math&gt; on MegaFace, the identification TPR@FAR = &lt;math&gt;1e^{-6}&lt;/math&gt; and the verification TPR@FAR = &lt;math&gt;1e^{-9}&lt;/math&gt; on Trillion-Pairs are reported on Table 4 and 5.<br /> <br /> On the test sets MegaFace and Trillion-Pairs, Search-Softmax achieves the best performance over all other alternative methods. On MegaFace, Search-Softmax beat the best competitor AM-softmax by a large margin. It also outperformed AM-LFS due to new designed search space. <br /> <br /> &lt;center&gt;Table 4. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''CASIA-WebFace-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table4.png|450px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> <br /> &lt;center&gt;Table 5. Performance (%) of different loss functions on the test sets MegaFace and Trillion-Pairs. The training set is '''MS-Celeb-1M-v1c-R''' .&lt;/center&gt;<br /> &lt;center&gt;[[Image:G25_Table5.png|450px |alt=Alt text|Title text]]&lt;/center&gt;<br /> <br /> From the CMC curves and ROC curves in Figure 2, similar trends are observed at other measures. There is a similar trend with Trillion-Pairs where Search-Softmax loss is found to be superior with 4% improvements with CASIA-WebFace-R and 1% improvements with MS-Celeb-1M-v1c-R at both the identification and verification. Based on these experiments, Search-Softmax loss can perform well, especially with a low false positive rate and it shows a strong generalization ability for face recognition.<br /> <br /> &lt;center&gt;[[Image:G25_Figure2_left.png|800px |alt=Alt text|Title text]] [[Image:G25_Figure2_right.png|800px |alt=Alt text|Title text]]&lt;/center&gt;<br /> &lt;center&gt;Figure 2. From Left to Right: CMC curves and ROC curves on MegaFace Set with training set CASIA-WebFace-R, CMC curves and ROC curves on MegaFace Set with training set MS-Celeb-1M-v1c-R .&lt;/center&gt;<br /> <br /> == Conclusion ==<br /> In this paper, it is discussed that in order to enhance feature discrimination for face recognition, it is key to know how to reduce the softmax probability. To achieve this goal, unified formulation for the margin-based softmax losses is designed. Two search methods have been developed using a random and a reward-guided loss function and they were validated to be effective over six other methods using nine different test data sets. While these developed methods were generally more effective in increasing accuracy versus previous methods, there is very little difference between the two. It can be seen that Search-Softmax performs slightly better than Random-Softmax most of the time.<br /> <br /> == Critiques ==<br /> * Thorough experimentation and comparison of results to state-of-the-art provided a convincing argument​.<br /> * Datasets used did require some preprocessing, which may have improved the results beyond what the method otherwise would​.<br /> * AM-LFS was created by the authors for experimentation (the code was not made public) so the comparison may not be accurate​.<br /> * The test data set they used to test Search-Softmax and Random-Softmax are simple and they saturate in other methods. So the results of their methods didn’t show many advantages since they produce very similar results. A more complicated data set needs to be tested to prove the method's reliability.<br /> * There is another paper Large-Margin Softmax Loss for Convolutional Neural Networks[https://arxiv.org/pdf/1612.02295.pdf] that provides a more detailed explanation about how to reduce margin-based softmax loss.<br /> * It is questionable when it comes to the accuracy of testing sets, as they only used the clean version of CASIA-WebFace and MS-Celeb-1M-vlc for training instead of these two training sets with noisy labels.<br /> * In a similar [https://arxiv.org/pdf/1905.09773.pdf?utm_source=thenewstack&amp;utm_medium=website&amp;utm_campaign=platform paper], written by Tae-Hyun Oh et al., they also discuss an optimal loss function for face recognition. However, since in the other paper, they were doing face recognition from voice audio, the loss function used was slightly different than the ones discussed in this paper.<br /> * This model has many applications such as identifying disguised prisoners for police. But we need to do a good data preprocessing otherwise we might not get a good predicted result. But authors did not mention about the data preprocessing which is a key part of this model.<br /> * It will be better if we can know what kind of noises was removed in the clean version. Also, simply removing the overlapping data is wasteful. It would be better to just put them into one of the train and test samples.<br /> * This paper indicate that the new searching method and loss function have induced more effective face recognition result than other six methods. But there is no mention of the increase or decrease in computational efficiency since only very little difference exist between those methods and the real time evaluation is often required at the face recognition application level.<br /> * There are some loss functions that receives more than 2 inputs. For example, the ''triplet loss'' function, developed by Google, takes 3 inputs: positive input, negative input and anchor input. This makes sense because for face recognition, we want to model to learn not only what it is supposed to predict but also what it is not supposed to predict. Typically, triplet loss handles false positives much better. This paper can extend its scope to such loss function that takes more than 2 inputs.<br /> * It would be good to also know what the training time is like for the method, specifically the &quot;Reward-Guided Search&quot; which uses RL. Also the authors mention some data preprocessing that was performed, was this same preprocessing also performed for the methods they compared against?<br /> * Sections on Data Processing and Results can be improved. About the datasets, I have some questions about why they are divided in the current fashion. It is mentioned that &quot;CASIA-WebFace and MS-Celeb-1M-v1c&quot; are used as training datasets. But the comparison of algorithms are divided into three groups: Megaface and TrillionPairs, RFW, and a group of other datasets. In general, when we are comparing algorithms, we want to have a holistic view of how each algorithm compare. So I have some concerns about dividing the results into three section. More explanation can be provided. It also seems like Random-Softmax and Search Softmax outperform all other algorithms across all datasets. So it would make even more sense to have a big table including all the results. About data preprocessing, I believe that giving more information about which noisy data are removed would be nice.<br /> * Despite thorough comparison between each method against the proposed method, it does not give a reason to why it was the case that it was either better or worse, and it does not necessarily need to be a mathematical explanation but an intuitive one to demonstrate how it can be replicated and whether the results require a certain condition to achieve. <br /> * Though we have a graph demonstrating the training loss with Random-Softmax and Search-Softmax with regards to the number of Epochs as an independent variable which we may deduce the number of epochs used in later graphs but since one of the main features is that &quot;Meanwhile, our optimization strategy enables that the dynamic loss can guide<br /> * Did the paper address why the average model performs worse on African faces, would it be a lack of data points?<br /> the model training of different epochs, which helps further boost the discrimination power.&quot; it is imperative that the results are comparable along the same scale (for example, for 20 epochs, then take the average of the losses).<br /> <br /> == References ==<br />  X. Wang, S. Wang, C. Chi, S. Zhang and T. Mei, &quot;Loss Function Search for Face Recognition&quot;, in International Conference on Machine Learning, 2020, pp. 1-10.<br /> <br />  Li, C., Yuan, X., Lin, C., Guo, M., Wu, W., Yan, J., and Ouyang, W. Am-lfs: Automl for loss function search. In Proceedings of the IEEE International Conference on Computer Vision, pp. 8410–8419, 2019.<br /> 2020].<br /> <br />  S. L. AI, “Reinforcement Learning algorithms - an intuitive overview,” Medium, 18-Feb-2019. [Online]. Available: https://medium.com/@SmartLabAI/reinforcement-learning-algorithms-an-intuitive-overview-904e2dff5bbc. [Accessed: 25-Nov-2020]. <br /> <br />  “Reinforcement learning,” Wikipedia, 17-Nov-2020. [Online]. Available: https://en.wikipedia.org/wiki/Reinforcement_learning. [Accessed: 24-Nov-2020].<br /> <br />  B. Osiński, “What is reinforcement learning? The complete guide,” deepsense.ai, 23-Jul-2020. [Online]. Available: https://deepsense.ai/what-is-reinforcement-learning-the-complete-guide/. [Accessed: 25-Nov-2020].</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Being_Bayesian_about_Categorical_Probability&diff=49238 Being Bayesian about Categorical Probability 2020-12-05T19:02:33Z <p>Sh68lee: /* Conclusion and Critiques */</p> <hr /> <div>== Presented By ==<br /> Evan Li, Jason Pu, Karam Abuaisha, Nicholas Vadivelu<br /> <br /> == Introduction ==<br /> <br /> Since the outputs of neural networks are not probabilities, Softmax (Bridle, 1990) is a staple for neural network’s performing classification--it exponentiates each logit then normalizes by the sum, giving a distribution over the target classes. Logit is a raw output/prediction of the model which is hard for humans to interpret, thus we transform/normalize these raw values into categories or meaningful numbers for interpretability. However, networks with softmax outputs give no information about uncertainty (Blundell et al., 2015; Gal &amp; Ghahramani, 2016), and the resulting distribution over classes is poorly calibrated (Guo et al., 2017), often giving overconfident predictions even when the classification is wrong. In addition, softmax also raises concerns about overfitting NNs due to its confident predictive behaviors(Xie et al., 2016; Pereyra et al., 2017). To achieve better generalization performance, this may require some effective regularization techniques. <br /> <br /> Bayesian Neural Networks (BNNs; MacKay, 1992) can alleviate these issues, but the resulting posteriors over the parameters are often intractable. Approximations such as variational inference (Graves, 2011; Blundell et al., 2015) and Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) can still be expensive or give poor estimates for the posteriors. This work proposes a Bayesian treatment of the output logits of the neural network, treating the targets as a categorical random variable instead of a fixed label. This gives a computationally cheap way to get well-calibrated uncertainty estimates on neural network classifications.<br /> <br /> == Related Work ==<br /> <br /> Using Bayesian Neural Networks is the dominant way of applying Bayesian techniques to neural networks. Many techniques have been developed to make posterior approximation more accurate and scalable, despite these, BNNs do not scale to the state of the art techniques or large data sets. There are techniques to explicitly avoid modeling the full weight posterior that are more scalable, such as with Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) or tracking mean/covariance of the posterior during training (Mandt et al., 2017; Zhang et al., 2018; Maddox et al., 2019; Osawa et al., 2019). Non-Bayesian uncertainty estimation techniques such as deep ensembles (Lakshminarayanan et al., 2017) and temperature scaling (Guo et al., 2017; Neumann et al., 2018).<br /> <br /> == Preliminaries ==<br /> === Definitions ===<br /> Let's formalize our classification problem and define some notations for the rest of this summary:<br /> <br /> ::Dataset:<br /> $$\mathcal D = \{(x_i,y_i)\} \in (\mathcal X \times \mathcal Y)^N$$<br /> ::General classification model<br /> $$f^W: \mathcal X \to \mathbb R^K$$<br /> ::Softmax function: <br /> $$\phi(x): \mathbb R^K \to [0,1]^K \;\;|\;\; \phi_k(X) = \frac{\exp(f_k^W(x))}{\sum_{k \in K} \exp(f_k^W(x))}$$<br /> ::Softmax activated NN:<br /> $$\phi \;\circ\; f^W: \chi \to \Delta^{K-1}$$<br /> ::NN as a true classifier:<br /> $$arg\max_i \;\circ\; \phi_i \;\circ\; f^W \;:\; \mathcal X \to \mathcal Y$$<br /> <br /> We'll also define the '''count function''' - a &lt;math&gt;K&lt;/math&gt;-vector valued function that outputs the occurences of each class coincident with &lt;math&gt;x&lt;/math&gt;:<br /> $$c^{\mathcal D}(x) = \sum_{(x',y') \in \mathcal D} \mathbb y' I(x' = x)$$<br /> <br /> === Classification With a Neural Network ===<br /> A typical loss function used in classification is cross-entropy. It's well known that optimizing &lt;math&gt;f^W&lt;/math&gt; for &lt;math&gt;l_{CE}&lt;/math&gt; is equivalent to optimizing for &lt;math&gt;l_{KL}&lt;/math&gt;, the &lt;math&gt;KL&lt;/math&gt; divergence between the true distribution and the distribution modeled by NN, that is:<br /> $$l_{KL}(W) = KL(\text{true distribution} \;|\; \text{distribution encoded by }NN(W))$$<br /> Let's introduce notations for the underlying (true) distributions of our problem. Let &lt;math&gt;(x_0,y_0) \sim (\mathcal X \times \mathcal Y)&lt;/math&gt;:<br /> $$\text{Full Distribution} = F(x,y) = P(x_0 = x,y_0 = y)$$<br /> $$\text{Marginal Distribution} = P(x) = F(x_0 = x)$$<br /> $$\text{Point Class Distribution} = P(y_0 = y \;|\; x_0 = x) = F_x(y)$$<br /> Then we have the following factorization:<br /> $$F(x,y) = P(x,y) = P(y|x)P(x) = F_x(y)F(x)$$<br /> Substitute this into the definition of KL divergence:<br /> $$= \sum_{(x,y) \in \mathcal X \times \mathcal Y} F(x,y) \log\left(\frac{F(x,y)}{\phi_y(f^W(x))}\right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F(y|x) \log\left( \frac{F(y|x)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F_x(y) \log\left( \frac{F_x(y)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) KL(F_x \;||\; \phi\left( f^W(x) \right))$$<br /> As usual, we don't have an analytic form for &lt;math&gt;l&lt;/math&gt; (if we did, this would imply we know &lt;math&gt;F_X&lt;/math&gt; meaning we knew the distribution in the first place). Instead, estimate from &lt;math&gt;\mathcal D&lt;/math&gt;:<br /> $$F(x) \approx \hat F(x) = \frac{||c^{\mathcal D}(x)||_1}{N}$$<br /> $$F_x(y) \approx \hat F_x(y) = \frac{c^{\mathcal D}(x)}{|| c^{\mathcal D}(x) ||_1}$$<br /> $$\to l_{KL}(W) = \sum_{x \in \mathcal D} \frac{||c^{\mathcal D}(x)||_1}{N} KL \left( \frac{c^{\mathcal D}(x)}{||c^{\mathcal D}(x)||_1} \;||\; \phi(f^W(x)) \right)$$<br /> The approximations &lt;math&gt;\hat F, \hat F_X&lt;/math&gt; are often not very good though: consider a typical classification such as MNIST, we would never expect two handwritten digits to produce the exact same image. Hence &lt;math&gt;c^{\mathcal D}(x)&lt;/math&gt; is (almost) always going to have a single index 1 and the rest 0. This has implications for our approximations:<br /> $$\hat F(x) \text{ is uniform for all } x \in \mathcal D$$<br /> $$\hat F_x(y) \text{ is degenerate for all } x \in \mathcal D$$<br /> This clearly has implications for overfitting: to minimize the KL term in &lt;math&gt;l_{KL}(W)&lt;/math&gt; we want &lt;math&gt;\phi(f^W(x))&lt;/math&gt; to be very close to &lt;math&gt;\hat F_x(y)&lt;/math&gt; at each point - this means that the loss function is in fact encouraging the neural network to output near degenerate distributions! <br /> <br /> '''Labal Smoothing'''<br /> One form of regularization to help this problem is called label smoothing. Instead of using the degenerate $$F_x(y)$$ as a target function, let's &quot;smooth&quot; it (by adding a scaled uniform distribution to it) so it's no longer degenerate:<br /> $$F'_x(y) = (1-\lambda)\hat F_x(y) + \frac \lambda K \vec 1$$<br /> <br /> '''BNNs'''<br /> BBNs balances the complexity of the model and the distance to target distribution without choosing a single beset configuration (one-hot encoding). Specifically, BNNs with the Gaussian Weight prior $$F_x(y) = N (0,T^{-1} I)$$ has score of configuration &lt;math&gt;W&lt;/math&gt; measured by the posterior density $$p_W(W|D) = p(D|W)p_W(W), \log(p_W(W)) = T||W||^2_2$$<br /> Here &lt;math&gt;||W||^2_2&lt;/math&gt; could be a poor proxy to penalized for the model complexity due to its linear nature.<br /> <br /> == Method ==<br /> The main technical proposal of the paper is a Bayesian framework to estimate the (former) target distribution &lt;math&gt;F_x(y)&lt;/math&gt;. That is, we construct a posterior distribution of &lt;math&gt; F_x(y) &lt;/math&gt; and use that as our new target distribution. We call it the ''belief matching'' (BM) framework.<br /> <br /> === Constructing Target Distribution ===<br /> Recall that &lt;math&gt;F_x(y)&lt;/math&gt; is a k-categorical probability distribution - it's PMF can be fully characterized by k numbers that sum to 1. Hence we can encode any such &lt;math&gt;F_x&lt;/math&gt; as a point in &lt;math&gt;\Delta^{k-1}&lt;/math&gt;. We'll do exactly that - let's call this vecor &lt;math&gt;z&lt;/math&gt;:<br /> $$z \in \Delta^{k-1}$$<br /> $$\text{prior} = p_{z|x}(z)$$<br /> $$\text{conditional} = p_{y|z,x}(y)$$<br /> $$\text{posterior} = p_{z|x,y}(z)$$<br /> Then if we perform inference:<br /> $$p_{z|x,y}(z) \propto p_{z|x}(z)p_{y|z,x}(y)$$<br /> The distribution chosen to model prior was &lt;math&gt;dir_K(\beta)&lt;/math&gt;:<br /> $$p_{z|x}(z) = \frac{\Gamma(||\beta||_1)}{\prod_{k=1}^K \Gamma(\beta_k)} \prod_{k=1}^K z_k^{\beta_k - 1}$$<br /> Note that by definition of &lt;math&gt;z&lt;/math&gt;: &lt;math&gt; p_{y|x,z} = z_y &lt;/math&gt;. Since the Dirichlet is a conjugate prior to categorical distributions we have a convenient form for the mean of the posterior:<br /> $$\bar{p_{z|x,y}}(z) = \frac{\beta + c^{\mathcal D}(x)}{||\beta + c^{\mathcal D}(x)||_1} \propto \beta + c^{\mathcal D}(x)$$<br /> This is in fact a generalization of (uniform) label smoothing (label smoothing is a special case where &lt;math&gt;\beta = \frac 1 K \vec{1} &lt;/math&gt;).<br /> <br /> === Representing Approximate Distribution ===<br /> Our new target distribution is &lt;math&gt;p_{z|x,y}(z)&lt;/math&gt; (as opposed to &lt;math&gt;F_x(y)&lt;/math&gt;). That is, we want to construct an interpretation of our neural network weights to construct a distribution with support in &lt;math&gt; \Delta^{K-1} &lt;/math&gt; - the NN can then be trained so this encoded distribution closely approximates &lt;math&gt;p_{z|x,y}&lt;/math&gt;. Let's denote the PMF of this encoded distribution &lt;math&gt;q_{z|x}^W&lt;/math&gt;. This is how the BM framework defines it:<br /> $$\alpha^W(x) := \exp(f^W(x))$$<br /> $$q_{z|x}^W(z) = \frac{\Gamma(||\alpha^W(x)||_1)}{\sum_{k=1}^K \Gamma(\alpha_k^W(x))} \prod_{k=1}^K z_{k}^{\alpha_k^W(x) - 1}$$<br /> $$\to Z^W_x \sim dir(\alpha^W(x))$$<br /> Apply &lt;math&gt;\log&lt;/math&gt; then &lt;math&gt;\exp&lt;/math&gt; to &lt;math&gt;q_{z|x}^W&lt;/math&gt;:<br /> $$q^W_{z|x}(z) \propto \exp \left( \sum_k (\alpha_k^W(x) \log(z_k)) - \sum_k \log(z_k) \right)$$<br /> $$\propto -l_{CE}(\phi(f^W(x)),z) + \frac{K}{||\alpha^W(x)||}KL(\mathcal U_k \;||\; z)$$<br /> It can actually be shown that the mean of &lt;math&gt;Z_x^W&lt;/math&gt; is identical to &lt;math&gt;\phi(f^W(x))&lt;/math&gt; - in other words, if we output the mean of the encoded distribution of our neural network under the BM framework, it is theoretically identical to a traditional neural network.<br /> <br /> === Distribution Matching ===<br /> <br /> We now need a way to fit our approximate distribution from our neural network &lt;math&gt;q_{\mathbf{z | x}}^{\mathbf{W}}&lt;/math&gt; to our target distribution &lt;math&gt;p_{\mathbf{z|x},y}&lt;/math&gt;. The authors achieve this by maximizing the evidence lower bound (ELBO):<br /> <br /> $$l_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}})$$<br /> <br /> Each term can be computed analytically:<br /> <br /> $$\mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf W }} \left[\log z_y \right] = \psi(\alpha_y^{\mathbf W} ( \mathbf x )) - \psi(\alpha_0^{\mathbf W} ( \mathbf x ))$$<br /> <br /> Where &lt;math&gt;\psi(\cdot)&lt;/math&gt; represents the digamma function (logarithmic derivative of gamma function). Intuitively, we maximize the probability of the correct label. For the KL term:<br /> <br /> $$KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}}) = \log \frac{\Gamma(a_0^{\mathbf W}(\mathbf x)) \prod_k \Gamma(\beta_k)}{\prod_k \Gamma(\alpha_k^{\mathbf W}(x)) \Gamma (\beta_0)} + \sum_k (\alpha_k^{\mathbf W}(x)-\beta_k)(\psi(\alpha_k^{\mathbf W}(\mathbf x)) - \psi(\alpha_0^{\mathbf W}(\mathbf x))$$<br /> <br /> In the first term, for intuition, we can ignore &lt;math&gt;\alpha_0&lt;/math&gt; and &lt;math&gt;\beta_0&lt;/math&gt; since those just calibrate the distributions. Otherwise, we want the ratio of the products to be as close to 1 as possible to minimize the KL. In the second term, we want to minimize the difference between each individual &lt;math&gt;\alpha_k&lt;/math&gt; and &lt;math&gt;\beta_k&lt;/math&gt;, scaled by the normalized output of the neural network. <br /> <br /> This loss function can be used as a drop-in replacement for the standard softmax cross-entropy, as it has an analytic form and the same time complexity as typical softmax-cross entropy with respect to the number of classes (&lt;math&gt;O(K)&lt;/math&gt;).<br /> <br /> === On Prior Distributions ===<br /> <br /> We must choose our concentration parameter, &lt;math&gt;\beta&lt;/math&gt;, for our dirichlet prior. We see our prior essentially disappears as &lt;math&gt;\beta_0 \to 0&lt;/math&gt; and becomes stronger as &lt;math&gt;\beta_0 \to \infty&lt;/math&gt;. Thus, we want a small &lt;math&gt;\beta_0&lt;/math&gt; so the posterior isn't dominated by the prior. But, the authors claim that a small &lt;math&gt;\beta_0&lt;/math&gt; makes &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small, which causes &lt;math&gt;\psi (\alpha_0^{\mathbf W}(\mathbf x))&lt;/math&gt; to be large, which is problematic for gradient based optimization. In practice, many neural network techniques aim to make &lt;math&gt;\mathbb E [f^{\mathbf W} (\mathbf x)] \approx \mathbf 0&lt;/math&gt; and thus &lt;math&gt;\mathbb E [\alpha^{\mathbf W} (\mathbf x)] \approx \mathbf 1&lt;/math&gt;, which means making &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small can be counterproductive.<br /> <br /> So, the authors set &lt;math&gt;\beta = \mathbf 1&lt;/math&gt; and introduce a new hyperparameter &lt;math&gt;\lambda&lt;/math&gt; which is multiplied with the KL term in the ELBO:<br /> <br /> $$l^\lambda_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - \lambda KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; \mathcal P^D (\mathbf 1))$$<br /> <br /> This stabilizes the optimization, as we can tell from the gradients:<br /> <br /> $$\frac{\partial l_{E B}\left(\mathbf{y}, \alpha^{\mathbf W}(\mathbf{x})\right)}{\partial \alpha_{k}^{\mathbf W}(\mathbf {x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\alpha_{k}^{\mathbf W}(\mathbf{x})-\beta_{k}\right)\right) \psi^{\prime}\left(\alpha_{k}^{\mathbf{W}}(\boldsymbol{x})\right)<br /> -\left(1-\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})-\beta_{0}\right)\right) \psi^{\prime}\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})\right)$$<br /> <br /> $$\frac{\partial l_{E B}^{\lambda}\left(\mathbf{y}, \alpha^{\mathbf{W}}(\mathbf{x})\right)}{\partial \alpha_{k}^{W}(\mathbf{x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})-\lambda\right)\right) \frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}<br /> -\left(1-\left(\tilde{\alpha}_{0}^{W}(\mathbf{x})-\lambda K\right)\right)$$<br /> <br /> As we can see, the first expression is affected by the magnitude of &lt;math&gt;\alpha^{\boldsymbol{W}}(\boldsymbol{x})&lt;/math&gt;, whereas the second expression is not due to the &lt;math&gt;\frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}&lt;/math&gt; ratio.<br /> <br /> == Experiments ==<br /> <br /> Throughout the experiments in this paper, the authors employ various models based on residual connections (He et al., 2016 ) which are the models used for benchmarking in practice. We will first demonstrate improvements provided by BM, then we will show versatility in other applications. For fairness of comparisons, all configurations in the reference implementation will be fixed. The only additions in the experiments are initial learning rate warm-up and gradient clipping which are extremely helpful for stable training of BM. <br /> <br /> === Generalization performance === <br /> The paper compares the generalization performance of BM with softmax and MC dropout on CIFAR-10 and CIFAR-100 benchmarks.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T1.png]]<br /> <br /> The next comparison was performed between BM and softmax on the ImageNet benchmark. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T2.png]]<br /> <br /> For both datasets and In all configurations, BM achieves the best generalization and outperforms softmax and MC dropout.<br /> <br /> ===== Regularization effect of prior =====<br /> <br /> In theory, BM has 2 regularization effects:<br /> The prior distribution, which smooths the target posterior<br /> Averaging all of the possible categorical probabilities to compute the distribution matching loss<br /> The authors perform an ablation study to examine the 2 effects separately - removing the KL term in the ELBO removes the effect of the prior distribution.<br /> For ResNet-50 on CIFAR-100 and CIFAR-10 the resulting test error rates were 24.69% and 5.68% respectively. <br /> <br /> This demonstrates that both regularization effects are significant since just having one of them improves the generalization performance compared to the softmax baseline, and having both improves the performance even more.<br /> <br /> ===== Impact of &lt;math&gt;\beta&lt;/math&gt; =====<br /> <br /> The effect of β on generalization performance is studied by training ResNet-18 on CIFAR-10 by tuning the value of β on its own, as well as jointly with λ. It was found that robust generalization performance is obtained for β ∈ [&lt;math&gt;e^{−1}, e^4&lt;/math&gt;] when tuning β on its own; and β ∈ [&lt;math&gt;e^{−4}, e^{8}&lt;/math&gt;] when tuning β jointly with λ. The figure below shows a plot of the error rate with varying β.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F3.png]]<br /> <br /> === Uncertainty Representation ===<br /> <br /> One of the big advantages of BM is the ability to represent uncertainty about the prediction. The authors evaluate the uncertainty representation on in-distribution (ID) and out-of-distribution (OOD) samples. <br /> <br /> ===== ID uncertainty =====<br /> <br /> For ID (in-distribution) samples, calibration performance is measured, which is a measure of how well the model’s confidence matches its actual accuracy. This measure can be visualized using reliability plots and quantified using a metric called expected calibration error (ECE). ECE is calculated by grouping predictions into M groups based on their confidence score and then finding the absolute difference between the average accuracy and average confidence for each group. We can define the ECE of &lt;math&gt;f^W &lt;/math&gt; on &lt;math&gt;D &lt;/math&gt; with &lt;math&gt;M&lt;/math&gt; groups as <br /> <br /> &lt;center&gt;<br /> &lt;math&gt;ECE_M(f^W, D) = \sum^M_{i=1} \frac{|G_i|}{|D|}|acc(G_i) - conf(G_i)|&lt;/math&gt;<br /> &lt;/center&gt;<br /> Where &lt;math&gt;G_i&lt;/math&gt; is a set of samples int the i-th group defined as &lt;math&gt;G_i = \{j:i/M &lt; max_k\phi_k(f^Wx^{(j)}) \leq (1+i)/M\}&lt;/math&gt;, &lt;math&gt;acc(G_i)&lt;/math&gt; is an average accuracy in the i-th group and &lt;math&gt;conf(G_i)&lt;/math&gt; is an average confidence in the i-th group.<br /> <br /> The figure below is a reliability plot of ResNet-50 on CIFAR-10 and CIFAR-100 with 15 groups. It shows that BM has a significantly better calibration performance than softmax since the confidence matches the accuracy more closely (this is also reflected in the lower ECE).<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F4.png]]<br /> <br /> ===== OOD uncertainty =====<br /> <br /> Here, the authors quantify uncertainty using predictive entropy - the larger the predictive entropy, the larger the uncertainty about a prediction. <br /> <br /> The figure below is a density plot of the predictive entropy of ResNet-50 on CIFAR-10. It shows that BM provides significantly better uncertainty estimation compared to other methods since BM is the only method that has a clear peak of high predictive entropy for OOD samples which should have high uncertainty. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F5.png]]<br /> <br /> === Transfer learning ===<br /> <br /> Belief matching applies the Bayesian principle outside the neural network, which means it can easily be applied to already trained models. Thus, belief matching can be employed in transfer learning scenarios. The authors downloaded the ImageNet pre-trained ResNet-50 weights and fine-tuned the weights of the last linear layer for 100 epochs using an Adam optimizer.<br /> <br /> This table shows the test error rates from transfer learning on CIFAR-10, Food-101, and Cars datasets. Belief matching consistently performs better than softmax. <br /> <br /> [[File:being_bayesian_about_categorical_probability_transfer_learning.png]]<br /> <br /> Belief matching was also tested for the predictive uncertainty for out of dataset samples based on CIFAR-10 as the in distribution sample. Looking at the figure below, it is observed that belief matching significantly improves the uncertainty representation of pre-trained models by only fine-tuning the last layer’s weights. Note that belief matching confidently predicts examples in Cars since CIFAR-10 contains the object category automobiles. In comparison, softmax produces confident predictions on all datasets. Thus, belief matching could also be used to enhance the uncertainty representation ability of pre-trained models without sacrificing their generalization performance.<br /> <br /> [[File: being_bayesian_about_categorical_probability_transfer_learning_uncertainty.png]]<br /> <br /> === Semi-Supervised Learning ===<br /> <br /> Belief matching’s ability to allow neural networks to represent rich information in their predictions can be exploited to aid consistency based loss function for semi-supervised learning. Consistency-based loss functions use unlabelled samples to determine where to promote the robustness of predictions based on stochastic perturbations. This can be done by perturbing the inputs (which is the VAT model) or the networks (which is the pi-model). Both methods minimize the divergence between two categorical probabilities under some perturbations, thus belief matching can be used by the following replacements in the loss functions. The hope is that belief matching can provide better prediction consistencies using its Dirichlet distributions.<br /> <br /> [[File: being_bayesian_about_categorical_probability_semi_supervised_equation.png]]<br /> <br /> The results of training on ResNet28-2 with consistency based loss functions on CIFAR-10 are shown in this table. Belief matching does have lower classification error rates compared to using a softmax.<br /> <br /> [[File:being_bayesian_about_categorical_probability_semi_supervised_table.png]]<br /> <br /> == Conclusion and Critiques ==<br /> <br /> Bayesian principles can be used to construct the target distribution by using the categorical probability as a random variable rather than a training label. This can be applied to neural network models by replacing only the softmax and cross-entropy loss, while improving the generalization performance and uncertainty estimation. <br /> <br /> In the future, the authors would like to allow for more expressive distributions in the belief matching framework, such as logistic normal distributions to capture strong semantic similarities among class labels. Furthermore, using input dependent priors would allow for interesting properties that would aid imbalanced datasets and multi-domain learning.<br /> <br /> * Overall I think this summary is very good. The Method(Algorithm) section is described clearly, and the Results section is detailed, with many diagrams illustrating the main points. I just have one technical suggestion: the difference in performance for SOFTMAX and BM differs by model. For example, for RESNEXT-50 model, the difference in top1 is 0.2, whereas for the RESNEXT-100 model, the difference in top one is 0.5, which is significantly higher. It's true that BM method generally outperforms SOFTMAX. But seeing the relation between the choice of model and the magnitude of performance increase could definitely strengthen the paper even further.<br /> <br /> The summary is good and topic is interesting. Bayesian is a well know probabilistic model but did not know that it can be used as a neural network. Comparison between softmax and bayesian was interesting and more details would be great.<br /> <br /> == Citations ==<br /> <br />  Bridle, J. S. Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neurocomputing, pp. 227–236. Springer, 1990.<br /> <br />  Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. Weight uncertainty in neural networks. In International Conference on Machine Learning, 2015.<br /> <br />  Gal, Y. and Ghahramani, Z. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In International Conference on Machine Learning, 2016.<br /> <br />  Guo, C., Pleiss, G., Sun, Y., and Weinberger, K. Q. On calibration of modern neural networks. In International Conference on Machine Learning, 2017. <br /> <br />  MacKay, D. J. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448– 472, 1992.<br /> <br />  Graves, A. Practical variational inference for neural networks. In Advances in Neural Information Processing Systems, 2011. <br /> <br />  Mandt, S., Hoffman, M. D., and Blei, D. M. Stochastic gradient descent as approximate Bayesian inference. Journal of Machine Learning Research, 18(1):4873–4907, 2017.<br /> <br />  Zhang, G., Sun, S., Duvenaud, D., and Grosse, R. Noisy natural gradient as variational inference. In International Conference of Machine Learning, 2018.<br /> <br />  Maddox, W. J., Izmailov, P., Garipov, T., Vetrov, D. P., and Wilson, A. G. A simple baseline for Bayesian uncertainty in deep learning. In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Osawa, K., Swaroop, S., Jain, A., Eschenhagen, R., Turner, R. E., Yokota, R., and Khan, M. E. Practical deep learning with Bayesian principles. In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Lakshminarayanan, B., Pritzel, A., and Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in Neural Information Processing Systems, 2017.<br /> <br />  Neumann, L., Zisserman, A., and Vedaldi, A. Relaxed softmax: Efficient confidence auto-calibration for safe pedestrian detection. In NIPS Workshop on Machine Learning for Intelligent Transportation Systems, 2018.<br /> <br />  Xie, L., Wang, J., Wei, Z., Wang, M., and Tian, Q. Disturblabel: Regularizing cnn on the loss layer. In IEEE Conference on Computer Vision and Pattern Recognition, 2016.<br /> <br />  Pereyra, G., Tucker, G., Chorowski, J., Kaiser, Ł., and Hinton, G. Regularizing neural networks by penalizing confident output distributions. arXiv preprint arXiv:1701.06548, 2017.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Being_Bayesian_about_Categorical_Probability&diff=49234 Being Bayesian about Categorical Probability 2020-12-05T18:53:05Z <p>Sh68lee: /* Classification With a Neural Network */</p> <hr /> <div>== Presented By ==<br /> Evan Li, Jason Pu, Karam Abuaisha, Nicholas Vadivelu<br /> <br /> == Introduction ==<br /> <br /> Since the outputs of neural networks are not probabilities, Softmax (Bridle, 1990) is a staple for neural network’s performing classification--it exponentiates each logit then normalizes by the sum, giving a distribution over the target classes. Logit is a raw output/prediction of the model which is hard for humans to interpret, thus we transform/normalize these raw values into categories or meaningful numbers for interpretability. However, networks with softmax outputs give no information about uncertainty (Blundell et al., 2015; Gal &amp; Ghahramani, 2016), and the resulting distribution over classes is poorly calibrated (Guo et al., 2017), often giving overconfident predictions even when the classification is wrong. In addition, softmax also raises concerns about overfitting NNs due to its confident predictive behaviors(Xie et al., 2016; Pereyra et al., 2017). To achieve better generalization performance, this may require some effective regularization techniques. <br /> <br /> Bayesian Neural Networks (BNNs; MacKay, 1992) can alleviate these issues, but the resulting posteriors over the parameters are often intractable. Approximations such as variational inference (Graves, 2011; Blundell et al., 2015) and Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) can still be expensive or give poor estimates for the posteriors. This work proposes a Bayesian treatment of the output logits of the neural network, treating the targets as a categorical random variable instead of a fixed label. This gives a computationally cheap way to get well-calibrated uncertainty estimates on neural network classifications.<br /> <br /> == Related Work ==<br /> <br /> Using Bayesian Neural Networks is the dominant way of applying Bayesian techniques to neural networks. Many techniques have been developed to make posterior approximation more accurate and scalable, despite these, BNNs do not scale to the state of the art techniques or large data sets. There are techniques to explicitly avoid modeling the full weight posterior that are more scalable, such as with Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) or tracking mean/covariance of the posterior during training (Mandt et al., 2017; Zhang et al., 2018; Maddox et al., 2019; Osawa et al., 2019). Non-Bayesian uncertainty estimation techniques such as deep ensembles (Lakshminarayanan et al., 2017) and temperature scaling (Guo et al., 2017; Neumann et al., 2018).<br /> <br /> == Preliminaries ==<br /> === Definitions ===<br /> Let's formalize our classification problem and define some notations for the rest of this summary:<br /> <br /> ::Dataset:<br /> $$\mathcal D = \{(x_i,y_i)\} \in (\mathcal X \times \mathcal Y)^N$$<br /> ::General classification model<br /> $$f^W: \mathcal X \to \mathbb R^K$$<br /> ::Softmax function: <br /> $$\phi(x): \mathbb R^K \to [0,1]^K \;\;|\;\; \phi_k(X) = \frac{\exp(f_k^W(x))}{\sum_{k \in K} \exp(f_k^W(x))}$$<br /> ::Softmax activated NN:<br /> $$\phi \;\circ\; f^W: \chi \to \Delta^{K-1}$$<br /> ::NN as a true classifier:<br /> $$arg\max_i \;\circ\; \phi_i \;\circ\; f^W \;:\; \mathcal X \to \mathcal Y$$<br /> <br /> We'll also define the '''count function''' - a &lt;math&gt;K&lt;/math&gt;-vector valued function that outputs the occurences of each class coincident with &lt;math&gt;x&lt;/math&gt;:<br /> $$c^{\mathcal D}(x) = \sum_{(x',y') \in \mathcal D} \mathbb y' I(x' = x)$$<br /> <br /> === Classification With a Neural Network ===<br /> A typical loss function used in classification is cross-entropy. It's well known that optimizing &lt;math&gt;f^W&lt;/math&gt; for &lt;math&gt;l_{CE}&lt;/math&gt; is equivalent to optimizing for &lt;math&gt;l_{KL}&lt;/math&gt;, the &lt;math&gt;KL&lt;/math&gt; divergence between the true distribution and the distribution modeled by NN, that is:<br /> $$l_{KL}(W) = KL(\text{true distribution} \;|\; \text{distribution encoded by }NN(W))$$<br /> Let's introduce notations for the underlying (true) distributions of our problem. Let &lt;math&gt;(x_0,y_0) \sim (\mathcal X \times \mathcal Y)&lt;/math&gt;:<br /> $$\text{Full Distribution} = F(x,y) = P(x_0 = x,y_0 = y)$$<br /> $$\text{Marginal Distribution} = P(x) = F(x_0 = x)$$<br /> $$\text{Point Class Distribution} = P(y_0 = y \;|\; x_0 = x) = F_x(y)$$<br /> Then we have the following factorization:<br /> $$F(x,y) = P(x,y) = P(y|x)P(x) = F_x(y)F(x)$$<br /> Substitute this into the definition of KL divergence:<br /> $$= \sum_{(x,y) \in \mathcal X \times \mathcal Y} F(x,y) \log\left(\frac{F(x,y)}{\phi_y(f^W(x))}\right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F(y|x) \log\left( \frac{F(y|x)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F_x(y) \log\left( \frac{F_x(y)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) KL(F_x \;||\; \phi\left( f^W(x) \right))$$<br /> As usual, we don't have an analytic form for &lt;math&gt;l&lt;/math&gt; (if we did, this would imply we know &lt;math&gt;F_X&lt;/math&gt; meaning we knew the distribution in the first place). Instead, estimate from &lt;math&gt;\mathcal D&lt;/math&gt;:<br /> $$F(x) \approx \hat F(x) = \frac{||c^{\mathcal D}(x)||_1}{N}$$<br /> $$F_x(y) \approx \hat F_x(y) = \frac{c^{\mathcal D}(x)}{|| c^{\mathcal D}(x) ||_1}$$<br /> $$\to l_{KL}(W) = \sum_{x \in \mathcal D} \frac{||c^{\mathcal D}(x)||_1}{N} KL \left( \frac{c^{\mathcal D}(x)}{||c^{\mathcal D}(x)||_1} \;||\; \phi(f^W(x)) \right)$$<br /> The approximations &lt;math&gt;\hat F, \hat F_X&lt;/math&gt; are often not very good though: consider a typical classification such as MNIST, we would never expect two handwritten digits to produce the exact same image. Hence &lt;math&gt;c^{\mathcal D}(x)&lt;/math&gt; is (almost) always going to have a single index 1 and the rest 0. This has implications for our approximations:<br /> $$\hat F(x) \text{ is uniform for all } x \in \mathcal D$$<br /> $$\hat F_x(y) \text{ is degenerate for all } x \in \mathcal D$$<br /> This clearly has implications for overfitting: to minimize the KL term in &lt;math&gt;l_{KL}(W)&lt;/math&gt; we want &lt;math&gt;\phi(f^W(x))&lt;/math&gt; to be very close to &lt;math&gt;\hat F_x(y)&lt;/math&gt; at each point - this means that the loss function is in fact encouraging the neural network to output near degenerate distributions! <br /> <br /> '''Labal Smoothing'''<br /> One form of regularization to help this problem is called label smoothing. Instead of using the degenerate $$F_x(y)$$ as a target function, let's &quot;smooth&quot; it (by adding a scaled uniform distribution to it) so it's no longer degenerate:<br /> $$F'_x(y) = (1-\lambda)\hat F_x(y) + \frac \lambda K \vec 1$$<br /> <br /> '''BNNs'''<br /> BBNs balances the complexity of the model and the distance to target distribution without choosing a single beset configuration (one-hot encoding). Specifically, BNNs with the Gaussian Weight prior $$F_x(y) = N (0,T^{-1} I)$$ has score of configuration &lt;math&gt;W&lt;/math&gt; measured by the posterior density $$p_W(W|D) = p(D|W)p_W(W), \log(p_W(W)) = T||W||^2_2$$<br /> Here &lt;math&gt;||W||^2_2&lt;/math&gt; could be a poor proxy to penalized for the model complexity due to its linear nature.<br /> <br /> == Method ==<br /> The main technical proposal of the paper is a Bayesian framework to estimate the (former) target distribution &lt;math&gt;F_x(y)&lt;/math&gt;. That is, we construct a posterior distribution of &lt;math&gt; F_x(y) &lt;/math&gt; and use that as our new target distribution. We call it the ''belief matching'' (BM) framework.<br /> <br /> === Constructing Target Distribution ===<br /> Recall that &lt;math&gt;F_x(y)&lt;/math&gt; is a k-categorical probability distribution - it's PMF can be fully characterized by k numbers that sum to 1. Hence we can encode any such &lt;math&gt;F_x&lt;/math&gt; as a point in &lt;math&gt;\Delta^{k-1}&lt;/math&gt;. We'll do exactly that - let's call this vecor &lt;math&gt;z&lt;/math&gt;:<br /> $$z \in \Delta^{k-1}$$<br /> $$\text{prior} = p_{z|x}(z)$$<br /> $$\text{conditional} = p_{y|z,x}(y)$$<br /> $$\text{posterior} = p_{z|x,y}(z)$$<br /> Then if we perform inference:<br /> $$p_{z|x,y}(z) \propto p_{z|x}(z)p_{y|z,x}(y)$$<br /> The distribution chosen to model prior was &lt;math&gt;dir_K(\beta)&lt;/math&gt;:<br /> $$p_{z|x}(z) = \frac{\Gamma(||\beta||_1)}{\prod_{k=1}^K \Gamma(\beta_k)} \prod_{k=1}^K z_k^{\beta_k - 1}$$<br /> Note that by definition of &lt;math&gt;z&lt;/math&gt;: &lt;math&gt; p_{y|x,z} = z_y &lt;/math&gt;. Since the Dirichlet is a conjugate prior to categorical distributions we have a convenient form for the mean of the posterior:<br /> $$\bar{p_{z|x,y}}(z) = \frac{\beta + c^{\mathcal D}(x)}{||\beta + c^{\mathcal D}(x)||_1} \propto \beta + c^{\mathcal D}(x)$$<br /> This is in fact a generalization of (uniform) label smoothing (label smoothing is a special case where &lt;math&gt;\beta = \frac 1 K \vec{1} &lt;/math&gt;).<br /> <br /> === Representing Approximate Distribution ===<br /> Our new target distribution is &lt;math&gt;p_{z|x,y}(z)&lt;/math&gt; (as opposed to &lt;math&gt;F_x(y)&lt;/math&gt;). That is, we want to construct an interpretation of our neural network weights to construct a distribution with support in &lt;math&gt; \Delta^{K-1} &lt;/math&gt; - the NN can then be trained so this encoded distribution closely approximates &lt;math&gt;p_{z|x,y}&lt;/math&gt;. Let's denote the PMF of this encoded distribution &lt;math&gt;q_{z|x}^W&lt;/math&gt;. This is how the BM framework defines it:<br /> $$\alpha^W(x) := \exp(f^W(x))$$<br /> $$q_{z|x}^W(z) = \frac{\Gamma(||\alpha^W(x)||_1)}{\sum_{k=1}^K \Gamma(\alpha_k^W(x))} \prod_{k=1}^K z_{k}^{\alpha_k^W(x) - 1}$$<br /> $$\to Z^W_x \sim dir(\alpha^W(x))$$<br /> Apply &lt;math&gt;\log&lt;/math&gt; then &lt;math&gt;\exp&lt;/math&gt; to &lt;math&gt;q_{z|x}^W&lt;/math&gt;:<br /> $$q^W_{z|x}(z) \propto \exp \left( \sum_k (\alpha_k^W(x) \log(z_k)) - \sum_k \log(z_k) \right)$$<br /> $$\propto -l_{CE}(\phi(f^W(x)),z) + \frac{K}{||\alpha^W(x)||}KL(\mathcal U_k \;||\; z)$$<br /> It can actually be shown that the mean of &lt;math&gt;Z_x^W&lt;/math&gt; is identical to &lt;math&gt;\phi(f^W(x))&lt;/math&gt; - in other words, if we output the mean of the encoded distribution of our neural network under the BM framework, it is theoretically identical to a traditional neural network.<br /> <br /> === Distribution Matching ===<br /> <br /> We now need a way to fit our approximate distribution from our neural network &lt;math&gt;q_{\mathbf{z | x}}^{\mathbf{W}}&lt;/math&gt; to our target distribution &lt;math&gt;p_{\mathbf{z|x},y}&lt;/math&gt;. The authors achieve this by maximizing the evidence lower bound (ELBO):<br /> <br /> $$l_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}})$$<br /> <br /> Each term can be computed analytically:<br /> <br /> $$\mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf W }} \left[\log z_y \right] = \psi(\alpha_y^{\mathbf W} ( \mathbf x )) - \psi(\alpha_0^{\mathbf W} ( \mathbf x ))$$<br /> <br /> Where &lt;math&gt;\psi(\cdot)&lt;/math&gt; represents the digamma function (logarithmic derivative of gamma function). Intuitively, we maximize the probability of the correct label. For the KL term:<br /> <br /> $$KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}}) = \log \frac{\Gamma(a_0^{\mathbf W}(\mathbf x)) \prod_k \Gamma(\beta_k)}{\prod_k \Gamma(\alpha_k^{\mathbf W}(x)) \Gamma (\beta_0)} + \sum_k (\alpha_k^{\mathbf W}(x)-\beta_k)(\psi(\alpha_k^{\mathbf W}(\mathbf x)) - \psi(\alpha_0^{\mathbf W}(\mathbf x))$$<br /> <br /> In the first term, for intuition, we can ignore &lt;math&gt;\alpha_0&lt;/math&gt; and &lt;math&gt;\beta_0&lt;/math&gt; since those just calibrate the distributions. Otherwise, we want the ratio of the products to be as close to 1 as possible to minimize the KL. In the second term, we want to minimize the difference between each individual &lt;math&gt;\alpha_k&lt;/math&gt; and &lt;math&gt;\beta_k&lt;/math&gt;, scaled by the normalized output of the neural network. <br /> <br /> This loss function can be used as a drop-in replacement for the standard softmax cross-entropy, as it has an analytic form and the same time complexity as typical softmax-cross entropy with respect to the number of classes (&lt;math&gt;O(K)&lt;/math&gt;).<br /> <br /> === On Prior Distributions ===<br /> <br /> We must choose our concentration parameter, &lt;math&gt;\beta&lt;/math&gt;, for our dirichlet prior. We see our prior essentially disappears as &lt;math&gt;\beta_0 \to 0&lt;/math&gt; and becomes stronger as &lt;math&gt;\beta_0 \to \infty&lt;/math&gt;. Thus, we want a small &lt;math&gt;\beta_0&lt;/math&gt; so the posterior isn't dominated by the prior. But, the authors claim that a small &lt;math&gt;\beta_0&lt;/math&gt; makes &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small, which causes &lt;math&gt;\psi (\alpha_0^{\mathbf W}(\mathbf x))&lt;/math&gt; to be large, which is problematic for gradient based optimization. In practice, many neural network techniques aim to make &lt;math&gt;\mathbb E [f^{\mathbf W} (\mathbf x)] \approx \mathbf 0&lt;/math&gt; and thus &lt;math&gt;\mathbb E [\alpha^{\mathbf W} (\mathbf x)] \approx \mathbf 1&lt;/math&gt;, which means making &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small can be counterproductive.<br /> <br /> So, the authors set &lt;math&gt;\beta = \mathbf 1&lt;/math&gt; and introduce a new hyperparameter &lt;math&gt;\lambda&lt;/math&gt; which is multiplied with the KL term in the ELBO:<br /> <br /> $$l^\lambda_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - \lambda KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; \mathcal P^D (\mathbf 1))$$<br /> <br /> This stabilizes the optimization, as we can tell from the gradients:<br /> <br /> $$\frac{\partial l_{E B}\left(\mathbf{y}, \alpha^{\mathbf W}(\mathbf{x})\right)}{\partial \alpha_{k}^{\mathbf W}(\mathbf {x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\alpha_{k}^{\mathbf W}(\mathbf{x})-\beta_{k}\right)\right) \psi^{\prime}\left(\alpha_{k}^{\mathbf{W}}(\boldsymbol{x})\right)<br /> -\left(1-\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})-\beta_{0}\right)\right) \psi^{\prime}\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})\right)$$<br /> <br /> $$\frac{\partial l_{E B}^{\lambda}\left(\mathbf{y}, \alpha^{\mathbf{W}}(\mathbf{x})\right)}{\partial \alpha_{k}^{W}(\mathbf{x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})-\lambda\right)\right) \frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}<br /> -\left(1-\left(\tilde{\alpha}_{0}^{W}(\mathbf{x})-\lambda K\right)\right)$$<br /> <br /> As we can see, the first expression is affected by the magnitude of &lt;math&gt;\alpha^{\boldsymbol{W}}(\boldsymbol{x})&lt;/math&gt;, whereas the second expression is not due to the &lt;math&gt;\frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}&lt;/math&gt; ratio.<br /> <br /> == Experiments ==<br /> <br /> Throughout the experiments in this paper, the authors employ various models based on residual connections (He et al., 2016 ) which are the models used for benchmarking in practice. We will first demonstrate improvements provided by BM, then we will show versatility in other applications. For fairness of comparisons, all configurations in the reference implementation will be fixed. The only additions in the experiments are initial learning rate warm-up and gradient clipping which are extremely helpful for stable training of BM. <br /> <br /> === Generalization performance === <br /> The paper compares the generalization performance of BM with softmax and MC dropout on CIFAR-10 and CIFAR-100 benchmarks.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T1.png]]<br /> <br /> The next comparison was performed between BM and softmax on the ImageNet benchmark. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T2.png]]<br /> <br /> For both datasets and In all configurations, BM achieves the best generalization and outperforms softmax and MC dropout.<br /> <br /> ===== Regularization effect of prior =====<br /> <br /> In theory, BM has 2 regularization effects:<br /> The prior distribution, which smooths the target posterior<br /> Averaging all of the possible categorical probabilities to compute the distribution matching loss<br /> The authors perform an ablation study to examine the 2 effects separately - removing the KL term in the ELBO removes the effect of the prior distribution.<br /> For ResNet-50 on CIFAR-100 and CIFAR-10 the resulting test error rates were 24.69% and 5.68% respectively. <br /> <br /> This demonstrates that both regularization effects are significant since just having one of them improves the generalization performance compared to the softmax baseline, and having both improves the performance even more.<br /> <br /> ===== Impact of &lt;math&gt;\beta&lt;/math&gt; =====<br /> <br /> The effect of β on generalization performance is studied by training ResNet-18 on CIFAR-10 by tuning the value of β on its own, as well as jointly with λ. It was found that robust generalization performance is obtained for β ∈ [&lt;math&gt;e^{−1}, e^4&lt;/math&gt;] when tuning β on its own; and β ∈ [&lt;math&gt;e^{−4}, e^{8}&lt;/math&gt;] when tuning β jointly with λ. The figure below shows a plot of the error rate with varying β.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F3.png]]<br /> <br /> === Uncertainty Representation ===<br /> <br /> One of the big advantages of BM is the ability to represent uncertainty about the prediction. The authors evaluate the uncertainty representation on in-distribution (ID) and out-of-distribution (OOD) samples. <br /> <br /> ===== ID uncertainty =====<br /> <br /> For ID (in-distribution) samples, calibration performance is measured, which is a measure of how well the model’s confidence matches its actual accuracy. This measure can be visualized using reliability plots and quantified using a metric called expected calibration error (ECE). ECE is calculated by grouping predictions into M groups based on their confidence score and then finding the absolute difference between the average accuracy and average confidence for each group. We can define the ECE of &lt;math&gt;f^W &lt;/math&gt; on &lt;math&gt;D &lt;/math&gt; with &lt;math&gt;M&lt;/math&gt; groups as <br /> <br /> &lt;center&gt;<br /> &lt;math&gt;ECE_M(f^W, D) = \sum^M_{i=1} \frac{|G_i|}{|D|}|acc(G_i) - conf(G_i)|&lt;/math&gt;<br /> &lt;/center&gt;<br /> Where &lt;math&gt;G_i&lt;/math&gt; is a set of samples int the i-th group defined as &lt;math&gt;G_i = \{j:i/M &lt; max_k\phi_k(f^Wx^{(j)}) \leq (1+i)/M\}&lt;/math&gt;, &lt;math&gt;acc(G_i)&lt;/math&gt; is an average accuracy in the i-th group and &lt;math&gt;conf(G_i)&lt;/math&gt; is an average confidence in the i-th group.<br /> <br /> The figure below is a reliability plot of ResNet-50 on CIFAR-10 and CIFAR-100 with 15 groups. It shows that BM has a significantly better calibration performance than softmax since the confidence matches the accuracy more closely (this is also reflected in the lower ECE).<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F4.png]]<br /> <br /> ===== OOD uncertainty =====<br /> <br /> Here, the authors quantify uncertainty using predictive entropy - the larger the predictive entropy, the larger the uncertainty about a prediction. <br /> <br /> The figure below is a density plot of the predictive entropy of ResNet-50 on CIFAR-10. It shows that BM provides significantly better uncertainty estimation compared to other methods since BM is the only method that has a clear peak of high predictive entropy for OOD samples which should have high uncertainty. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F5.png]]<br /> <br /> === Transfer learning ===<br /> <br /> Belief matching applies the Bayesian principle outside the neural network, which means it can easily be applied to already trained models. Thus, belief matching can be employed in transfer learning scenarios. The authors downloaded the ImageNet pre-trained ResNet-50 weights and fine-tuned the weights of the last linear layer for 100 epochs using an Adam optimizer.<br /> <br /> This table shows the test error rates from transfer learning on CIFAR-10, Food-101, and Cars datasets. Belief matching consistently performs better than softmax. <br /> <br /> [[File:being_bayesian_about_categorical_probability_transfer_learning.png]]<br /> <br /> Belief matching was also tested for the predictive uncertainty for out of dataset samples based on CIFAR-10 as the in distribution sample. Looking at the figure below, it is observed that belief matching significantly improves the uncertainty representation of pre-trained models by only fine-tuning the last layer’s weights. Note that belief matching confidently predicts examples in Cars since CIFAR-10 contains the object category automobiles. In comparison, softmax produces confident predictions on all datasets. Thus, belief matching could also be used to enhance the uncertainty representation ability of pre-trained models without sacrificing their generalization performance.<br /> <br /> [[File: being_bayesian_about_categorical_probability_transfer_learning_uncertainty.png]]<br /> <br /> === Semi-Supervised Learning ===<br /> <br /> Belief matching’s ability to allow neural networks to represent rich information in their predictions can be exploited to aid consistency based loss function for semi-supervised learning. Consistency-based loss functions use unlabelled samples to determine where to promote the robustness of predictions based on stochastic perturbations. This can be done by perturbing the inputs (which is the VAT model) or the networks (which is the pi-model). Both methods minimize the divergence between two categorical probabilities under some perturbations, thus belief matching can be used by the following replacements in the loss functions. The hope is that belief matching can provide better prediction consistencies using its Dirichlet distributions.<br /> <br /> [[File: being_bayesian_about_categorical_probability_semi_supervised_equation.png]]<br /> <br /> The results of training on ResNet28-2 with consistency based loss functions on CIFAR-10 are shown in this table. Belief matching does have lower classification error rates compared to using a softmax.<br /> <br /> [[File:being_bayesian_about_categorical_probability_semi_supervised_table.png]]<br /> <br /> == Conclusion and Critiques ==<br /> <br /> Bayesian principles can be used to construct the target distribution by using the categorical probability as a random variable rather than a training label. This can be applied to neural network models by replacing only the softmax and cross-entropy loss, while improving the generalization performance and uncertainty estimation. <br /> <br /> In the future, the authors would like to allow for more expressive distributions in the belief matching framework, such as logistic normal distributions to capture strong semantic similarities among class labels. Furthermore, using input dependent priors would allow for interesting properties that would aid imbalanced datasets and multi-domain learning.<br /> <br /> * Overall I think this summary is very good. The Method(Algorithm) section is described clearly, and the Results section is detailed, with many diagrams illustrating the main points. I just have one technical suggestion: the difference in performance for SOFTMAX and BM differs by model. For example, for RESNEXT-50 model, the difference in top1 is 0.2, whereas for the RESNEXT-100 model, the difference in top one is 0.5, which is significantly higher. It's true that BM method generally outperforms SOFTMAX. But seeing the relation between the choice of model and the magnitude of performance increase could definitely strengthen the paper even further.<br /> <br /> == Citations ==<br /> <br />  Bridle, J. S. Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neurocomputing, pp. 227–236. Springer, 1990.<br /> <br />  Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. Weight uncertainty in neural networks. In International Conference on Machine Learning, 2015.<br /> <br />  Gal, Y. and Ghahramani, Z. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. In International Conference on Machine Learning, 2016.<br /> <br />  Guo, C., Pleiss, G., Sun, Y., and Weinberger, K. Q. On calibration of modern neural networks. In International Conference on Machine Learning, 2017. <br /> <br />  MacKay, D. J. A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3):448– 472, 1992.<br /> <br />  Graves, A. Practical variational inference for neural networks. In Advances in Neural Information Processing Systems, 2011. <br /> <br />  Mandt, S., Hoffman, M. D., and Blei, D. M. Stochastic gradient descent as approximate Bayesian inference. Journal of Machine Learning Research, 18(1):4873–4907, 2017.<br /> <br />  Zhang, G., Sun, S., Duvenaud, D., and Grosse, R. Noisy natural gradient as variational inference. In International Conference of Machine Learning, 2018.<br /> <br />  Maddox, W. J., Izmailov, P., Garipov, T., Vetrov, D. P., and Wilson, A. G. A simple baseline for Bayesian uncertainty in deep learning. In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Osawa, K., Swaroop, S., Jain, A., Eschenhagen, R., Turner, R. E., Yokota, R., and Khan, M. E. Practical deep learning with Bayesian principles. In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Lakshminarayanan, B., Pritzel, A., and Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in Neural Information Processing Systems, 2017.<br /> <br />  Neumann, L., Zisserman, A., and Vedaldi, A. Relaxed softmax: Efficient confidence auto-calibration for safe pedestrian detection. In NIPS Workshop on Machine Learning for Intelligent Transportation Systems, 2018.<br /> <br />  Xie, L., Wang, J., Wei, Z., Wang, M., and Tian, Q. Disturblabel: Regularizing cnn on the loss layer. In IEEE Conference on Computer Vision and Pattern Recognition, 2016.<br /> <br />  Pereyra, G., Tucker, G., Chorowski, J., Kaiser, Ł., and Hinton, G. Regularizing neural networks by penalizing confident output distributions. arXiv preprint arXiv:1701.06548, 2017.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Being_Bayesian_about_Categorical_Probability&diff=49233 Being Bayesian about Categorical Probability 2020-12-05T18:52:19Z <p>Sh68lee: /* Classification With a Neural Network */</p> <hr /> <div>== Presented By ==<br /> Evan Li, Jason Pu, Karam Abuaisha, Nicholas Vadivelu<br /> <br /> == Introduction ==<br /> <br /> Since the outputs of neural networks are not probabilities, Softmax (Bridle, 1990) is a staple for neural network’s performing classification--it exponentiates each logit then normalizes by the sum, giving a distribution over the target classes. Logit is a raw output/prediction of the model which is hard for humans to interpret, thus we transform/normalize these raw values into categories or meaningful numbers for interpretability. However, networks with softmax outputs give no information about uncertainty (Blundell et al., 2015; Gal &amp; Ghahramani, 2016), and the resulting distribution over classes is poorly calibrated (Guo et al., 2017), often giving overconfident predictions even when the classification is wrong. In addition, softmax also raises concerns about overfitting NNs due to its confident predictive behaviors(Xie et al., 2016; Pereyra et al., 2017). To achieve better generalization performance, this may require some effective regularization techniques. <br /> <br /> Bayesian Neural Networks (BNNs; MacKay, 1992) can alleviate these issues, but the resulting posteriors over the parameters are often intractable. Approximations such as variational inference (Graves, 2011; Blundell et al., 2015) and Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) can still be expensive or give poor estimates for the posteriors. This work proposes a Bayesian treatment of the output logits of the neural network, treating the targets as a categorical random variable instead of a fixed label. This gives a computationally cheap way to get well-calibrated uncertainty estimates on neural network classifications.<br /> <br /> == Related Work ==<br /> <br /> Using Bayesian Neural Networks is the dominant way of applying Bayesian techniques to neural networks. Many techniques have been developed to make posterior approximation more accurate and scalable, despite these, BNNs do not scale to the state of the art techniques or large data sets. There are techniques to explicitly avoid modeling the full weight posterior that are more scalable, such as with Monte Carlo Dropout (Gal &amp; Ghahramani, 2016) or tracking mean/covariance of the posterior during training (Mandt et al., 2017; Zhang et al., 2018; Maddox et al., 2019; Osawa et al., 2019). Non-Bayesian uncertainty estimation techniques such as deep ensembles (Lakshminarayanan et al., 2017) and temperature scaling (Guo et al., 2017; Neumann et al., 2018).<br /> <br /> == Preliminaries ==<br /> === Definitions ===<br /> Let's formalize our classification problem and define some notations for the rest of this summary:<br /> <br /> ::Dataset:<br /> $$\mathcal D = \{(x_i,y_i)\} \in (\mathcal X \times \mathcal Y)^N$$<br /> ::General classification model<br /> $$f^W: \mathcal X \to \mathbb R^K$$<br /> ::Softmax function: <br /> $$\phi(x): \mathbb R^K \to [0,1]^K \;\;|\;\; \phi_k(X) = \frac{\exp(f_k^W(x))}{\sum_{k \in K} \exp(f_k^W(x))}$$<br /> ::Softmax activated NN:<br /> $$\phi \;\circ\; f^W: \chi \to \Delta^{K-1}$$<br /> ::NN as a true classifier:<br /> $$arg\max_i \;\circ\; \phi_i \;\circ\; f^W \;:\; \mathcal X \to \mathcal Y$$<br /> <br /> We'll also define the '''count function''' - a &lt;math&gt;K&lt;/math&gt;-vector valued function that outputs the occurences of each class coincident with &lt;math&gt;x&lt;/math&gt;:<br /> $$c^{\mathcal D}(x) = \sum_{(x',y') \in \mathcal D} \mathbb y' I(x' = x)$$<br /> <br /> === Classification With a Neural Network ===<br /> A typical loss function used in classification is cross-entropy. It's well known that optimizing &lt;math&gt;f^W&lt;/math&gt; for &lt;math&gt;l_{CE}&lt;/math&gt; is equivalent to optimizing for &lt;math&gt;l_{KL}&lt;/math&gt;, the &lt;math&gt;KL&lt;/math&gt; divergence between the true distribution and the distribution modeled by NN, that is:<br /> $$l_{KL}(W) = KL(\text{true distribution} \;|\; \text{distribution encoded by }NN(W))$$<br /> Let's introduce notations for the underlying (true) distributions of our problem. Let &lt;math&gt;(x_0,y_0) \sim (\mathcal X \times \mathcal Y)&lt;/math&gt;:<br /> $$\text{Full Distribution} = F(x,y) = P(x_0 = x,y_0 = y)$$<br /> $$\text{Marginal Distribution} = P(x) = F(x_0 = x)$$<br /> $$\text{Point Class Distribution} = P(y_0 = y \;|\; x_0 = x) = F_x(y)$$<br /> Then we have the following factorization:<br /> $$F(x,y) = P(x,y) = P(y|x)P(x) = F_x(y)F(x)$$<br /> Substitute this into the definition of KL divergence:<br /> $$= \sum_{(x,y) \in \mathcal X \times \mathcal Y} F(x,y) \log\left(\frac{F(x,y)}{\phi_y(f^W(x))}\right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F(y|x) \log\left( \frac{F(y|x)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) \sum_{y \in \mathcal Y} F_x(y) \log\left( \frac{F_x(y)}{\phi_y(f^W(x))} \right)$$<br /> $$= \sum_{x \in \mathcal X} F(x) KL(F_x \;||\; \phi\left( f^W(x) \right))$$<br /> As usual, we don't have an analytic form for &lt;math&gt;l&lt;/math&gt; (if we did, this would imply we know &lt;math&gt;F_X&lt;/math&gt; meaning we knew the distribution in the first place). Instead, estimate from &lt;math&gt;\mathcal D&lt;/math&gt;:<br /> $$F(x) \approx \hat F(x) = \frac{||c^{\mathcal D}(x)||_1}{N}$$<br /> $$F_x(y) \approx \hat F_x(y) = \frac{c^{\mathcal D}(x)}{|| c^{\mathcal D}(x) ||_1}$$<br /> $$\to l_{KL}(W) = \sum_{x \in \mathcal D} \frac{||c^{\mathcal D}(x)||_1}{N} KL \left( \frac{c^{\mathcal D}(x)}{||c^{\mathcal D}(x)||_1} \;||\; \phi(f^W(x)) \right)$$<br /> The approximations &lt;math&gt;\hat F, \hat F_X&lt;/math&gt; are often not very good though: consider a typical classification such as MNIST, we would never expect two handwritten digits to produce the exact same image. Hence &lt;math&gt;c^{\mathcal D}(x)&lt;/math&gt; is (almost) always going to have a single index 1 and the rest 0. This has implications for our approximations:<br /> $$\hat F(x) \text{ is uniform for all } x \in \mathcal D$$<br /> $$\hat F_x(y) \text{ is degenerate for all } x \in \mathcal D$$<br /> This clearly has implications for overfitting: to minimize the KL term in &lt;math&gt;l_{KL}(W)&lt;/math&gt; we want &lt;math&gt;\phi(f^W(x))&lt;/math&gt; to be very close to &lt;math&gt;\hat F_x(y)&lt;/math&gt; at each point - this means that the loss function is in fact encouraging the neural network to output near degenerate distributions! <br /> <br /> '''Labal Smoothing'''<br /> One form of regularization to help this problem is called label smoothing. Instead of using the degenerate $$F_x(y)$$ as a target function, let's &quot;smooth&quot; it (by adding a scaled uniform distribution to it) so it's no longer degenerate:<br /> $$F'_x(y) = (1-\lambda)\hat F_x(y) + \frac \lambda K \vec 1$$<br /> <br /> '''BNNs'''<br /> BBNs balances the complexity of the model and the distance to target distribution without choosing a single beset configuration (one-hot encoding). Specifically, BNNs with the Gaussian Weight prior $$F_x(y) = N (0,T^{-1} I)$$ has score of configuration W measured by the posterior density $$p_W(W|D) = p(D|W)p_W(W), \log(p_W(W)) = T||W||^2_2$$<br /> Here &lt;math&gt;||W||^2_2&lt;/math&gt; could be a poor proxy to penalized for the model complexity due to its linear nature.<br /> <br /> == Method ==<br /> The main technical proposal of the paper is a Bayesian framework to estimate the (former) target distribution &lt;math&gt;F_x(y)&lt;/math&gt;. That is, we construct a posterior distribution of &lt;math&gt; F_x(y) &lt;/math&gt; and use that as our new target distribution. We call it the ''belief matching'' (BM) framework.<br /> <br /> === Constructing Target Distribution ===<br /> Recall that &lt;math&gt;F_x(y)&lt;/math&gt; is a k-categorical probability distribution - it's PMF can be fully characterized by k numbers that sum to 1. Hence we can encode any such &lt;math&gt;F_x&lt;/math&gt; as a point in &lt;math&gt;\Delta^{k-1}&lt;/math&gt;. We'll do exactly that - let's call this vecor &lt;math&gt;z&lt;/math&gt;:<br /> $$z \in \Delta^{k-1}$$<br /> $$\text{prior} = p_{z|x}(z)$$<br /> $$\text{conditional} = p_{y|z,x}(y)$$<br /> $$\text{posterior} = p_{z|x,y}(z)$$<br /> Then if we perform inference:<br /> $$p_{z|x,y}(z) \propto p_{z|x}(z)p_{y|z,x}(y)$$<br /> The distribution chosen to model prior was &lt;math&gt;dir_K(\beta)&lt;/math&gt;:<br /> $$p_{z|x}(z) = \frac{\Gamma(||\beta||_1)}{\prod_{k=1}^K \Gamma(\beta_k)} \prod_{k=1}^K z_k^{\beta_k - 1}$$<br /> Note that by definition of &lt;math&gt;z&lt;/math&gt;: &lt;math&gt; p_{y|x,z} = z_y &lt;/math&gt;. Since the Dirichlet is a conjugate prior to categorical distributions we have a convenient form for the mean of the posterior:<br /> $$\bar{p_{z|x,y}}(z) = \frac{\beta + c^{\mathcal D}(x)}{||\beta + c^{\mathcal D}(x)||_1} \propto \beta + c^{\mathcal D}(x)$$<br /> This is in fact a generalization of (uniform) label smoothing (label smoothing is a special case where &lt;math&gt;\beta = \frac 1 K \vec{1} &lt;/math&gt;).<br /> <br /> === Representing Approximate Distribution ===<br /> Our new target distribution is &lt;math&gt;p_{z|x,y}(z)&lt;/math&gt; (as opposed to &lt;math&gt;F_x(y)&lt;/math&gt;). That is, we want to construct an interpretation of our neural network weights to construct a distribution with support in &lt;math&gt; \Delta^{K-1} &lt;/math&gt; - the NN can then be trained so this encoded distribution closely approximates &lt;math&gt;p_{z|x,y}&lt;/math&gt;. Let's denote the PMF of this encoded distribution &lt;math&gt;q_{z|x}^W&lt;/math&gt;. This is how the BM framework defines it:<br /> $$\alpha^W(x) := \exp(f^W(x))$$<br /> $$q_{z|x}^W(z) = \frac{\Gamma(||\alpha^W(x)||_1)}{\sum_{k=1}^K \Gamma(\alpha_k^W(x))} \prod_{k=1}^K z_{k}^{\alpha_k^W(x) - 1}$$<br /> $$\to Z^W_x \sim dir(\alpha^W(x))$$<br /> Apply &lt;math&gt;\log&lt;/math&gt; then &lt;math&gt;\exp&lt;/math&gt; to &lt;math&gt;q_{z|x}^W&lt;/math&gt;:<br /> $$q^W_{z|x}(z) \propto \exp \left( \sum_k (\alpha_k^W(x) \log(z_k)) - \sum_k \log(z_k) \right)$$<br /> $$\propto -l_{CE}(\phi(f^W(x)),z) + \frac{K}{||\alpha^W(x)||}KL(\mathcal U_k \;||\; z)$$<br /> It can actually be shown that the mean of &lt;math&gt;Z_x^W&lt;/math&gt; is identical to &lt;math&gt;\phi(f^W(x))&lt;/math&gt; - in other words, if we output the mean of the encoded distribution of our neural network under the BM framework, it is theoretically identical to a traditional neural network.<br /> <br /> === Distribution Matching ===<br /> <br /> We now need a way to fit our approximate distribution from our neural network &lt;math&gt;q_{\mathbf{z | x}}^{\mathbf{W}}&lt;/math&gt; to our target distribution &lt;math&gt;p_{\mathbf{z|x},y}&lt;/math&gt;. The authors achieve this by maximizing the evidence lower bound (ELBO):<br /> <br /> $$l_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}})$$<br /> <br /> Each term can be computed analytically:<br /> <br /> $$\mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf W }} \left[\log z_y \right] = \psi(\alpha_y^{\mathbf W} ( \mathbf x )) - \psi(\alpha_0^{\mathbf W} ( \mathbf x ))$$<br /> <br /> Where &lt;math&gt;\psi(\cdot)&lt;/math&gt; represents the digamma function (logarithmic derivative of gamma function). Intuitively, we maximize the probability of the correct label. For the KL term:<br /> <br /> $$KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; p_{\mathbf{z|x}}) = \log \frac{\Gamma(a_0^{\mathbf W}(\mathbf x)) \prod_k \Gamma(\beta_k)}{\prod_k \Gamma(\alpha_k^{\mathbf W}(x)) \Gamma (\beta_0)} + \sum_k (\alpha_k^{\mathbf W}(x)-\beta_k)(\psi(\alpha_k^{\mathbf W}(\mathbf x)) - \psi(\alpha_0^{\mathbf W}(\mathbf x))$$<br /> <br /> In the first term, for intuition, we can ignore &lt;math&gt;\alpha_0&lt;/math&gt; and &lt;math&gt;\beta_0&lt;/math&gt; since those just calibrate the distributions. Otherwise, we want the ratio of the products to be as close to 1 as possible to minimize the KL. In the second term, we want to minimize the difference between each individual &lt;math&gt;\alpha_k&lt;/math&gt; and &lt;math&gt;\beta_k&lt;/math&gt;, scaled by the normalized output of the neural network. <br /> <br /> This loss function can be used as a drop-in replacement for the standard softmax cross-entropy, as it has an analytic form and the same time complexity as typical softmax-cross entropy with respect to the number of classes (&lt;math&gt;O(K)&lt;/math&gt;).<br /> <br /> === On Prior Distributions ===<br /> <br /> We must choose our concentration parameter, &lt;math&gt;\beta&lt;/math&gt;, for our dirichlet prior. We see our prior essentially disappears as &lt;math&gt;\beta_0 \to 0&lt;/math&gt; and becomes stronger as &lt;math&gt;\beta_0 \to \infty&lt;/math&gt;. Thus, we want a small &lt;math&gt;\beta_0&lt;/math&gt; so the posterior isn't dominated by the prior. But, the authors claim that a small &lt;math&gt;\beta_0&lt;/math&gt; makes &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small, which causes &lt;math&gt;\psi (\alpha_0^{\mathbf W}(\mathbf x))&lt;/math&gt; to be large, which is problematic for gradient based optimization. In practice, many neural network techniques aim to make &lt;math&gt;\mathbb E [f^{\mathbf W} (\mathbf x)] \approx \mathbf 0&lt;/math&gt; and thus &lt;math&gt;\mathbb E [\alpha^{\mathbf W} (\mathbf x)] \approx \mathbf 1&lt;/math&gt;, which means making &lt;math&gt;\alpha_0^{\mathbf W}(\mathbf x)&lt;/math&gt; small can be counterproductive.<br /> <br /> So, the authors set &lt;math&gt;\beta = \mathbf 1&lt;/math&gt; and introduce a new hyperparameter &lt;math&gt;\lambda&lt;/math&gt; which is multiplied with the KL term in the ELBO:<br /> <br /> $$l^\lambda_{EB}(\mathbf y, \alpha^{\mathbf W}(\mathbf x)) = \mathbb E_{q_{\mathbf{z | x}}^{\mathbf{W}}} \left[\log p(\mathbf {y | x, z})\right] - \lambda KL (q_{\mathbf{z | x}}^{\mathbf W} \; || \; \mathcal P^D (\mathbf 1))$$<br /> <br /> This stabilizes the optimization, as we can tell from the gradients:<br /> <br /> $$\frac{\partial l_{E B}\left(\mathbf{y}, \alpha^{\mathbf W}(\mathbf{x})\right)}{\partial \alpha_{k}^{\mathbf W}(\mathbf {x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\alpha_{k}^{\mathbf W}(\mathbf{x})-\beta_{k}\right)\right) \psi^{\prime}\left(\alpha_{k}^{\mathbf{W}}(\boldsymbol{x})\right)<br /> -\left(1-\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})-\beta_{0}\right)\right) \psi^{\prime}\left(\alpha_{0}^{\boldsymbol{W}}(\boldsymbol{x})\right)$$<br /> <br /> $$\frac{\partial l_{E B}^{\lambda}\left(\mathbf{y}, \alpha^{\mathbf{W}}(\mathbf{x})\right)}{\partial \alpha_{k}^{W}(\mathbf{x})}=\left(\tilde{\mathbf{y}}_{k}-\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})-\lambda\right)\right) \frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}<br /> -\left(1-\left(\tilde{\alpha}_{0}^{W}(\mathbf{x})-\lambda K\right)\right)$$<br /> <br /> As we can see, the first expression is affected by the magnitude of &lt;math&gt;\alpha^{\boldsymbol{W}}(\boldsymbol{x})&lt;/math&gt;, whereas the second expression is not due to the &lt;math&gt;\frac{\psi^{\prime}\left(\tilde{\alpha}_{k}^{\mathbf W}(\mathbf{x})\right)}{\psi^{\prime}\left(\tilde{\alpha}_{0}^{\mathbf W}(\mathbf{x})\right)}&lt;/math&gt; ratio.<br /> <br /> == Experiments ==<br /> <br /> Throughout the experiments in this paper, the authors employ various models based on residual connections (He et al., 2016 ) which are the models used for benchmarking in practice. We will first demonstrate improvements provided by BM, then we will show versatility in other applications. For fairness of comparisons, all configurations in the reference implementation will be fixed. The only additions in the experiments are initial learning rate warm-up and gradient clipping which are extremely helpful for stable training of BM. <br /> <br /> === Generalization performance === <br /> The paper compares the generalization performance of BM with softmax and MC dropout on CIFAR-10 and CIFAR-100 benchmarks.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T1.png]]<br /> <br /> The next comparison was performed between BM and softmax on the ImageNet benchmark. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_T2.png]]<br /> <br /> For both datasets and In all configurations, BM achieves the best generalization and outperforms softmax and MC dropout.<br /> <br /> ===== Regularization effect of prior =====<br /> <br /> In theory, BM has 2 regularization effects:<br /> The prior distribution, which smooths the target posterior<br /> Averaging all of the possible categorical probabilities to compute the distribution matching loss<br /> The authors perform an ablation study to examine the 2 effects separately - removing the KL term in the ELBO removes the effect of the prior distribution.<br /> For ResNet-50 on CIFAR-100 and CIFAR-10 the resulting test error rates were 24.69% and 5.68% respectively. <br /> <br /> This demonstrates that both regularization effects are significant since just having one of them improves the generalization performance compared to the softmax baseline, and having both improves the performance even more.<br /> <br /> ===== Impact of &lt;math&gt;\beta&lt;/math&gt; =====<br /> <br /> The effect of β on generalization performance is studied by training ResNet-18 on CIFAR-10 by tuning the value of β on its own, as well as jointly with λ. It was found that robust generalization performance is obtained for β ∈ [&lt;math&gt;e^{−1}, e^4&lt;/math&gt;] when tuning β on its own; and β ∈ [&lt;math&gt;e^{−4}, e^{8}&lt;/math&gt;] when tuning β jointly with λ. The figure below shows a plot of the error rate with varying β.<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F3.png]]<br /> <br /> === Uncertainty Representation ===<br /> <br /> One of the big advantages of BM is the ability to represent uncertainty about the prediction. The authors evaluate the uncertainty representation on in-distribution (ID) and out-of-distribution (OOD) samples. <br /> <br /> ===== ID uncertainty =====<br /> <br /> For ID (in-distribution) samples, calibration performance is measured, which is a measure of how well the model’s confidence matches its actual accuracy. This measure can be visualized using reliability plots and quantified using a metric called expected calibration error (ECE). ECE is calculated by grouping predictions into M groups based on their confidence score and then finding the absolute difference between the average accuracy and average confidence for each group. We can define the ECE of &lt;math&gt;f^W &lt;/math&gt; on &lt;math&gt;D &lt;/math&gt; with &lt;math&gt;M&lt;/math&gt; groups as <br /> <br /> &lt;center&gt;<br /> &lt;math&gt;ECE_M(f^W, D) = \sum^M_{i=1} \frac{|G_i|}{|D|}|acc(G_i) - conf(G_i)|&lt;/math&gt;<br /> &lt;/center&gt;<br /> Where &lt;math&gt;G_i&lt;/math&gt; is a set of samples int the i-th group defined as &lt;math&gt;G_i = \{j:i/M &lt; max_k\phi_k(f^Wx^{(j)}) \leq (1+i)/M\}&lt;/math&gt;, &lt;math&gt;acc(G_i)&lt;/math&gt; is an average accuracy in the i-th group and &lt;math&gt;conf(G_i)&lt;/math&gt; is an average confidence in the i-th group.<br /> <br /> The figure below is a reliability plot of ResNet-50 on CIFAR-10 and CIFAR-100 with 15 groups. It shows that BM has a significantly better calibration performance than softmax since the confidence matches the accuracy more closely (this is also reflected in the lower ECE).<br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F4.png]]<br /> <br /> ===== OOD uncertainty =====<br /> <br /> Here, the authors quantify uncertainty using predictive entropy - the larger the predictive entropy, the larger the uncertainty about a prediction. <br /> <br /> The figure below is a density plot of the predictive entropy of ResNet-50 on CIFAR-10. It shows that BM provides significantly better uncertainty estimation compared to other methods since BM is the only method that has a clear peak of high predictive entropy for OOD samples which should have high uncertainty. <br /> <br /> [[File:Being_Bayesian_about_Categorical_Probability_F5.png]]<br /> <br /> === Transfer learning ===<br /> <br /> Belief matching applies the Bayesian principle outside the neural network, which means it can easily be applied to already trained models. Thus, belief matching can be employed in transfer learning scenarios. The authors downloaded the ImageNet pre-trained ResNet-50 weights and fine-tuned the weights of the last linear layer for 100 epochs using an Adam optimizer.<br /> <br /> This table shows the test error rates from transfer learning on CIFAR-10, Food-101, and Cars datasets. Belief matching consistently performs better than softmax. <br /> <br /> [[File:being_bayesian_about_categorical_probability_transfer_learning.png]]<br /> <br /> Belief matching was also tested for the predictive uncertainty for out of dataset samples based on CIFAR-10 as the in distribution sample. Looking at the figure below, it is observed that belief matching significantly improves the uncertainty representation of pre-trained models by only fine-tuning the last layer’s weights. Note that belief matching confidently predicts examples in Cars since CIFAR-10 contains the object category automobiles. In comparison, softmax produces confident predictions on all datasets. Thus, belief matching could also be used to enhance the uncertainty representation ability of pre-trained models without sacrificing their generalization performance.<br /> <br /> [[File: being_bayesian_about_categorical_probability_transfer_learning_uncertainty.png]]<br /> <br /> === Semi-Supervised Learning ===<br /> <br /> Belief matching’s ability to allow neural networks to represent rich information in their predictions can be exploited to aid consistency based loss function for semi-supervised learning. Consistency-based loss functions use unlabelled samples to determine where to promote the robustness of predictions based on stochastic perturbations. This can be done by perturbing the inputs (which is the VAT model) or the networks (which is the pi-model). Both methods minimize the divergence between two categorical probabilities under some perturbations, thus belief matching can be used by the following replacements in the loss functions. The hope is that belief matching can provide better prediction consistencies using its Dirichlet distributions.<br /> <br /> [[File: being_bayesian_about_categorical_probability_semi_supervised_equation.png]]<br /> <br /> The results of training on ResNet28-2 with consistency based loss functions on CIFAR-10 are shown in this table. Belief matching does have lower classification error rates compared to using a softmax.<br /> <br /> [[File:being_bayesian_about_categorical_probability_semi_supervised_table.png]]<br /> <br /> == Conclusion and Critiques ==<br /> <br /> Bayesian principles can be used to construct the target distribution by using the categorical probability as a random variable rather than a training label. This can be applied to neural network models by replacing only the softmax and cross-entropy loss, while improving the generalization performance and uncertainty estimation. <br /> <br /> In the future, the authors would like to allow for more expressive distributions in the belief matching framework, such as logistic normal distributions to capture strong semantic similarities among class labels. Furthermore, using input dependent priors would allow for interesting properties that would aid imbalanced datasets and multi-domain learning.<br /> <br /> * Overall I think this summary is very good. The Method(Algorithm) section is described clearly, and the Results section is detailed, with many diagrams illustrating the main points. I just have one technical suggestion: the difference in performance for SOFTMAX and BM differs by model. For example, for RESNEXT-50 model, the difference in top1 is 0.2, whereas for the RESNEXT-100 model, the difference in top one is 0.5, which is significantly higher. It's true that BM method generally outperforms SOFTMAX. But seeing the relation between the choice of model and the magnitude of performance increase could definitely strengthen the paper even further.<br /> <br /> == Citations ==<br /> <br />  Bridle, J. S. Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In Neurocomputing, pp. 227–236. Springer, 1990.<br /> <br />  Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. Weight uncertainty in neural networks. In International Conference on Machine Learning, 2015.<br /> <br />  Gal, Y. and Ghahramani, Z. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. 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In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Osawa, K., Swaroop, S., Jain, A., Eschenhagen, R., Turner, R. E., Yokota, R., and Khan, M. E. Practical deep learning with Bayesian principles. In Advances in Neural Information Processing Systems, 2019.<br /> <br />  Lakshminarayanan, B., Pritzel, A., and Blundell, C. Simple and scalable predictive uncertainty estimation using deep ensembles. In Advances in Neural Information Processing Systems, 2017.<br /> <br />  Neumann, L., Zisserman, A., and Vedaldi, A. Relaxed softmax: Efficient confidence auto-calibration for safe pedestrian detection. In NIPS Workshop on Machine Learning for Intelligent Transportation Systems, 2018.<br /> <br />  Xie, L., Wang, J., Wei, Z., Wang, M., and Tian, Q. Disturblabel: Regularizing cnn on the loss layer. In IEEE Conference on Computer Vision and Pattern Recognition, 2016.<br /> <br />  Pereyra, G., Tucker, G., Chorowski, J., Kaiser, Ł., and Hinton, G. Regularizing neural networks by penalizing confident output distributions. arXiv preprint arXiv:1701.06548, 2017.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Mask_RCNN&diff=49230 Mask RCNN 2020-12-05T18:36:06Z <p>Sh68lee: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Qing Guo, Xueguang Ma, James Ni, Yuanxin Wang<br /> <br /> == Introduction == <br /> Mask RCNN  is a deep neural network architecture that aims to solve instance segmentation problems in computer vision which is important when attempting to identify different objects within the same image. RCNN base architectures first extract a regional proposal (a region of the image where the object of interest is proposed to lie) and then attempts to classify the object within it. <br /> Mask R-CNN extends Faster R-CNN  by adding a branch for predicting an object mask in parallel with the existing branch for bounding box recognition. This is done by using a Fully Convolutional Network as each mask branch in a pixel-by-pixel way. Mask R-CNN is simple to train and adds only a small overhead to Faster R-CNN, running at 5 fps. Moreover, Mask R-CNN is easy to generalize to other tasks, e.g., allowing us to estimate human poses in the same framework. Mask R-CNN achieved top results in all three tracks of the COCO suite of challenges , including instance segmentation, bounding-box object detection, and person keypoint detection.<br /> <br /> == Visual Perception Tasks == <br /> <br /> Figure 1 shows a visual representation of different types of visual perception tasks:<br /> <br /> - Image Classification: Predict a set of labels to characterize the contents of an input image<br /> <br /> - Object Detection: Build on image classification but localize each object in an image by placing bounding boxes around the objects<br /> <br /> - Semantic Segmentation: Associate every pixel in an input image with a class label<br /> <br /> - Instance Segmentation: Associate every pixel in an input image to a specific object. Instance segmentation combines image classification, object detection and semantic segmentation making it a complex task .<br /> <br /> [[File:instance segmentation.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Visual Perception tasks&lt;/div&gt;<br /> <br /> <br /> Mask RCNN is a deep neural network architecture for Instance Segmentation.<br /> <br /> == Related Work == <br /> Region Proposal Network: A Region Proposal Network (RPN) takes an image (of any size) as input and outputs a set of rectangular object proposals, each with an objectness score.<br /> <br /> ROI Pooling: The main use of ROI (Region of Interest) Pooling is to adjust the proposal to a uniform size. It’s better for the subsequent network to process. It maps the proposal to the corresponding position of the feature map, divide the mapped area into sections of the same size, and performs max pooling or average pooling operations on each section.<br /> <br /> Faster R-CNN: Faster R-CNN consists of two stages: Region Proposal Network and ROI Pooling. Region Proposal Network proposes candidate object bounding boxes. ROI Pooling, which is in essence Fast R-CNN, extracts features using RoIPool from each candidate box and performs classification and bounding-box regression. The features used by both stages can be shared for faster inference.<br /> <br /> [[File:FasterRCNN.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 2: Faster RCNN architecture&lt;/div&gt;<br /> <br /> <br /> ResNet-FPN: FPN uses a top-down architecture with lateral connections to build an in-network feature pyramid from a single-scale input. FPN is a general architecture that can be used in conjunction with various networks, such as VGG, ResNet, etc. Faster R-CNN with an FPN backbone extracts RoI features from different levels of the feature pyramid according to their scale. Other than FPN, the rest of the approach is similar to vanilla ResNet. Using a ResNet-FPN backbone for feature extraction with Mask RCNN gives excellent gains in both accuracy and speed.<br /> <br /> [[File:ResNetFPN.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 3: ResNetFPN architecture&lt;/div&gt;<br /> <br /> == Model Architecture == <br /> The structure of mask R-CNN is quite similar to the structure of faster R-CNN. <br /> Faster R-CNN has two stages, the RPN(Region Proposal Network) first proposes candidate object bounding boxes. Then RoIPool extracts the features from these boxes. After the features are extracted, these features data can be analyzed using classification and bounding-box regression. Mask R-CNN shares the identical first stage. But the second stage is adjusted to tackle the issue of simplifying the stages pipeline. Instead of only performing classification and bounding-box regression, it also outputs a binary mask for each RoI as &lt;math&gt;L=L_{cls}+L_{box}+L_{mask}&lt;/math&gt;, where &lt;math&gt;L_{cls}&lt;/math&gt;, &lt;math&gt;L_{box}&lt;/math&gt;, &lt;math&gt;L_{mask}&lt;/math&gt; represent the classification loss, bounding box loss and the average binary cross-entropy loss respectively.<br /> <br /> The important concept here is that, for most recent network systems, there's a certain order to follow when performing classification and regression, because classification depends on mask predictions. Mask R-CNN, on the other hand, applies bounding-box classification and regression in parallel, which effectively simplifies the multi-stage pipeline of the original R-CNN. And just for comparison, complete R-CNN pipeline stages involve 1. Make region proposals; 2. Feature extraction from region proposals; 3. SVM for object classification; 4. Bounding box regression. In conclusion, stages 3 and 4 are adjusted to simplify the network procedures.<br /> <br /> The system follows the multi-task loss, which by formula equals classification loss plus bounding-box loss plus the average binary cross-entropy loss.<br /> One thing worth noticing is that for other network systems, those masks across classes compete with each other, but in this particular case, with a <br /> per-pixel sigmoid and a binary loss the masks across classes no longer compete, which makes this formula the key for good instance segmentation results.<br /> <br /> '' RoIAlign''<br /> <br /> This concept is useful in stage 2 where the RoIPool extracts features from bounding-boxes. For each RoI as input, there will be a mask and a feature map as output. The mask is obtained using the FCN(Fully Convolutional Network) and the feature map is obtained using the RoIPool. The mask helps with spatial layout, which is crucial to the pixel-to-pixel correspondence. <br /> <br /> The two things we desire along the procedure are: pixel-to-pixel correspondence; no quantization is performed on any coordinates involved in the RoI, its bins, or the sampling points. Pixel-to-pixel correspondence makes sure that the input and output match in size. If there is a size difference, there will be information loss, and coordinates cannot be matched. <br /> <br /> RoIPool is standard for extracting a small feature map from each RoI. However, it performs quantization before subdividing into spatial bins which are further quantized. Quantization produces misalignments when it comes to predicting pixel accurate masks. Therefore, instead of quantization, the coordinates are computed using bilinear interpolation They use bilinear interpolation to get the exact values of the inputs features at the 4 RoI bins and aggregate the result (using max or average). These results are robust to the sampling location and number of points and to guarantee spatial correspondence.<br /> <br /> The network architectures utilized are called ResNet and ResNeXt. The depth can be either 50 or 101.​ ResNet-FPN(Feature Pyramid Network) is used for feature extraction.​ <br /> <br /> Some implementation details should be mentioned: first, an RoI is considered positive if it has IoU with a ground-truth box of at least 0.5 and negative otherwise. It is important because the mask loss Lmask is defined only on positive RoIs. Second, image-centric training is used to rescale images so that pixel correspondence is achieved. An example complete structure is, the proposal number is 1000 for FPN, and then run the box prediction branch on these proposals. The mask branch is then applied to the highest scoring 100 detection boxes. The mask branch can predict K masks per RoI, but only the kth mask will be used, where k is the predicted class by the classification branch. The m-by-m floating-number mask output is then resized to the RoI size and binarized at a threshold of 0.5.<br /> <br /> == Results ==<br /> [[File:ExpInstanceSeg.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 4: Instance Segmentation Experiments&lt;/div&gt;<br /> <br /> Instance Segmentation: Based on COCO dataset, Mask R-CNN outperforms all categories comparing to MNC and FCIS which are state of the art model <br /> <br /> [[File:BoundingBoxExp.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 5: Bounding Box Detection Experiments&lt;/div&gt;<br /> <br /> Bounding Box Detection: Mask R-CNN outperforms the base variants of all previous state-of-the-art models, including the winner of the COCO 2016 Detection Challenge.<br /> <br /> == Ablation Experiments ==<br /> [[File:BackboneExp.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 6: Backbone Architecture Experiments&lt;/div&gt;<br /> <br /> (a) Backbone Architecture: Better backbones bring expected gains: deeper networks do better, FPN outperforms C4 features, and ResNeXt improves on ResNet. <br /> <br /> [[File:MultiVSInde.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 7: Multinomial vs. Independent Masks Experiments&lt;/div&gt;<br /> <br /> (b) Multinomial vs. Independent Masks (ResNet-50-C4): Decoupling via perclass binary masks (sigmoid) gives large gains over multinomial masks (softmax).<br /> <br /> [[File: RoIAlign.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 8: RoIAlign Experiments 1&lt;/div&gt;<br /> <br /> (c) RoIAlign (ResNet-50-C4): Mask results with various RoI layers. Our RoIAlign layer improves AP by ∼3 points and AP75 by ∼5 points. Using proper alignment is the only factor that contributes to the large gap between RoI layers. <br /> <br /> [[File: RoIAlignExp.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 9: RoIAlign Experiments w Experiments&lt;/div&gt;<br /> <br /> (d) RoIAlign (ResNet-50-C5, stride 32): Mask-level and box-level AP using large-stride features. Misalignments are more severe than with stride-16 features, resulting in big accuracy gaps.<br /> <br /> [[File:MaskBranchExp.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 10: Mask Branch Experiments&lt;/div&gt;<br /> <br /> (e) Mask Branch (ResNet-50-FPN): Fully convolutional networks (FCN) vs. multi-layer perceptrons (MLP, fully-connected) for mask prediction. FCNs improve results as they take advantage of explicitly encoding spatial layout.<br /> <br /> == Human Pose Estimation ==<br /> Mask RCNN can be extended to human pose estimation.<br /> <br /> The simple approach the paper presents is to model a keypoint’s location as a one-hot mask, and adopt Mask R-CNN to predict K masks, one for each of K keypoint types such as left shoulder, right elbow. The model has minimal knowledge of human pose and this example illustrates the generality of the model.<br /> <br /> [[File:HumanPose.png | center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 11: Keypoint Detection Results&lt;/div&gt;<br /> <br /> == Experiments on Cityscapes ==<br /> The model was also tested on Cityscapes dataset. From this dataset the authors used 2975 annotated images for training, 500 for validation, and 1525 for testing. The instance segmentation task involved eight categories: person, rider, car, truck, bus, train, motorcycle and bicycle. When the Mask R-CNN model was applied to the data it achieved 26.2 AP on the testing data which was an over 30% improvement on the previous best entry. <br /> <br /> &lt;center&gt;<br /> [[ File:cityscapeDataset.png ]]<br /> <br /> <br /> Figure 12. Cityscapes Results<br /> &lt;/center&gt;<br /> <br /> == Conclusion ==<br /> Mask RCNN is a deep neural network aimed to solve the instance segmentation problems in machine learning or computer vision. Mask R-CNN is a conceptually simple, flexible, and general framework for object instance segmentation. It can efficiently detect objects in an image while simultaneously generating a high-quality segmentation mask for each instance. It does object detection and instance segmentation, and can also be extended to human pose estimation.<br /> It extends Faster R-CNN by adding a branch for predicting an object mask in parallel with the existing branch for bounding box recognition. Mask R-CNN is simple to train and adds only a small overhead to Faster R-CNN, running at 5 fps.<br /> <br /> == Critiques ==<br /> In Faster RCNN, the ROI boundary is quantized. However, mask RCNN avoids quantization and used the bilinear interpolation to compute exact values of features. By solving the misalignments due to quantization, the number and location of sampling points have no impact on the result.<br /> <br /> It may be better to compare the proposed model with other NN models or even non-NN methods like spectral clustering. Also, the applications can be further discussed like geometric mesh processing and motion analysis.<br /> <br /> The paper lacks the comparisons of different methods and Mask RNN on unlabeled data, as the paper only briefly mentioned that the authors found out that Mask R_CNN can benefit from extra data, even if the data is unlabelled.<br /> <br /> The Mask RCNN has many practical applications as well. A particular example, where Mask RCNNs are applied would be in autonomous vehicles. Namely, it would be able to help with isolating pedestrians, other vehicles, lights, etc.<br /> <br /> The Mask RCNN could be a candidate model to do short-term predictions on the physical behaviors of a person, which could be very useful at crime scenes.<br /> <br /> An interesting application of Mask RCNN would be on face recognition from CCTVs. Flurry pictures of crowded people could be obtained from CCTV, so that mask RCNN can be applied to distinguish each person.<br /> <br /> The main problem for CNN architectures like Mask RCNN is the running time. Due to slow running times, Single Shot Detector algorithms are preferred for applications like video or live stream detections, where a faster running time would mean a better response to changes in frames. It would be beneficial to have a graphical representation of the Mask RCNN running times against single shot detector algorithms such as YOLOv3.<br /> <br /> It is interesting to investigate a solution of embedding instance segmentation with semantic segmentation to improve time performance. Because in many situations, knowing the exact boundary of an object is not necessary.<br /> <br /> <br /> It will be better if we can have more comparisons with other models. It will also be nice if we can have more details about why Mask RCNN can perform better, and how about the efficiency of it?<br /> The authors mentioned that Mask R-CNN is a deep neural network architecture for Instance Segmentation. It's better to include more background information about this task. For example, challenges of this task (e.g. the model will need to take into account the overlapping of objects) and limitations of existing methods.<br /> <br /> It would be interesting to see how a postprocessing step with conditional random fields (CRF) might improve (or not?) segmentation. It would also have been interesting to see the performance of the method with lighter backbones since the backbones used to have a very large inference time which makes them unsuitable for many applications.<br /> <br /> An extension of the application of Mask RCNN in medical AI is to highlight areas of an MRI scan that correlate to certain behavioral/psychological patterns.<br /> <br /> The use of these in medical imaging systems seems rather useful, but it can also be extended to more general CCTV camera systems which can also detect physiological patterns.<br /> <br /> In the Human Pose Estimation section, we assume that Mask RCNN does not have any knowledge of human poses, and all the predictions are based on keypoints on human bodies, for example, left shoulder and right elbow. While in fact we may be able to achieve better performances here because currently this approach is strongly dependent on correct classifications of human body parts. That is, if the model messed up the position of left shoulder, the position estimation will be awful. It is important to remove the dependency on preceding predictions, so that even when previous steps fail, we may still expect a fair performance.<br /> <br /> It will be interesting to see if applying dropout can boost this Mask RCNN architecture's performance.<br /> <br /> It will be interesting if mask RCNN is applied to human faces and how it classify each individual also would be nice to see how the technical calculations such as classification and predictions are done.<br /> <br /> == References ==<br />  Kaiming He, Georgia Gkioxari, Piotr Dollár, Ross Girshick. Mask R-CNN. arXiv:1703.06870, 2017.<br /> <br />  Shaoqing Ren, Kaiming He, Ross Girshick, Jian Sun. Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks, arXiv:1506.01497, 2015.<br /> <br />  Tsung-Yi Lin, Michael Maire, Serge Belongie, Lubomir Bourdev, Ross Girshick, James Hays, Pietro Perona, Deva Ramanan, C. Lawrence Zitnick, Piotr Dollár. Microsoft COCO: Common Objects in Context. arXiv:1405.0312, 2015</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Describtion_of_Text_Mining&diff=49226 Describtion of Text Mining 2020-12-05T18:17:17Z <p>Sh68lee: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Yawen Wang, Danmeng Cui, Zijie Jiang, Mingkang Jiang, Haotian Ren, Haris Bin Zahid<br /> <br /> == Introduction ==<br /> This paper focuses on the different text mining techniques and the applications of text mining in the healthcare and biomedical domain. The text mining field has been popular as a result of the amount of text data that is available in different forms. The text data is bound to grow even more in 2020, indicating a 50 times growth since 2010. Text is unstructured information, which is easy for humans to construct and understand but difficult for machines. Hence, there is a need to design algorithms to effectively process this avalanche of text. To further explore the text mining field, the related text mining approaches can be considered. The different text mining approaches relate to two main methods: knowledge delivery and traditional data mining methods. <br /> <br /> The authors note that knowledge delivery methods involve the application of different steps to a specific data set to create specific patterns. Research in knowledge delivery methods has evolved over the years due to advances in hardware and software technology. On the other hand, data mining has experienced substantial development through the intersection of three fields: databases, machine learning, and statistics. As brought out by the authors, text mining approaches focus on the exploration of information from a specific text. The information explored is in the form of structured, semi-structured, and unstructured text. It is important to note that text mining covers different sets of algorithms and topics that include information retrieval. The topics and algorithms are used for analyzing different text forms.<br /> <br /> ==Text Representation and Encoding ==<br /> The authors review multiple methods of preprocessing text, including 4 methods to preprocess and recognize influence and frequency of individual group of words in a document. In many text mining algorithms, one of the key components is preprocessing. Preprocessing consists of different tasks that include filtering, tokenization, stemming, and lemmatization. The first step is tokenization, where a character sequence is broken down into different words or phrases. After the breakdown, filtering is carried out to remove some words. The various word inflected forms are grouped together through lemmatization, and later, the derived roots of the derived words are obtained through stemming.<br /> <br /> '''1. Tokenization'''<br /> <br /> This process splits text (i.e. a sentence) into a single unit of words, known as tokens while removing unnecessary characters. Tokenization relies on indentifying word boundaries, that is ending of a word and beginning of another word, usually separated by space. Characters such as punctuation are removed and the text is split at space characters. An example of this would be converting the string &quot;This is my string&quot; to &quot;This&quot;, &quot;is&quot;, &quot;my&quot;, &quot;string&quot;.<br /> <br /> '''2. Filtering'''<br /> <br /> Filtering is a process by which unnecessary words or characters are removed. Often these include punctuation, prepositions, and conjugations. The resulting corpus then contains words with maximal importance in distinguishing between classes.<br /> <br /> '''3. Lemmatization'''<br /> <br /> Lemmatization is a task where the various inflected forms of a word are converted to a single form. However, unlike in stemming (see below), we must specify the part of speech (POS) of each word, i.e its intended meaning in the given sentence or document, which can prone to human error. For example, &quot;geese&quot; and &quot;goose&quot; have the same lemma &quot;goose&quot;, as they have the same meaning.<br /> <br /> '''4. Stemming'''<br /> <br /> Stemming extracts the roots of words. It is a language dependent process. The goal of both stemming is to reduce inflectional and related (definition wise) forms of a word to a common base form. An example of this would be changing &quot;am&quot;, &quot;are&quot;, or &quot;is&quot; to &quot;be&quot;.<br /> <br /> '''Vector Space Model'''<br /> In this section of the paper, the authors explore the different ways in which the text can be represented on a large collection of documents. One common way of representing the documents is in the form of a bag of words. The bag of words considers the occurrences of different terms.<br /> In different text mining applications, documents are ranked and represented as vectors so as to display the significance of any word. <br /> The authors note that the three basic models used are vector space, inference network, and the probabilistic models. The vector space model is used to represent documents by converting them into vectors. In the model, a variable is used to represent each model to indicate the importance of the word in the document. <br /> <br /> The weights have 2 main models used Boolean model and TF-IDF model: <br /> '''Boolean model'''<br /> terms are assignment with a positive wij if the term appears in the document. otherwise, it will be assigned a weight of 0. <br /> <br /> '''Term Frequency - inverse document frequency (TF-IDF)'''<br /> The words are weighted using the TF-IDF scheme computed as <br /> <br /> $$<br /> q(w)=f_d(w)*\log{\frac{|D|}{f_D(w)}}<br />$$<br /> <br /> The frequency of each term is normalized by the inverse of document frequency, which helps distinct words with low frequency is recognized its importance. Each document is represented by a vector of term weights, &lt;math&gt;\omega(d) = (\omega(d, w_1), \omega(d,w_2),...,\omega(d,w_v))&lt;/math&gt;. The similarity between two documents &lt;math&gt;d_1, d_2&lt;/math&gt; is commonly measured by cosine similarity:<br /> $$<br /> S(d_1,d_2) = \cos(\theta) = \frac{d_1\cdot d_2}{\sum_{i=1}^vw^2_{1i}\cdot\sum_{i=1}^vw^2_{2i}}<br />$$<br /> <br /> == Classification ==<br /> Classification in Text Mining aims to assign predefined classes to text documents. For a set &lt;math&gt;\mathcal{D} = {d_1, d_2, ... d_n}&lt;/math&gt; of documents, each &lt;math&gt;d_i&lt;/math&gt; is mapped to a label &lt;math&gt;l_i&lt;/math&gt; from the set &lt;math&gt;\mathcal{L} = {l_1, l_2, ... l_k}&lt;/math&gt;. The goal is to find a classification model &lt;math&gt;f&lt;/math&gt; such that: &lt;math&gt;\\&lt;/math&gt;<br /> $$<br /> f: \mathcal{D} \rightarrow \mathcal{L} \quad \quad \quad f(\mathcal{d}) = \mathcal{l}<br />$$<br /> The author illustrates 4 different classifiers that are commonly used in text mining.<br /> <br /> <br /> '''1. Naive Bayes Classifier''' <br /> <br /> Bayes rule is used to classify new examples and select the class that has the generated result that occurs most often. <br /> Naive Bayes Classifier models the distribution of documents in each class using a probabilistic model assuming that the distribution<br /> of different terms is independent of each other. The models commonly used in this classifier tried to find the posterior probability of a class based on the distribution and assumes that the documents generated are based on a mixture model parameterized by &lt;math&gt;\theta&lt;/math&gt; and compute the likelihood of a document using the sum of probabilities over all mixture component. In addition, the Naive Bayes Classifier can help get around the curse of dimensionality, which may arise with high-dimensional data, such as text. <br /> <br /> '''2. Nearest Neighbour Classifier'''<br /> <br /> Nearest Neighbour Classifier uses distance-based measures to perform the classification. The documents which belong to the same class are more likely &quot;similar&quot; or close to each other based on the similarity measure. The classification of the test documents is inferred from the class labels of similar documents in the training set. K-Nearest Neighbor classification is well known to suffer from the &quot;curse of dimensionality&quot;, as the proportional volume of each $d$-sphere surrounding each datapoint compared to the volume of the sample space shrinks exponentially in $d$. <br /> <br /> '''3. Decision Tree Classifier'''<br /> <br /> A hierarchical tree of the training instances, in which a condition on the attribute value is used to divide the data hierarchically. The decision tree recursively partitions the training data set into smaller subdivisions based on a set of tests defined at each node or branch. Each node of the tree is a test of some attribute of the training instance, and each branch descending from the node corresponds to one of the values of this attribute. The conditions on the nodes are commonly defined by the terms in the text documents.<br /> <br /> '''4. Support Vector Machines'''<br /> <br /> SVM is a form of Linear Classifiers which are models that makes a classification decision based on the value of the linear combinations of the documents features. The output of a linear predictor is defined to the &lt;math&gt; y=\vec{a} \cdot \vec{x} + b&lt;/math&gt; where &lt;math&gt;\vec{x}&lt;/math&gt; is the normalized document word frequency vector, &lt;math&gt;\vec{a}&lt;/math&gt; is a vector of coefficient and &lt;math&gt;b&lt;/math&gt; is a scalar. Support Vector Machines attempts to find a linear separators between various classes. An advantage of the SVM method is it is robust to high dimensionality.<br /> <br /> == Clustering ==<br /> Clustering has been extensively studied in the context of the text as it has a wide range of applications such as visualization and document organization.<br /> <br /> Clustering algorithms are used to group similar documents and thus aid in information retrieval. Text clustering can be in different levels of granularities, where clusters can be documents, paragraphs, sentences, or terms. Since text data has numerous distance characteristics that demand the design of text-specific algorithms for the task, using a binary vector to represent the text document is simply not enough. Here are some unique properties of text representation:<br /> <br /> 1. Text representation has a large dimensionality, in which the size of the vocabulary from which the documents are drawn is massive, but a document might only contain a small number of words.<br /> <br /> 2. The words in the documents are usually correlated with each other. Need to take the correlation into consideration when designing algorithms.<br /> <br /> 3. The number of words differs from one another of the document. Thus the document needs to be normalized first before the clustering process.<br /> <br /> Three most commonly used text clustering algorithms are presented below.<br /> <br /> <br /> '''1. Hierarchical Clustering algorithms''' <br /> <br /> Hierarchical Clustering algorithms builds a group of clusters that can be depicted as a hierarchy of clusters. The hierarchy can be constructed in top-down (divisive) or bottom-up (agglomeration). Hierarchical clustering algorithms are one of the Distanced-based clustering algorithms, i.e., using a similarity function to measure the closeness between text documents.<br /> <br /> In the top-down approach, the algorithm begins with one cluster which includes all the documents. we recursively split this cluster into sub-clusters.<br /> Here is an example of a Hierarchical Clustering algorithm, the data is to be clustered by the euclidean distance. This method builds the hierarchy from the individual elements by progressively merging clusters. In our example, we have six elements {a} {b} {c} {d} {e} and {f}. The first step determines which elements to merge in a cluster by taking the two closest elements, according to the chosen distance.<br /> <br /> <br /> [[File:418px-Hierarchical clustering simple diagram.svg.png| 300px | center]]<br /> <br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Hierarchical Clustering Raw Data&lt;/div&gt;<br /> <br /> <br /> <br /> [[File:250px-Clusters.svg (1).png| 200px | center]]<br /> <br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 2: Hierarchical Clustering Clustered Data&lt;/div&gt;<br /> <br /> A main advantage of hierarchical clustering is that the algorithm only needs to be done once for any number of clusters (ie. if an individual wishes to use a different number of clusters than originally intended, they do not need to repeat the algorithm)<br /> <br /> '''2. k-means Clustering'''<br /> <br /> k-means clustering is a partitioning algorithm that partitions n documents in the context of text data into k clusters.<br /> <br /> Input: Document D, similarity measure S, number k of cluster<br /> Output: Set of k clusters<br /> Select randomly ''k'' datapoints as starting centroids<br /> While ''not converged'' do <br /> Assign documents to the centroids based on the closest similarity<br /> Calculate the cluster centroids for all clusters<br /> return ''k clusters''<br /> <br /> The main disadvantage of k-means clustering is that it is indeed very sensitive to the initial choice of the number of k. Also, since the function is run until clusters converges, k-means clustering tends to take longer to perform than hierarchical clustering. On the other hand, advantages of k-means clustering are that it is simple to implement, the algorithm scales well to large datasets, and the results are easily interpretable.<br /> <br /> <br /> '''3. Probabilistic Clustering and Topic Models'''<br /> <br /> Topic modeling is one of the most popular probabilistic clustering algorithms in recent studies. The main idea is to create a *probabilistic generative model* for the corpus of text documents. In topic models, documents are a mixture of topics, where each topic represents a probability distribution over words.<br /> <br /> There are two main topic models:<br /> * Probabilistic Latent Semantic Analysis (pLSA)<br /> * Latent Dirichlet Allocation (LDA)<br /> <br /> The paper covers LDA in more detail. LDA is a state-of-the-art unsupervised algorithm for extracting topics from a collection of documents.<br /> <br /> Given &lt;math&gt;\mathcal{D} = \{d_1, d_2, \cdots, d_{|\mathcal{D}|}\}&lt;/math&gt; is the corpus and &lt;math&gt;\mathcal{V} = \{w_1, w_2, \cdots, w_{|\mathcal{V}|}\}&lt;/math&gt; is the vocabulary of the corpus. <br /> <br /> A topic is &lt;math&gt;z_j, 1 \leq j \leq K&lt;/math&gt; is a multinomial probability distribution over &lt;math&gt;|\mathcal{V}|&lt;/math&gt; words. <br /> <br /> The distribution of words in a given document is:<br /> <br /> &lt;math&gt;p(w_i|d) = \Sigma_{j=1}^K p(w_i|z_j)p(z_j|d)&lt;/math&gt;<br /> <br /> The LDA assumes the following generative process for the corpus of &lt;math&gt;\mathcal{D}&lt;/math&gt;<br /> * For each topic &lt;math&gt;k\in \{1,2,\cdots, K\}&lt;/math&gt;, sample a word distribution &lt;math&gt;\phi_k \sim Dir(\beta)&lt;/math&gt;<br /> * For each document &lt;math&gt;d \in \{1,2,\cdots,D\}&lt;/math&gt;<br /> ** Sample a topic distribution &lt;math&gt;\theta_d \sim Dir(\alpha)&lt;/math&gt;<br /> ** For each word &lt;math&gt;w_n, n \in \{1,2,\cdots,N\}&lt;/math&gt; in document &lt;math&gt;d&lt;/math&gt;<br /> *** Sample a topic &lt;math&gt;z_i \sim Mult(\theta_d)&lt;/math&gt;<br /> *** Sample a word &lt;math&gt;w_n \sim Mult(\phi_{z_i})&lt;/math&gt;<br /> <br /> In practice, LDA is often used as a module in more complicated models and has already been applied to a wide variety of domains. In addition, many variations of LDA has been created, including supervised LDA (sLDA) and hierarchical LDA (hLDA)<br /> <br /> == Information Extraction ==<br /> Information Extraction (IE) is the process of extracting useful, structured information from unstructured or semi-structured text. It automatically extracts based on our command. <br /> <br /> For example, from the sentence “XYZ company was founded by Peter in the year of 1950”, we can identify the two following relations:<br /> <br /> 1. Founderof(Peter, XYZ)<br /> <br /> 2. Foundedin(1950, XYZ)<br /> <br /> IE is a crucial step in data mining and has a broad variety of applications, such as web mining and natural language processing. Among all the IE tasks, two have become increasingly important, which are name entity recognition and relation extraction.<br /> <br /> The author mentioned 4 parts that are important for Information Extraction<br /> <br /> '''1. Named Entity Recognition(NER)'''<br /> <br /> This is the process of identifying real-world entity from free text, such as &quot;Apple Inc.&quot;, &quot;Donald Trump&quot;, &quot;PlayStation 5&quot; etc. Moreover, the task is to identify the category of these entities, such as &quot;Apple Inc.&quot; is in the category of the company, &quot;Donald Trump&quot; is in the category of the USA president, and &quot;PlayStation 5&quot; is in the category of the entertainment system. <br /> <br /> '''2. Hidden Markov Model'''<br /> <br /> Since traditional probabilistic classification does not consider the predicted labels of neighbor words, we use the Hidden Markov Model when doing Information Extraction. This model is different because it considers that the label of one word depends on the previous words that appeared. The Hidden Markov model allows us to model the situation, given a sequence of labels &lt;math&gt; Y= (y_1, y_2, \cdots, y_n) &lt;/math&gt;and sequence of observations &lt;math&gt; X= (x_1, x_2, \cdots, x_n) &lt;/math&gt; we get<br /> <br /> &lt;center&gt;<br /> &lt;math&gt;<br /> y_i \sim p(y_i|y_{i-1}) \qquad x_i \sim p(x_i|x_{i-1})<br /> &lt;/math&gt;<br /> &lt;/center&gt;<br /> <br /> '''3. Conditional Random Fields'''<br /> <br /> This is a technique that is widely used in Information Extraction. The definition of it is related to graph theory. <br /> let G = (V, E) be a graph and Yv stands for the index of the vertices in G. Then (X, Y) is a conditional random field, when the random variables Yv, conditioned on X, obey Markov property with respect to the graph, and:<br /> &lt;math&gt;p(Y_v |X, Y_w ,w , v) = p(Y_v |X, Y_w ,w ∼ v)&lt;/math&gt;, where w ∼ v means w and v are neighbors in G.<br /> <br /> '''4. Relation Extraction'''<br /> <br /> This is a task of finding semantic relationships between word entities in text documents, for example in a sentence such as &quot;Seth Curry is the brother of Stephen Curry&quot;. If there is a document including these two names, the task is to identify the relationship of these two entities. There are currently numerous techniques to perform relation extraction, but the most common is to consider it a classification problem. The problem is structured as, given two entities in that occur in a sentence classify their relation into fixed relation types.<br /> <br /> == Biomedical Application ==<br /> <br /> Text mining has several applications in the domain of biomedical sciences. The explosion of academic literature in the field has made it quite hard for scientists to keep up with novel research. This is why text mining techniques are ever so important in making the knowledge digestible.<br /> <br /> The text mining techniques are able to extract meaningful information from large data by making use of biomedical ontology, which is a compilation of a common set of terms used in an area of knowledge. The Unified Medical Language System (UMLS) is the most comprehensive such resource, consisting of definitions of biomedical jargon. Several information extraction algorithms rely on the ontology to perform tasks such as Named Entity Recognition (NER) and Relation Extraction.<br /> <br /> NER involves locating and classifying biomedical entities into meaningful categories and assigning semantic representation to those entities. The NER methods can be broadly grouped into Dictionary-based, Rule-based, and Statistical approaches. NER tasks are challenging in the biomedical domain due to three key reasons: (1) There is a continuously growing volume of semantically related entities in the biomedical domain due to continuous scientific progress, so NER systems depend on dictionaries of terms which can never be complete; (2) There are often numerous names for the same concept in the biomedical domain, such as &quot;heart attack&quot; and &quot;myocardial infarction&quot;; and (3) Acronyms and abbreviations are frequently used which makes it complicated to identify the concepts these terms express.<br /> <br /> Relation extraction, on the other hand, is the process of determining relationships between the entities. This is accomplished mainly by identifying the correlation between entities through analyzing the frequency of terms, as well as rules defined by domain experts. Moreover, modern algorithms are also able to summarize large documents and answer natural language questions posed by humans.<br /> <br /> Summarization is a common biomedical text mining task that largely utilizes information extraction tasks. The idea is the automatically identify significant aspects of documents and represent them in a coherent fashion. However, evaluating summarization methods becomes very difficult since deciding whether a summary is &quot;good&quot; is often subjective, although there are some automatic evaluation techniques for summaries such as ROUGE (Recall-Oriented Understudy for Gisting Evaluation), which compares automatically generated summaries with those created by humans.<br /> <br /> == Conclusion ==<br /> <br /> This paper gave a holistic overview of the methods and applications of text mining, particularly its relevance in the biomedical domain. It highlights several popular algorithms and summarizes them along with their advantages, limitations and some potential situations where they could be used. Because of ever-growing data, for example, the very high volume of scientific literature being produced every year, the interest in this field is massive and is bound to grow in the future.<br /> <br /> == Critiques==<br /> <br /> This is a very detailed approach to introduce some different algorithms on text mining. Since many algorithms are given, it might be a good idea to compare their performances on text mining by training them on some text data and compare them to the former baselines, to see if there exists any improvement.<br /> <br /> it is a detailed summary of the techniques used in text mining. It would be more helpful if some dataset can be included for training and testing. The algorithms were grouped by different topics so that different datasets and measurements are required.<br /> <br /> It would be better for the paper to include test accuracy for testing and training sets to support text mining is a more efficient and effective algorithm compared to other techniques. Moreover, this paper mentioned Text Mining approach can be used to extract high-quality information from videos. It is to believe that extracting from videos is much more difficult than images and texts. How is it possible to retain its test accuracy at a good level for videos?<br /> <br /> Preprocessing an important step to analyze text, so it might be better to have the more details about that. For example, what types of words are usually removed and show we record the relative position of each word in the sentence. If one close related sentences were split into two sentences, how can we capture their relations?<br /> <br /> The authors could give more details on the applications of text mining in the healthcare and biomedical domain. For example, how could preprocessing, classification, clustering, and information extraction process be applied to this domain. Other than introduction of existing algorithms (e.g. NER), authors can provide more information about how they performs (with a sample dataset), what are their limitations, and comparisons among different algorithms.<br /> <br /> In the preprocessing section, it seems like the authors incorrectly describe what stemming is - stemming just removes the last few letters of a word (ex. studying -&gt; study, studies -&gt; studi). What the authors actually describe is lemmatization which is much more informative than stemming. The down side of lemmatization is that it takes more effort to build a lemmatizer than a stemmer and even once it is built it is slow in comparison with a stemmer.<br /> <br /> One of the challenges of text mining in the biomedical field is that a lot of patient data are still in the form of paper documents. Text mining can speed up the digitization of patient data and allow for the development of disease diagnosis algorithms. It'll be interesting to see how text mining can be integrated with healthcare AI such as the doppelganger algorithm to enhance question answering accuracy. (Cresswell et al, 2018)<br /> <br /> It might be helpful if the authors discuss more about the accuracy-wise performances of some text mining techniques, especially in the healthcare and biomedical domain, given the focus. It would be interesting if more information were provided about the level of accuracy needed in order to produce reliable and actionable information in such fields. Also, in these domains, sometimes a false negative could be more harmful than a false positive, such as a clinical misdiagnosis. It might be helpful to discuss a bit more about how to combats such issues in text mining.<br /> <br /> This is a survey paper that talks about many general aspects about text mining, without going into any specific one in detail. Overall it's interesting. My first feedback is on the &quot;Information Retrieval&quot; section of the paper. Hidden markov model is mentioned as one of the algorithms used for IR. Yet, hidden markov makes the strong assumption that given the current state, next state is independent of all the previous states. This is a very strong assumption to make in IR, as words in a sentence usually have a very strong connection to each other. This limitation should be discussed more extensively in the paper. Also, the overall structure of the paper seems to be a bit imbalanced. It solely talks about IR's application in biomedical sciences. Yet, IR has application in many different areas and subjects.<br /> <br /> This paper surveys through multiple methods and algorithms on test mining, more specifically, information extraction, test classification, and clustering. In the Information Extraction section, four possible methods are mentioned to deal with different examples of semantic texts. In the latest studies of machine learning, it is ubiquitous to see multiple methods or algorithms are combined together to achieve better performances. For a survey paper, it will be more interesting to see some connections between the four methods, and some insights such as how we can boost the accuracy of extracting precise information by combining 2 of the 4 methods together.<br /> <br /> The summary is well-organized and gives enough information to first-time readers about text mining and different algorithms to model the data and predict using different classifiers. However, it would be better to add comparison between each classifier since the performance is important to know.<br /> <br /> == References ==<br /> <br /> Allahyari, M., Pouriyeh, S., Assefi, M., Safaei, S., Trippe, E. D., Gutierrez, J. B., &amp; Kochut, K. (2017). A brief survey of text mining: Classification, clustering, and extraction techniques. arXiv preprint arXiv:1707.02919.<br /> <br /> Cresswell, Kathrin &amp; Cunningham-Burley, Sarah &amp; Sheikh, Aziz. (2018). Healthcare robotics � a qualitative exploration of key challenges and future directions (Preprint). Journal of Medical Internet Research. 20. 10.2196/10410.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Research_Papers_Classification_System&diff=49225 Research Papers Classification System 2020-12-05T18:04:34Z <p>Sh68lee: /* Critique */</p> <hr /> <div>= Presented by =<br /> Jill Wang, Junyi (Jay) Yang, Yu Min (Chris) Wu, Chun Kit (Calvin) Li<br /> <br /> = Introduction =<br /> With the increasing advance of computer science and information technology, there is an increasingly overwhelming number of papers that have been published. Because of the mass number of papers, it has become incredibly hard to find and categorize papers. This paper introduces a paper classification system that utilizes the Term Frequency-Inverse Document Frequency (TF-IDF), Latent Dirichlet Allocation (LDA), and K-means clustering. The most important technology the system used to process big data is the Hadoop Distributed File System (HDFS). The system can handle quantitatively complex research paper classification problems efficiently and accurately.<br /> <br /> ===General Framework===<br /> <br /> The paper classification system classifies research papers based on the abstracts given that the core of most papers is presented in the abstracts. <br /> <br /> [[ File:Systemflow.png |right|image on right| 400px]]<br /> &lt;ol&gt;&lt;li&gt;Paper Crawling <br /> &lt;p&gt;Collects abstracts from research papers published during a given period&lt;/p&gt;&lt;/li&gt;<br /> &lt;li&gt;Preprocessing<br /> &lt;p&gt; &lt;ol style=&quot;list-style-type:lower-alpha&quot;&gt;&lt;li&gt;Removes stop words in the papers crawled, in which only nouns are extracted from the papers&lt;/li&gt;<br /> &lt;li&gt;generates a keyword dictionary, keeping only the top-N keywords with the highest frequencies&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/p&gt;&lt;/li&gt; <br /> &lt;li&gt;Topic Modelling<br /> &lt;p&gt; Use the LDA to group the keywords into topics&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;Paper Length Calculation<br /> &lt;p&gt; Calculates the total number of occurrences of words to prevent an unbalanced TF values caused by the various length of abstracts using the map-reduce algorithm&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;Word Frequency Calculation<br /> &lt;p&gt; Calculates the Term Frequency (TF) values which represent the frequency of keywords in a research paper&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;Document Frequency Calculation<br /> &lt;p&gt; Calculates the Document Frequency (DF) values which represents the frequency of keywords in a collection of research papers. The higher the DF value, the lower the importance of a keyword.&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;TF-IDF calculation<br /> &lt;p&gt; Calculates the inverse of the DF which represents the importance of a keyword.&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;Paper Classification<br /> &lt;p&gt; Classify papers by topics using the K-means clustering algorithm.&lt;/p&gt;<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> <br /> <br /> ===Technologies===<br /> <br /> The HDFS with a Hadoop cluster composed of one master node, one sub-node, and four data nodes is what is used to process the massive paper data. Hadoop-2.6.5 version in Java is what is used to perform the TF-IDF calculation. Spark MLlib is what is used to perform the LDA. The Scikit-learn library is what is used to perform the K-means clustering.<br /> <br /> ===HDFS===<br /> <br /> Hadoop Distributed File System(HDFS) was used to process big data in this system. HFDS has been shown to process big data rapidly and stably with high scalability which makes it a perfect choice for this problem. What Hadoop does is to break a big collection of data into different partitions and pass each partition to one individual processor. Each processor will only have information about the partition of data it has received.<br /> <br /> '''In this summary, we are going to focus on introducing the main algorithms of what this system uses, namely LDA, TF-IDF, and K-Means.'''<br /> <br /> =Data Preprocessing=<br /> ===Crawling of Abstract Data===<br /> <br /> Under the assumption that audiences tend to first read the abstract of a paper to gain an overall understanding of the material, it is reasonable to assume the abstract section includes “core words” that can be used to effectively classify a paper's subject.<br /> <br /> An abstract is crawled to have its stop words removed. Stop words are words that are usually ignored by search engines, such as “the”, “a”, and etc. Afterward, nouns are extracted, as a more condensed representation for efficient analysis.<br /> <br /> This is managed on HDFS. The TF-IDF value of each paper is calculated through map-reduce.<br /> <br /> ===Managing Paper Data===<br /> <br /> To construct an effective keyword dictionary using abstract data and keywords data in all of the crawled papers, the authors categorized keywords with similar meanings using a single representative keyword. The approach is called stemming, which is common in cleaning data, where words are reduced to their word stem. An example is &quot;running&quot; and &quot;ran&quot; would be reduced to &quot;run&quot;. 1394 keyword categories are extracted, which is still too much to compute. Hence, only the top 30 keyword categories are used.<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:table_1_kswf.JPG|700px]]&lt;/div&gt;<br /> <br /> =Topic Modeling Using LDA=<br /> <br /> Latent Dirichlet allocation (LDA) is a generative probabilistic model that views documents as random mixtures over latent topics. Each topic is a distribution over words, and the goal is to extract these topics from documents.<br /> <br /> LDA estimates the topic-word distribution &lt;math&gt;P\left(t | z\right)&lt;/math&gt; (probability of word &quot;z&quot; having topic &quot;t&quot;) and the document-topic distribution &lt;math&gt;P\left(z | d\right)&lt;/math&gt; (probability of finding word &quot;z&quot; within a given document &quot;d&quot;) using Dirichlet priors for the distributions with a fixed number of topics. For each document, obtain a feature vector:<br /> <br /> $F = \left( P\left(z_1 | d\right), P\left(z_2 | d\right), \cdots, P\left(z_k | d\right) \right)$<br /> <br /> In the paper, authors extract topics from preprocessed paper to generate three kinds of topic sets, each with 10, 20, and 30 topics respectively. The following is a table of the 10 topic sets of highest frequency keywords.<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:table_2_tswtebls.JPG|700px]]&lt;/div&gt;<br /> <br /> <br /> ===LDA Intuition===<br /> <br /> LDA uses the Dirichlet priors of the Dirichlet distribution, which allows the algorithm to model a probability distribution ''over prior probability distributions of words and topics''. The following picture illustrates 2-simplex Dirichlet distributions with different alpha values, one for each corner of the triangles. <br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:dirichlet_dist.png|700px]]&lt;/div&gt;<br /> <br /> Simplex is a generalization of the notion of a triangle. In Dirichlet distribution, each parameter will be represented by a corner in simplex, so adding additional parameters implies increasing the dimensions of simplex. As illustrated, when alphas are smaller than 1 the distribution is dense at the corners. When the alphas are greater than 1 the distribution is dense at the centers.<br /> <br /> The following illustration shows an example LDA with 3 topics, 4 words and 7 documents.<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:LDA_example.png|800px]]&lt;/div&gt;<br /> <br /> In the left diagram, there are three topics, hence it is a 2-simplex. In the right diagram there are four words, hence it is a 3-simplex. LDA essentially adjusts parameters in Dirichlet distributions and multinomial distributions (represented by the points), such that, in the left diagram, all the yellow points representing documents and, in the right diagram, all the points representing topics, are as close to a corner as possible. In other words, LDA finds topics for documents and also finds words for topics. At the end topic-word distribution &lt;math&gt;P\left(t | z\right)&lt;/math&gt; and the document-topic distribution &lt;math&gt;P\left(z | d\right)&lt;/math&gt; are produced.<br /> <br /> =Term Frequency Inverse Document Frequency (TF-IDF) Calculation=<br /> <br /> TF-IDF is widely used to evaluate the importance of a set of words in the fields of information retrieval and text mining. It is a combination of term frequency (TF) and inverse document frequency (IDF). The idea behind this combination is<br /> * It evaluates the importance of a word within a document, and<br /> * It evaluates the importance of the word among the collection of all documents<br /> <br /> The inverse of the document frequency accounts for the fact that term frequency will naturally increase as document frequency increases. Thus IDF is needed to counteract a word's TF to give an accurate representation of a word's importance.<br /> <br /> The TF-IDF formula has the following form:<br /> <br /> $TF-IDF_{i,j} = TF_{i,j} \times IDF_{i}$<br /> <br /> where i stands for the &lt;math&gt;i^{th}&lt;/math&gt; word and j stands for the &lt;math&gt;j^{th}&lt;/math&gt; document.<br /> <br /> ===Term Frequency (TF)===<br /> <br /> TF evaluates the percentage of a given word in a document. Thus, TF value indicates the importance of a word. The TF has a positive relation with the importance.<br /> <br /> In this paper, we only calculate TF for words in the keyword dictionary obtained. For a given keyword i, &lt;math&gt;TF_{i,j}&lt;/math&gt; is the number of times word i appears in document j divided by the total number of words in document j.<br /> <br /> The formula for TF has the following form:<br /> <br /> $TF_{i,j} = \frac{n_{i,j} }{\sum_k n_{k,j} }$<br /> <br /> where i stands for the &lt;math&gt;i^{th}&lt;/math&gt; word, j stands for the &lt;math&gt;j^{th}&lt;/math&gt; document, &lt;math&gt;n_{i,j}&lt;/math&gt; stands for the number of times words &lt;math&gt;t_i&lt;/math&gt; appear in document &lt;math&gt;d_j&lt;/math&gt; and &lt;math&gt;\sum_k n_{k,j} &lt;/math&gt; stands for total number of occurence of words in document &lt;math&gt;d_j&lt;/math&gt;.<br /> <br /> Note that the denominator is the total number of words remaining in document j after crawling.<br /> <br /> ===Document Frequency (DF)===<br /> <br /> DF evaluates the percentage of documents that contain a given word over the entire collection of documents. Thus, the higher DF value is, the less important the word is.<br /> <br /> &lt;math&gt;DF_{i}&lt;/math&gt; is the number of documents in the collection with word i divided by the total number of documents in the collection. The formula for DF has the following form:<br /> <br /> $DF_{i} = \frac{|d_k \in D: n_{i,k} &gt; 0|}{|D|}$<br /> <br /> where &lt;math&gt;n_{i,k}&lt;/math&gt; is the number of times word i appears in document k, |D| is the total number of documents in the collection.<br /> <br /> Since DF and the importance of the word have an inverse relation, we use inverse document frequency (IDF) instead of DF.<br /> <br /> ===Inverse Document Frequency (IDF)===<br /> <br /> In this paper, IDF is calculated in a log scale. Since we will receive a large number of documents, i.e, we will have a large |D|<br /> <br /> The formula for IDF has the following form:<br /> <br /> $IDF_{i} = log\left(\frac{|D|}{|\{d_k \in D: n_{i,k} &gt; 0\}|}\right)$<br /> <br /> As mentioned before, we will use HDFS. The actual formula applied is:<br /> <br /> $IDF_{i} = log\left(\frac{|D|+1}{|\{d_k \in D: n_{i,k} &gt; 0\}|+1}\right)$<br /> <br /> The inverse document frequency gives a measure of how rare a certain term is in a given document corpus.<br /> <br /> =Paper Classification Using K-means Clustering=<br /> <br /> The K-means clustering is an unsupervised classification algorithm that groups similar data into the same class. It is an efficient and simple method that can be applied to different types of data attributes. It is also flexible enough to handle various kinds of noise and outliers.<br /> &lt;br&gt;<br /> <br /> Given a set of &lt;math&gt;d&lt;/math&gt; by &lt;math&gt;n&lt;/math&gt; dataset &lt;math&gt;\mathbf{X} = \left[ \mathbf{x}_1 \cdots \mathbf{x}_n \right]&lt;/math&gt;, the algorithm will assign each &lt;math&gt;\mathbf{x}_j&lt;/math&gt; into &lt;math&gt;k&lt;/math&gt; different clusters based on the characteristics of &lt;math&gt;\mathbf{x}_j&lt;/math&gt; itself.<br /> &lt;br&gt;<br /> <br /> Moreover, when assigning data into a cluster, the algorithm will also try to minimise the distances between the data and the centre of the cluster which the data belongs to. That is, k-means clustering will minimize the sum of square error:<br /> <br /> \begin{align*}<br /> min \sum_{i=1}^{k} \sum_{j \in C_i} ||x_j - \mu_i||^2<br /> \end{align*}<br /> <br /> where<br /> &lt;ul&gt;<br /> &lt;li&gt;&lt;math&gt;k&lt;/math&gt;: the number of clusters&lt;/li&gt;<br /> &lt;li&gt;&lt;math&gt;C_i&lt;/math&gt;: the &lt;math&gt;i^th&lt;/math&gt; cluster&lt;/li&gt;<br /> &lt;li&gt;&lt;math&gt;x_j&lt;/math&gt;: the &lt;math&gt;j^th&lt;/math&gt; data in the &lt;math&gt;C_i&lt;/math&gt;&lt;/li&gt;<br /> &lt;li&gt;&lt;math&gt;mu_i&lt;/math&gt;: the centroid of &lt;math&gt;C_i&lt;/math&gt;&lt;/li&gt;<br /> &lt;li&gt;&lt;math&gt;||x_j - \mu_i||^2&lt;/math&gt;: the Euclidean distance between &lt;math&gt;x_j&lt;/math&gt; and &lt;math&gt;\mu_i&lt;/math&gt;&lt;/li&gt;<br /> &lt;/ul&gt;<br /> &lt;br&gt;<br /> <br /> K-means Clustering algorithm - an unsupervised algorithm- is chosen because of its advantages to deal with different types of attributes, to run with minimal requirement of domain knowledge, to deal with noise and outliers, to realize clusters with similarities. <br /> <br /> <br /> Since the goal for this paper is to classify research papers and group papers with similar topics based on keywords, the paper uses the K-means clustering algorithm. The algorithm first computes the cluster centroid for each group of papers with a specific topic. Then, it will assign a paper into a cluster based on the Euclidean distance between the cluster centroid and the paper’s TF-IDF value.<br /> &lt;br&gt;<br /> <br /> However, different values of &lt;math&gt;k&lt;/math&gt; (the number of clusters) will return different clustering results. Therefore, it is important to define the number of clusters before clustering. For example, in this paper, the authors choose to use the Elbow scheme to determine the value of &lt;math&gt;k&lt;/math&gt;. The Elbow scheme is a somewhat subjective way of choosing an optimal &lt;math&gt;k&lt;/math&gt; that involves plotting the average of the squared distances from the cluster centers of the respective clusters (distortion) as a function of &lt;math&gt;k&lt;/math&gt; and choosing a &lt;math&gt;k&lt;/math&gt; at which point the decrease in distortion is outweighed by the increase in complexity. Also, to measure the performance of clustering, the authors decide to use the Silhouette scheme. The results of clustering are validated if the Silhouette scheme returns a value greater than &lt;math&gt;0.5&lt;/math&gt;.<br /> <br /> =System Testing Results=<br /> <br /> In this paper, the dataset has 3264 research papers from the Future Generation Computer System (FGCS) journal between 1984 and 2017. For constructing keyword dictionaries for each paper, the authors have introduced three methods as shown below:<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:table_3_tmtckd.JPG|700px]]&lt;/div&gt;<br /> <br /> <br /> Then, the authors use the Elbow scheme to define the number of clusters for each method with different numbers of keywords before running the K-means clustering algorithm. The results are shown below:<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:table_4_nocobes.JPG|700px]]&lt;/div&gt;<br /> <br /> According to Table 4, there is a positive correlation between the number of keywords and the number of clusters. In addition, method 3 combines the advantages for both method 1 and method 2; thus, method 3 requires the least clusters in total. On the other hand, the wrong keywords might be presented in papers; hence, it might not be possible to group papers with similar subjects correctly by using method 1 and so method 1 needs the most number of clusters in total.<br /> <br /> <br /> Next, the Silhouette scheme had been used for measuring the performance for clustering. The average of the Silhouette values for each method with different numbers of keywords are shown below:<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:table_5_asv.JPG|700px]]&lt;/div&gt;<br /> <br /> Since the clustering is validated if the Silhouette’s value is greater than 0.5, for methods with 10 and 30 keywords, the K-means clustering algorithm produces good results.<br /> <br /> <br /> To evaluate the accuracy of the classification system in this paper, the authors use the F-Score. The authors execute 5 times of experiment and use 500 randomly selected research papers for each trial. The following histogram shows the average value of F-Score for the three methods and different numbers of keywords:<br /> <br /> &lt;div align=&quot;center&quot;&gt;[[File:fig_16_fsvotm.JPG|700px]]&lt;/div&gt;<br /> <br /> Note that “TFIDF” means method 1, “LDA” means method 2, and “TFIDF-LDA” means method 3. The number 10, 20, and 30 after each method is the number of keywords the method has used.<br /> According to the histogram above, method 3 has the highest F-Score values than the other two methods with different numbers of keywords. Therefore, the classification system is most accurate when using method 3 as it combines the advantages for both method 1 and method 2.<br /> <br /> =Conclusion=<br /> <br /> This paper introduces a classification system that classifies research papers into different topics by using TF-IDF and LDA scheme with K-means clustering algorithm. The experimental results showed that the proposed system can classify the papers with similar subjects according to the keywords extracted from the abstracts of papers. This system allows users to search the papers they want quickly and with the most productivity.<br /> <br /> Furthermore, this classification system might be also used in different types of texts (e.g. documents, tweets, etc.) instead of only classifying research papers.<br /> <br /> =Critique=<br /> <br /> In this paper, DF values are calculated within each partition. This results that for each partition, DF value for a given word will vary and may have an inconsistent result for different partition methods. As mentioned above, there might be a divide by zero problem since some partitions do not have documents containing a given word, but this can be solved by introducing a dummy document as the authors did. Another method that might be better at solving inconsistent results and the divide by zero problems is to have all partitions to communicate with their DF value. Then pass the merged DF value to all partitions to do the final IDF and TF-IDF value. Having all partitions to communicate with the DF value will guarantee a consistent DF value across all partitions and helps avoid a divide by zero problem as words in the keyword dictionary must appear in some documents in the whole collection.<br /> <br /> This paper treated the words in the different parts of a document equivalently, it might perform better if it gives different weights to the same word in different parts. For example, if a word appears in the title of the document, it usually shows it's a main topic of this document so we can put more weight on it to categorize.<br /> <br /> When discussing the potential processing advantages of this classification system for other types of text samples, has the effect of processing mixed samples (text and image or text and video) taken into consideration? IF not, in terms of text classification only, does it have an overwhelming advantage over traditional classification models?<br /> <br /> The preprocessing should also include &lt;math&gt;n&lt;/math&gt;-gram tokenization for topic modelling because some topics are inherently two words, such as machine learning where if it is seen separately, it implies different topics.<br /> <br /> This system is very compute-intensive due to the large volumes of dictionaries that can be generated by processing large volumes of data. It would be nice to see how much data HDFS had to process and similarly how much time was saved by using Hadoop for data processing as opposed to centralized approach.<br /> <br /> This system can be improved further in terms of computation times by utilizing other big data framework MapReduce, that can also use HDFS, by parallelizing their computation across multiple nodes for K-means clustering as discussed in (Jin, et al) .<br /> <br /> It's not exactly clear what method 3 (TFIDF-LDA) is doing, how is it performing TF-IDF on the topics? Also it seems like the preprocessing step only keeps 10/20/30 top words? This seems like an extremely low number especially in comparison with the LDA which has 10/20/30 topics - what is the reason for so strongly limiting the number of words? It would also be interesting to see if both key words and topics are necessary - an ablation study showing the significance of both would be interesting.<br /> <br /> It is better if the paper has an example with some topics on some research papers. Also it is better if we can visualize the distance between each research paper and the topic names<br /> <br /> I am interested in the first step of the general framework, which is the Paper Crawling step. Many conferences actually require the authors to indicate several key words that best describe a paper. For example, a database paper may have keywords such as &quot;large-scale database management&quot;, &quot;information retrieval&quot;, and &quot;relational table mining&quot;. So in addition to crawling text from abstract, it may be more effective to crawl these keywords directly. Not only does this require less time, these keywords may also lead to better performance than the nouns extracted from the abstract section. I am also slightly concerned about the claim made in the paper that &quot;Our methodologies can be applied to text outside of research papers&quot;. Research papers are usually carefully revised and well-structured. Extending the algorithm described in the paper to any kind of free-text could be difficult in practice.<br /> <br /> It would be better if the author could provide some application or example of the research algorithm in the real world. It would be helpful for the readers to understand the algorithm.<br /> <br /> The summary clearly goes through the model framework well, starting from data-preprocessing, prediction, and testing. It can be enhanced by applying this model to other similar use-cases and how well the prediction goes.<br /> <br /> =References=<br /> <br /> Blei DM, el. (2003). Latent Dirichlet allocation. J Mach Learn Res 3:993–1022<br /> <br /> Gil, JM, Kim, SW. (2019). Research paper classification systems based on TF-IDF and LDA schemes. ''Human-centric Computing and Information Sciences'', 9, 30. https://doi.org/10.1186/s13673-019-0192-7<br /> <br /> Liu, S. (2019, January 11). Dirichlet distribution Motivating LDA. Retrieved November 2020, from https://towardsdatascience.com/dirichlet-distribution-a82ab942a879<br /> <br /> Serrano, L. (Director). (2020, March 18). Latent Dirichlet Allocation (Part 1 of 2) [Video file]. Retrieved 2020, from https://www.youtube.com/watch?v=T05t-SqKArY<br /> <br /> Jin, Cui, Yu. (2016). A New Parallelization Method for K-means. https://arxiv.org/ftp/arxiv/papers/1608/1608.06347.pdf</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Speech2Face:_Learning_the_Face_Behind_a_Voice&diff=49224 Speech2Face: Learning the Face Behind a Voice 2020-12-05T17:57:31Z <p>Sh68lee: /* Discussion and Critiques */</p> <hr /> <div>== Presented by == <br /> Ian Cheung, Russell Parco, Scholar Sun, Jacky Yao, Daniel Zhang<br /> <br /> == Introduction ==<br /> This paper presents a deep neural network architecture called Speech2Face. This architecture utilizes millions of Internet/Youtube videos of people speaking to learn the correlation between a voice and the respective face. The model learns the correlations, allowing it to produce facial reconstruction images that capture specific physical attributes, such as a person's age, gender, or ethnicity, through a self-supervised procedure. Namely, the model utilizes the simultaneous occurrence of faces and speech in videos and does not need to model the attributes explicitly. This model explores what types of facial information could be extracted from speech without the constraints of predefined facial characterizations. Without any prior information or accurate classifiers, the reconstructions revealed correlations between craniofacial features and voice in addition to the correlation between dominant features (gender, age, ethnicity, etc.) and voice. The model is evaluated and numerically quantifies how closely the reconstruction, done by the Speech2Face model, resembles the true face images of the respective speakers.<br /> <br /> == Ethical Considerations ==<br /> <br /> The authors note that due to the potential sensitivity of facial information, they have chosen to explicitly state some ethical considerations. The first of which is privacy. The paper states that the method cannot recover the true identity of the face or produce faces of specific individuals, but rather will show average-looking faces. The paper also addresses that there are potential dataset biases that exist for the voice-face correlations, thus the faces may not accurately represent the intended population. Finally, it acknowledges that the model uses demographic categories that are defined by a commercial face attribute classifier.<br /> <br /> == Previous Work ==<br /> With visual and audio signals being so dominant and accessible in our daily life, there has been huge interest in how visual and audio perceptions interact with each other. Arandjelovic and Zisserman  leveraged the existing database of mp4 files to learn a generic audio representation to classify whether a video frame and an audio clip correspond to each other. These learned audio-visual representations have been used in a variety of setting, including cross-modal retrieval, sound source localization and sound source separation. This also paved the path for specifically studying the association between faces and voices of agents in the field of computer vision. In particular, cross-modal signals extracted from faces and voices have been proposed as a binary or multi-task classification task and there have been some promising results. Studies have been able to identify active speakers of a video, separate speech from multiple concurrent sources, predict lip motion from speech, and even learn the emotion of the agents based on their voices. Aytar et al.  proposed a student-teacher training procedure in which a well established visual recognition model was used to transfer the knowledge obtained in the visual modality to the sound modality, using unlabeled videos.<br /> <br /> Recently, various methods have been suggested to use various audio signals to reconstruct visual information, where the reconstructed subject is subjected to a priori. Notably, Duarte et al.  were able to synthesize the exact face images and expression of an agent from speech using a GAN model. A generative adversarial network (GAN) model is one that uses a generator to produce seemingly possible data for training and a discriminator that identifies if the training data is fabricated by the generator or if it is real . This paper instead hopes to recover the dominant and generic facial structure from a speech.<br /> <br /> == Motivation ==<br /> It seems to be a common trait among humans to imagine what some people look like when we hear their voices before we have seen what they look lke. There is a strong connection between speech and appearance, which is a direct result of the factors that affect speech, including age, gender, and facial bone structure. In addition, other voice-appearance correlations stem from the way in which we talk: language, accent, speed, pronunciations, etc. These properties of speech are often common among many different nationalities and cultures, which can, in turn, translate to common physical features among different voices. Namely, from an input audio segment of a person speaking, the method would reconstruct an image of the person’s face in a canonical form (frontal-facing, neutral expression). The goal was to study to what extent people can infer how someone else looks from the way they talk. Rather than predicting a recognizable image of the exact face, the authors were more interested in capturing the dominant facial features.<br /> <br /> == Model Architecture == <br /> <br /> '''Speech2Face model and training pipeline'''<br /> <br /> [[File:ModelFramework.jpg|center]]<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Figure 1. '''Speech2Face model and training pipeline''' &lt;/div&gt;<br /> <br /> <br /> <br /> The Speech2Face Model used to achieve the desired result consists of two parts - a voice encoder which takes in a spectrogram of speech as input and outputs low dimensional face features, and a face decoder which takes in face features as input and outputs a normalized image of a face (neutral expression, looking forward). Figure 1 gives a visual representation of the pipeline of the entire model, from video input to a recognizable face. The combination of the voice encoder and face decoder results are combined to form an image. The variability in facial expressions, head positions and lighting conditions of the face images creates a challenge to both the design and training of the Speech2Face model. It needs a model to figure out many irrelevant variations in the data, and to implicitly extract important internal representations of faces. To avoid this problem the model is trained to first regress to a low dimensional intermediate representation of the face. <br /> <br /> '''Face Decoder''' <br /> The face decoder itself was taken from previous work The VGG-Face model by Cole et al  (a face recognition model that is pretrained on a largescale face database  is used to extract a 4069-D face feature from the penultimate layer of the network.) and will not be explored in great detail here, but in essence the facenet model is combined with a single multilayer perceptron layer, the result of which is passed through a convolutional neural network to determine the texture of the image, and a multilayer perception to determine the landmark locations. The face decoder kept the VGG-Face model's dimension and weights. The weights were also trained separately and remained fixed during the voice encoder training. <br /> <br /> '''Voice Encoder Architecture''' <br /> <br /> [[File:VoiceEncoderArch.JPG|center]]<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Table 1: '''Voice encoder architecture''' &lt;/div&gt;<br /> <br /> <br /> <br /> The voice encoder itself is a convolutional neural network, which transforms the input spectrogram into pseudo face features. The exact architecture is given in Table 1. The model alternates between convolution, ReLU, batch normalization layers, and layers of max-pooling. In each max-pooling layer, pooling is only done along the temporal dimension of the data. This is to ensure that the frequency, an important factor in determining vocal characteristics such as tone, is preserved. In the final pooling layer, an average pooling is applied along the temporal dimension. This allows the model to aggregate information over time and allows the model to be used for input speeches of varying lengths. Two fully connected layers at the end are used to return a 4096-dimensional facial feature output.<br /> <br /> '''Training'''<br /> <br /> The AVSpeech dataset, a large-scale audio-visual dataset is used for the training. AVSpeech dataset is comprised of millions of video segments from Youtube with over 100,000 different people. The training data is composed of educational videos and does not provide an accurate representation of the global population, which will clearly affect the model. Also note that facial features that are irrelevant to speech, like hair color, may be predicted by the model. From each video, a 224x224 pixels image of the face was passed through the face decoder to compute a facial feature vector. Combined with a spectrogram of the audio, a training and test set of 1.7 and 0.15 million entries respectively were constructed.<br /> <br /> The voice encoder is trained in a self-supervised manner. A frame that contains the face is extracted from each video and then inputted to the VGG-Face model to extract the feature vector &lt;math&gt;v_f&lt;/math&gt;, the 4096-dimensional facial feature vector given by the face decoder on a single frame from the input video. This provides the supervision signal for the voice-encoder. The feature &lt;math&gt;v_s&lt;/math&gt;, the 4096 dimensional facial feature vector from the voice encoder, is trained to predict &lt;math&gt;v_f&lt;/math&gt;.<br /> <br /> In order to train this model, a proper loss function must be defined. The L1 norm of the difference between &lt;math&gt;v_s&lt;/math&gt; and &lt;math&gt;v_f&lt;/math&gt;, given by &lt;math&gt;||v_f - v_s||_1&lt;/math&gt;, may seem like a suitable loss function, but in actuality results in unstable results and long training times. Figure 2, below, shows the difference in predicted facial features given by &lt;math&gt;||v_f - v_s||_1&lt;/math&gt; and the following loss. Based on the work of Castrejon et al. , a loss function is used which penalizes the differences in the last layer of the VGG-Face model &lt;math&gt;f_{VGG}&lt;/math&gt;: &lt;math&gt; \mathbb{R}^{4096} \to \mathbb{R}^{2622}&lt;/math&gt; and the first layer of face decoder &lt;math&gt;f_{dec}&lt;/math&gt; : &lt;math&gt; \mathbb{R}^{4096} \to \mathbb{R}^{1000}&lt;/math&gt;. The final loss function is given by: $$L_{total} = ||f_{dec}(v_f) - f_{dec}(v_s)|| + \lambda_1||\frac{v_f}{||v_f||} - \frac{v_s}{||v_s||}||^2_2 + \lambda_2 L_{distill}(f_{VGG}(v_f), f_{VGG}(v_s))$$<br /> This loss penalizes on both the normalized Euclidean distance between the 2 facial feature vectors and the knowledge distillation loss, which is given by: $$L_{distill}(a,b) = -\sum_ip_{(i)}(a)\text{log}p_{(i)}(b)$$ $$p_{(i)}(a) = \frac{\text{exp}(a_i/T)}{\sum_j \text{exp}(a_j/T)}$$ Knowledge distillation is used as an alternative to Cross-Entropy. By recommendation of Cole et al , &lt;math&gt; T = 2 &lt;/math&gt; was used to ensure a smooth activation. &lt;math&gt;\lambda_1 = 0.025&lt;/math&gt; and &lt;math&gt;\lambda_2 = 200&lt;/math&gt; were chosen so that magnitude of the gradient of each term with respect to &lt;math&gt;v_s&lt;/math&gt; are of similar scale at the &lt;math&gt;1000^{th}&lt;/math&gt; iteration.<br /> <br /> &lt;center&gt;<br /> [[File:L1vsTotalLoss.png | 700px]]<br /> &lt;/center&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Figure 2: '''Qualitative results on the AVSpeech test set''' &lt;/div&gt;<br /> <br /> == Results ==<br /> <br /> '''Confusion Matrix and Dataset statistics'''<br /> <br /> &lt;center&gt;<br /> [[File:Confusionmatrix.png| 600px]]<br /> &lt;/center&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Figure 3. '''Facial attribute evaluation''' &lt;/div&gt;<br /> <br /> <br /> <br /> In order to determine the similarity between the generated images and the ground truth, a commercial service known as Face++ which classifies faces for distinct attributes (such as gender, ethnicity, etc) was used. Figure 3 gives a confusion matrix based on gender, ethnicity, and age. By examining these matrices, it is seen that the Speech2Face model performs very well on gender, only misclassifying 6% of the time. Similarly, the model performs fairly well on ethnicities, especially with white or Asian faces. Although the model performs worse on black and Indian faces, that can be attributed to the vastly unbalanced data, where 50% of the data represented a white face, and 80% represented a white or Asian face. <br /> <br /> '''Feature Similarity'''<br /> <br /> &lt;center&gt;<br /> [[File:FeatSim.JPG]]<br /> &lt;/center&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Table 2. '''Feature similarity''' &lt;/div&gt;<br /> <br /> <br /> <br /> Another examination of the result is the similarity of features predicted by the Speech2Face model. The cosine, L1, and L2 distance between the facial feature vector produced by the model and the true facial feature vector from the face decoder were computed, and presented, above, in Table 2. A comparison of facial similarity was also done based on the length of audio input. From the table, it is evident that the 6-second audio produced a lower cosine, L1, and L2 distance, resulting in a facial feature vector that is closer to the ground truth. <br /> <br /> '''S2F -&gt; Face retrieval performance'''<br /> <br /> &lt;center&gt;<br /> [[File: Retrieval.JPG]]<br /> &lt;/center&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; Table 3. '''S2F -&gt; Face retrieval performance''' &lt;/div&gt;<br /> <br /> <br /> <br /> The performance of the model was also examined on how well it could produce the original image. The R@K metric, also known as retrieval performance by recall at K, measures the probability that the K closest images to the model output includes the correct image of the speaker's face. A higher R@K score indicates better performance. From Table 3, above, we see that both the 3-second and 6-second audio showed significant improvement over random chance, with the 6-second audio performing slightly better.<br /> <br /> '''Additional Observations''' <br /> <br /> Ablation studies were carried out to test the effect of audio duration and batch normalization. It was found that the duration of input audio during the training stage had little effect on convergence speed (comparing 3 and 6-second speech segments), while in the test stage longer input speech yields improvement in reconstruction quality. With respect to batch normalization (BN), it was found that without BN reconstructed faces would converge to an average face, while the inclusion of BN led to results which contained much richer facial features.<br /> <br /> == Conclusion ==<br /> The report presented a novel study of face reconstruction from audio recordings of a person speaking. The model was demonstrated to be able to predict plausible face reconstructions with similar facial features to real images of the person speaking. The problem was addressed by learning to align the feature space of speech to that of a pretrained face decoder. The model was trained on millions of videos of people speaking from YouTube. The model was then evaluated by comparing the reconstructed faces with a commercial facial detection service. The authors believe that facial reconstruction allows a more comprehensive view of voice-face correlation compared to predicting individual features, which may lead to new research opportunities and applications.<br /> <br /> == Discussion and Critiques ==<br /> <br /> There is evidence that the results of the model may be heavily influenced by external factors:<br /> <br /> 1. Their method of sampling random YouTube videos resulted in an unbalanced sample in terms of ethnicity. Over half of the samples were white. We also saw a large bias in the model's prediction of ethnicity towards white. The bias in the results shows that the model may be overfitting the training data and puts into question what the performance of the model would be when trained and tested on a balanced dataset. Figure (11) highlights this shortcoming: The same man heard speaking in either English or Chinese was predicted to have a &quot;white&quot; appearance or an &quot;asian&quot; appearance respectively.<br /> <br /> 2. The model was shown to infer different face features based on language. This puts into question how heavily the model depends on the spoken language. The paper mentioned the quality of face reconstruction may be affected by uncommon languages, where English is the most popular language on Youtube(training set). Testing a more controlled sample where all speech recording was of the same language may help address this concern to determine the model's reliance on spoken language.<br /> <br /> 3. The evaluation of the result is also highly dependent on the Face++ classifiers. Since they compare the age, gender, and ethnicity by running the Face++ classifiers on the original images and the reconstructions to evaluate their model, the model that they create can only be as good as the one they are using to evaluate it. Therefore, any limitations of the Face++ classifier may become a limitation of Speech2Face and may result in a compounding effect on the miss-classification rate.<br /> <br /> 4. Figure 4.b shows the AVSpeech dataset statistics. However, it doesn't show the statistics about speakers' ethnicity and the language of the video. If we train the model with a more comprehensive dataset that includes enough Asian/Indian English speakers and native language speakers will this increase the accuracy?<br /> <br /> 5. One concern about the source of the training data, i.e. the Youtube videos, is that resolution varies a lot since the videos are randomly selected. That may be the reason why the proposed model performs badly on some certain features. For example, it is hard to tell the age when the resolution is bad because the wrinkles on the face are neglected.<br /> <br /> 6. The topic of this project is very interesting, but I highly doubt this model will be practical in real-world problems. Because there are many factors to affect a person's sound in a real-world environment. Sounds such as phone clock, TV, car horn and so on. These sounds will decrease the accuracy of the predicted result of the model.<br /> <br /> 7. A lot of information can be obtained from someone's voice, this can potentially be useful for detective work and crime scene investigation. In our world of increasing surveillance, public voice recording is quite common and we can reconstruct images of potential suspects based on their voice. In order for this to be achieved, the model has to be thoroughly trained and tested to avoid false positives as it could have a highly destructive outcome for a falsely convicted suspect.<br /> <br /> 8. This is a very interesting topic, and this summary has a good structure for readers. Since this model uses Youtube to train model, but I think one problem is that most of the YouTubers are adult, and many additional reasons make this dataset highly unbalanced. What is more, some people may have a baby voice, this also could affect the performance of the model. But overall, this is a meaningful topic, it might help police to locate the suspects. So it might be interesting to apply this to the police.<br /> <br /> 9. In addition, it seems very unlikely that any results coming from this model would ever be held in regard even remotely close to being admissible in court to identify a person of interest until the results are improved and the model can be shown to work in real-world applications. Otherwise, there seems to be very little use for such technology and it could have negative impacts on people if they were to be depicted in an unflattering way by the model based on their voice.<br /> <br /> 10. Using voice as a factor of constructing the face is a good idea, but it seems like the data they have will have lots of noise and bias. The voice of a video might not come from the person in the video. There are so many YouTubers adjusting their voices before uploading their video and it's really hard to know whether they adjust their voice. Also, most YouTubers are adults so the model cannot have enough training samples about teenagers and kids.<br /> <br /> 11. It would be interesting to see how the performance changes with different face encoding sizes (instead of just 4096-D) and also difference face models (encoder/decoders) to see if better performance can be achieved. Also given that the dataset used was unbalanced, was the dataset used to train the face model the same dataset? or was a different dataset used (the model was pretrained). This could affect the performance of the model as well.<br /> <br /> 12. The audio input is transformed into a spectrogram before being used for training. They use STFT with a Hann window of 25 mm, a hop length of 10 ms, and 512 FFT frequency bands. They cite this method from a paper that focuses on speech separation, not speech classification. So, it would be interesting to see if there is a better way to do STFT, possibly with different hyperparameters (eg. different windowing, different number of bands), or if another type of transform (eg. wavelet transform) would have better results.<br /> <br /> 13. A easy way to get somewhat balanced data is to duplicate the data that are fewer.<br /> <br /> 14. This problem is interesting but is hard to generalize. This algorithm didn't account for other genders and mixed-race. In addition, the face recognition software Face++ introduces bias which can carry forward to Speech2Face algorithm. Face recognition algorithms are known to have higher error rates classifying darker-skinned individuals. Thus, it'll be tough to apply it to real-life scenarios like identifying suspects.<br /> <br /> 15. This experiment raises a lot of ethical complications when it comes to possible applications in the real world. Even if this model was highly accurate, the implications of being able to discern a person's racial ethnicity, skin tone, etc. based solely on there voice could play in to inherent biases in the application user and this may end up being an issue that needs to be combatted in future research in this area. Another possible issue is that many people will change their intonation or vocal features based on the context (I'll likely have a different voice pattern in a job interview in terms of projection, intonation, etc. than if I was casually chatting/mumbling with a friend while playing video games for example).<br /> <br /> 16. Overall a very interesting topic. I want to talk about the technical challenged raised by using the AVSSpeech dataset for training. The paper acknowledges that the AVSSpeech is unbalanced, and 80% of the data are white and Asians. It also says in the results section that &quot;Our model does not perform on other races due to the imbalance in data&quot;. There does not seem to be any effort made in balancing the data. I think that there are definitely some data processing techniques that can be used (filtering, data augmentation, etc) to address the class imbalance problem. Not seeing any of these in the paper is a bit disappointing. Another issue I have noticed is that the model aims to predict an average-looking face from certain gender/racial group from voice input, due to ethical considerations. If we cannot reveal the identify of a person, why don't we predict the gender and race directly? Giving an average-looking face does not seem to be the most helpful.<br /> <br /> 17. Very interesting research paper to be studied and the main objective was also interesting. This research leads to open question which can be applied to another application such as predicting person's face using voice and can be used in more advanced way. The only risk is how the data is obtained from YouTube where data is not consistent.<br /> <br /> == References ==<br />  R. Arandjelovic and A. Zisserman. Look, listen and learn. In<br /> IEEE International Conference on Computer Vision (ICCV),<br /> 2017.<br /> <br />  A. Duarte, F. Roldan, M. Tubau, J. Escur, S. Pascual, A. Salvador, E. Mohedano, K. McGuinness, J. Torres, and X. Giroi-Nieto. Wav2Pix: speech-conditioned face generation using generative adversarial networks. In IEEE International<br /> Conference on Acoustics, Speech and Signal Processing<br /> (ICASSP), 2019.<br /> <br />  F. Cole, D. Belanger, D. Krishnan, A. Sarna, I. Mosseri, and W. T. Freeman. Synthesizing normalized faces from facial identity features. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.<br /> <br />  L. Castrejon, Y. Aytar, C. Vondrick, H. Pirsiavash, and A. Torralba. Learning aligned cross-modal representations from weakly aligned data. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.<br /> <br />  O. M. Parkhi, A. Vedaldi, and A. Zisserman. Deep face recognition. In British Machine Vision Conference (BMVC), 2015.<br /> <br />  “Overview of GAN Structure | Generative Adversarial Networks,” ''Google Developers'', 24-May-2019. [Online]. Available: https://developers.google.com/machine-learning/gan/gan_structure. [Accessed: 02-Dec-2020].</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Surround_Vehicle_Motion_Prediction&diff=49222 Surround Vehicle Motion Prediction 2020-12-05T17:31:07Z <p>Sh68lee: /* Critiques */</p> <hr /> <div>DROCC: '''Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn Intersections'''<br /> == Presented by == <br /> Mushi Wang, Siyuan Qiu, Yan Yu<br /> <br /> == Introduction ==<br /> <br /> This paper presents a surrounding vehicle motion prediction algorithm for multi-lane turn intersections using a Long Short-Term Memory (LSTM)-based Recurrent Neural Network (RNN). More specifically, it focused on the improvement of in-lane target recognition and achieving human-like acceleration decisions at multi-lane turn intersections by introducing the learning-based target motion predictor and prediction-based motion predictor. A data-driven approach for predicting the trajectory and velocity of surrounding vehicles on urban roads at multi-lane turn intersections was described. LSTM architecture, a specific kind of RNN capable of learning long-term dependencies, is designed to manage complex vehicle motions in multi-lane turn intersections. The results show that the forecaster improves the recognition time of the leading vehicle and contributes to the improvement of prediction ability.<br /> <br /> == Previous Work ==<br /> The autonomous vehicle trajectory approaches previously used motion models like Constant Velocity and Constant Acceleration. These models are linear and are only able to handle straight motions. There are curvilinear models such as Constant Turn Rate and Velocity and Constant Turn Rate and Acceleration which handle rotations and more complex motions. Together with these models, Kalman Filter is used to predicting the vehicle trajectory. Kalman filtering is a common technique used in sensor fusion for state estimation that allows the vehicle's state to be predicted while taking into account the uncertainty associated with inputs and measurements. However, the performance of the Kalman Filter in predicting multi-step problems is not that good. Recurrent Neural Network performs significantly better than it. <br /> <br /> There are 3 main challenges to achieving fully autonomous driving on urban roads, which are scene awareness, inferring other drivers’ intentions, and predicting their future motions. Researchers are developing prediction algorithms that can simulate a driver’s intuition to improve safety when autonomous vehicles and human drivers drive together. To predict driver behavior on an urban road, there are 3 categories for the motion prediction model: (1) physics-based; (2) maneuver-based; and (3) interaction-aware. Physics-based models are simple and direct, which only consider the states of prediction vehicles kinematically. The advantage is that it has minimal computational burden among the three types. However, it is impossible to consider the interactions between vehicles. Maneuver-based models consider the driver’s intention and classified them. By predicting the driver maneuver, the future trajectory can be predicted. Identifying similar behaviors in driving is able to infer different drivers' intentions which are stated to improve the prediction accuracy. However, it still an assistant to improve physics-based models. <br /> <br /> Recurrent Neural Network (RNN) is a type of approach proposed to infer driver intention in this paper. Interaction-aware models can reflect interactions between surrounding vehicles, and predict future motions of detected vehicles simultaneously as a scene. While the prediction algorithm is more complex in computation which is often used in offline simulations. As Schulz et al. indicate, interaction models are very difficult to create as &quot;predicting complete trajectories at once is challenging, as one needs to account for multiple hypotheses and long-term interactions between multiple agents&quot; .<br /> <br /> == Motivation == <br /> Research results indicate that little research has been dedicated on predicting the trajectory of intersections. Moreover, public data sets for analyzing driver behaviour at intersections are not enough, and these data sets are not easy to collect. A model is needed to predict the various movements of the target around a multi-lane turning intersection. It is very necessary to design a motion predictor that can be used for real-time traffic.<br /> <br /> &lt;center&gt;<br /> [[ File:intersection.png |300px]]<br /> &lt;/center&gt;<br /> <br /> == Framework == <br /> The LSTM-RNN-based motion predictor comprises three parts: (1) a data encoder; (2) an LSTM-based RNN; and (3) a data decoder depicts the architecture of the surrounding target trajectory predictor. The proposed architecture uses a perception algorithm to estimate the state of surrounding vehicles, which relies on six scanners. The output predicts the state of the surrounding vehicles and is used to determine the expected longitudinal acceleration in the actual traffic at the intersection. The following image gives a visual representation of the model.<br /> <br /> &lt;center&gt;[[Image:Figure1_Yan.png|800px|]]&lt;/center&gt;<br /> <br /> == LSTM-RNN based motion predictor == <br /> <br /> === Sensor Outputs ===<br /> <br /> The input of the target perceptions is from the output of the sensors. The data collected in this article uses 6 different sensors with feature fusion to detect traffic in the range up to 100m: 1) LiDAR system outputs: Relative position, heading, velocity, and box size in local coordinates; 2) Around0View Monitoring (AVM) and 3)GPS outputs: acquire lanes, road marker, global position; 4) Gateway engine outputs: precise global position in urban road environment; 5) Micro-Autobox II and 6) a MDPS are used to control and actuate the subject. All data are stored in an industrial PC.<br /> <br /> === Data ===<br /> Multi-lane turn intersections are the target roads in this paper. The dataset was collected using a human driven Autonomous Vehicle(AV) that was equipped with sensors to track motion the vehicle's surroundings. In addition the motion sensors they used a front camera, Around-View-Monitor and GPS to acquire the lanes, road markers and global position. The data was collected in the urban roads of Gwanak-gu, Seoul, South Korea. The training model is generated from 484 tracks collected when driving through intersections in real traffic. The previous and subsequent states of a vehicle at a particular time can be extracted. After post-processing, the collected data, a total of 16,660 data samples were generated, including 11,662 training data samples, and 4,998 evaluation data samples.<br /> <br /> === Motion predictor ===<br /> This article proposes a data-driven method to predict the future movement of surrounding vehicles based on their previous movement, which is the sequential previous motion. The motion predictor based on the LSTM-RNN architecture in this work only uses information collected from sensors on autonomous vehicles, as shown in the figure below. The contribution of the network architecture of this study is that the future state of the target vehicle is used as the input feature for predicting the field of view. <br /> <br /> <br /> &lt;center&gt;[[Image:Figure7b_Yan.png|500px|]]&lt;/center&gt;<br /> <br /> <br /> ==== Network architecture ==== <br /> A RNN is an artificial neural network, suitable for use with sequential data. It can also be used for time-series data, where the pattern of the data depends on the time flow. Also, it can contain feedback loops that allow activations to flow alternately in the loop.<br /> An LSTM avoids the problem of vanishing gradients by making errors flow backward without a limit on the number of virtual layers. This property prevents errors from increasing or declining over time, which can make the network train improperly. The figure below shows the various layers of the LSTM-RNN and the number of units in each layer. This structure is determined by comparing the accuracy of 72 RNNs, which consist of a combination of four input sets and 18 network configurations.<br /> <br /> &lt;center&gt;[[Image:Figure8_Yan.png|800px|]]&lt;/center&gt;<br /> <br /> ==== Input and output features ==== <br /> In order to apply the motion predictor to the AV in motion, the speed of the data collection vehicle is added to the input sequence. The input sequence consists of relative X/Y position, relative heading angle, speed of surrounding target vehicles, and speed of data collection vehicles. The output sequence is the same as the input sequence, such as relative position, heading, and speed.<br /> <br /> ==== Encoder and decoder ==== <br /> In this study, the authors introduced an encoder and decoder that process the input from the sensor and the output from the RNN, respectively. The encoder normalizes each component of the input data to rescale the data to mean 0 and standard deviation 1, while the decoder denormalizes the output data to use the same parameters as in the encoder to scale it back to the actual unit. <br /> ==== Sequence length ==== <br /> The sequence length of RNN input and output is another important factor to improve prediction performance. In this study, 5, 10, 15, 20, 25, and 30 steps of 100 millisecond sampling times were compared, and 15 steps showed relatively accurate results, even among candidates The observation time is very short.<br /> <br /> == Motion planning based on surrounding vehicle motion prediction == <br /> In daily driving, experienced drivers will predict possible risks based on observations of surrounding vehicles, and ensure safety by changing behaviors before the risks occur. In order to achieve a human-like motion plan, based on the model predictive control (MPC) method, a prediction-based motion planner for autonomous vehicles is designed, which takes into account the driver’s future behavior. The cost function of the motion planner is determined as follows:<br /> \begin{equation*}<br /> \begin{split}<br /> J = &amp; \sum_{k=1}^{N_p} (x(k|t) - x_{ref}(k|t)^T) Q(x(k|t) - x_{ref}(k|t)) +\\<br /> &amp; R \sum_{k=0}^{N_p-1} u(k|t)^2 + R_{\Delta \mu}\sum_{k=0}^{N_p-2} (u(k+1|t) - u(k|t))^2 <br /> \end{split}<br /> \end{equation*}<br /> where &lt;math&gt;k&lt;/math&gt; and &lt;math&gt;t&lt;/math&gt; are the prediction step index and time index, respectively; &lt;math&gt;x(k|t)&lt;/math&gt; and &lt;math&gt;x_{ref} (k|t)&lt;/math&gt; are the states and reference of the MPC problem, respectively; &lt;math&gt;x(k|t)&lt;/math&gt; is composed of travel distance px and longitudinal velocity vx; &lt;math&gt;x_{ref} (k|t)&lt;/math&gt; consists of reference travel distance &lt;math&gt;p_{x,ref}&lt;/math&gt; and reference longitudinal velocity &lt;math&gt;v_{x,ref}&lt;/math&gt; ; &lt;math&gt;u(k|t)&lt;/math&gt; is the control input, which is the longitudinal acceleration command; &lt;math&gt;N_p&lt;/math&gt; is the prediction horizon; and Q, R, and &lt;math&gt;R_{\Delta \mu}&lt;/math&gt; are the weight matrices for states, input, and input derivative, respectively, and these weight matrices were tuned to obtain control inputs from the proposed controller that were as similar as possible to those of human-driven vehicles. <br /> The constraints of the control input are defined as follows:<br /> \begin{equation*}<br /> \begin{split}<br /> &amp;\mu_{min} \leq \mu(k|t) \leq \mu_{max} \\<br /> &amp;||\mu(k+1|t) - \mu(k|t)|| \leq S<br /> \end{split}<br /> \end{equation*}<br /> Where &lt;math&gt;u_{min}&lt;/math&gt;, &lt;math&gt;u_{max}&lt;/math&gt;and S are the minimum/maximum control input and maximum slew rate of input respectively.<br /> <br /> Determine the position and speed boundary based on the predicted state:<br /> \begin{equation*}<br /> \begin{split}<br /> &amp; p_{x,max}(k|t) = p_{x,tar}(k|t) - c_{des}(k|t) \quad p_{x,min}(k|t) = 0 \\<br /> &amp; v_{x,max}(k|t) = min(v_{x,ret}(k|t), v_{x,limit}) \quad v_{x,min}(k|t) = 0<br /> \end{split}<br /> \end{equation*}<br /> Where &lt;math&gt;v_{x, limit}&lt;/math&gt; are the speed limits of the target vehicle.<br /> <br /> == Prediction performance analysis and application to motion planning ==<br /> === Accuracy analysis ===<br /> The proposed algorithm was compared with the results from three base algorithms, a path-following model with <br /> constant velocity, a path-following model with traffic flow and a CTRV model.<br /> <br /> We compare those algorithms according to four sorts of errors, The &lt;math&gt;x&lt;/math&gt; position error &lt;math&gt;e_{x,T_p}&lt;/math&gt;, <br /> &lt;math&gt;y&lt;/math&gt; position error &lt;math&gt;e_{y,T_p}&lt;/math&gt;, heading error &lt;math&gt;e_{\theta,T_p}&lt;/math&gt;, and velocity error &lt;math&gt;e_{v,T_p}&lt;/math&gt; where &lt;math&gt;T_p&lt;/math&gt; denotes time &lt;math&gt;p&lt;/math&gt;. These four errors are defined as follows:<br /> <br /> \begin{equation*}<br /> \begin{split}<br /> e_{x,Tp}=&amp; p_{x,Tp} -\hat {p}_{x,Tp}\\ <br /> e_{y,Tp}=&amp; p_{y,Tp} -\hat {p}_{y,Tp}\\ <br /> e_{\theta,Tp}=&amp; \theta _{Tp} -\hat {\theta }_{Tp}\\ <br /> e_{v,Tp}=&amp; v_{Tp} -\hat {v}_{Tp}<br /> \end{split}<br /> \end{equation*}<br /> &lt;center&gt;[[Image:Figure10.1_YanYu.png|500px|]]&lt;/center&gt;<br /> <br /> The proposed model shows significantly fewer prediction errors compare to the based algorithms in terms of mean, <br /> standard deviation(STD), and root mean square error(RMSE). Meanwhile, the proposed model exhibits a bell-shaped <br /> curve with a close to zero mean, which indicates that the proposed algorithm's prediction of human divers' <br /> intensions are relatively precise. On the other hand, &lt;math&gt;e_{x,T_p}&lt;/math&gt;, &lt;math&gt;e_{y,T_p}&lt;/math&gt;, &lt;math&gt;e_{v,T_p}&lt;/math&gt; are bounded within <br /> reasonable levels. For instant, the three-sigma range of &lt;math&gt;e_{y,T_p}&lt;/math&gt; is within the width of a lane. Therefore, <br /> the proposed algorithm can be precise and maintain safety simultaneously.<br /> <br /> === Motion planning application ===<br /> ==== Case study of a multi-lane left turn scenario ====<br /> The proposed method mimics a human driver better, by simulating a human driver's decision-making process. <br /> In a multi-lane left turn scenario, the proposed algorithm correctly predicted the trajectory of a target <br /> the vehicle, even when the target vehicle was not following the intersection guideline.<br /> <br /> ==== Statistical analysis of motion planning application results ====<br /> The data is analyzed from two perspectives, the time to recognize the in-lane target and the similarity to <br /> human driver commands. In most of cases, the proposed algorithm detects the in-line target no late than based <br /> algorithm. In addition, the proposed algorithm only recognized cases later than the base algorithm did when <br /> the surrounding target vehicles first appeared beyond the sensors’ region of interest boundaries. This means <br /> that these cases took place sufficiently beyond the safety distance, and had little influence on determining <br /> the behaviour of the subject vehicle.<br /> <br /> &lt;center&gt;[[Image:Figure11_YanYu.png|500px|]]&lt;/center&gt;<br /> <br /> In order to compare the similarities between the results form the proposed algorithm and human driving decisions, <br /> this article introduced another type of error, acceleration error &lt;math&gt;a_{x, error} = a_{x, human} - a_{x, cmd}&lt;/math&gt;. where &lt;math&gt;a_{x, human}&lt;/math&gt;<br /> and &lt;math&gt;a_{x, cmd}&lt;/math&gt; are the human driver’s acceleration history and the command from the proposed algorithm, <br /> respectively. The proposed algorithm showed more similar results to human drivers’ decisions than the base <br /> algorithm. &lt;math&gt;91.97\%&lt;/math&gt; of the acceleration error lies in the region &lt;math&gt;\pm 1 m/s^2&lt;/math&gt;. Moreover, the base algorithm <br /> possesses a limited ability to respond to different in-lane target behaviours in traffic flow. Hence, the proposed <br /> model is efficient and safe.<br /> <br /> == Conclusion ==<br /> A surrounding vehicle motion predictor based on an LSTM-RNN at multi-lane turn intersections was developed, and its application in an autonomous vehicle was evaluated. The model was trained by using the data captured on the urban road in Seoul in MPC. The evaluation results showed precise prediction accuracy and so the algorithm is safe to be applied on an autonomous vehicle. Also, the comparison with the other three base algorithms (CV/Path, V_flow/Path, and CTRV) revealed the superiority of the proposed algorithm. The evaluation results showed precise prediction accuracy. In addition, the time-to-recognize in-lane targets within the intersection improved significantly over the performance of the base algorithms. The proposed algorithm was compared with human driving data, and it showed similar longitudinal acceleration. The motion predictor can be applied to path planners when AVs travel in unconstructed environments, such as multi-lane turn intersections.<br /> <br /> == Future works ==<br /> This paper has identified several venues for future research, which include:<br /> <br /> 1.Developing trajectory prediction algorithms using other machine learning algorithms, such as attention-aware neural networks.<br /> <br /> 2.Applying the machine learning-based approach to infer lane change intention at motorways and main roads of urban environments.<br /> <br /> 3.Extending the target road of the trajectory predictor, such as roundabouts or uncontrolled intersections, to infer yield intention.<br /> <br /> 4.Learning the behavior of surrounding vehicles in real time while automated vehicles drive with real traffic.<br /> <br /> == Critiques ==<br /> The literature review is not sufficient. It should focus more on LSTM, RNN, and the study in different types of roads. Why the LSTM-RNN is used, and the background of the method is not stated clearly. There is a lack of concept so that it is difficult to distinguish between LSTM-RNN based motion predictor and motion planning.<br /> <br /> This is an interesting topic to discuss. This is a major topic for some famous vehicle companies such as Tesla, which now already has a good service called Autopilot to give self-driving and Motion Prediction. This summary can include more diagrams in architecture in the model to give readers a whole view of how the model looks like. Since it is using LSTM-RNN, include some pictures of the LSTM-RNN will be great. I think it will be interesting to discuss more applications by using this method, such as Airplane, boats.<br /> <br /> Autonomous driving is a very hot topic, and training the model with LSTM-RNN is also a meaningful topic to discuss. By the way, it would be an interesting approach to compare the performance of different algorithms or some other traditional motion planning algorithms like KF.<br /> <br /> There are some papers that discussed the accuracy of different models in vehicle predictions, such as Deep Kinematic Models for Kinematically Feasible Vehicle Trajectory Predictions[https://arxiv.org/pdf/1908.00219.pdf.] The LSTM didn't show good performance. They increased the accuracy by combing LSTM with an unconstrained model(UM) by adding an additional LSTM layer of size 128 that is used to recursively output positions instead of simultaneously outputting positions for all horizons.<br /> <br /> It may be better to provide the results of experiments to support the efficiency of LSTM-RNN, talk about the prediction of training and test sets, and compared it with other autonomous driving systems that exist in the world.<br /> <br /> The topic of surround vehicle motion prediction is analogous to the topic of autonomous vehicles. An example of an application of these frameworks would be the transportation services industry. Many companies, such as Lyft and Uber, have started testing their own commercial autonomous vehicles.<br /> <br /> It would be really helpful if some visualization or data summary can be provided to understand the content, such as the track of the car movement.<br /> <br /> The model should have been tested in other regions besides just Seoul, as driving behaviors can vary drastically from region to region.<br /> <br /> Understandably, a supervised learning problem should be evaluated on some test dataset. However, supervised learning techniques are inherently ill-suited for general planning problems. The test dataset was obtained from human driving data which is known to be extremely noisy as well as unpredictable when it comes to motion planning. It would be crucial to determine the successes of this paper based on the state-of-the-art reinforcement learning techniques.<br /> <br /> It would be better if the authors compared their method against other SOTA methods. Also one of the reasons motion planning is done using interpretable methods rather than black boxes (such as this model) is because it is hard to see where things go wrong and fix problems with the black box when they occur - this is something the authors should have also discussed.<br /> <br /> A future area of study is to combine other source of information such as signals from Lidar or car side cameras to make a better prediction model.<br /> <br /> It might be interesting and helpful to conduct some training and testing under different weather/environmental conditions, as it could provide more generalization to real-life driving scenarios. For example, foggy weather and evening (low light) conditions might affect the performance of sensors, and rainy weather might require a longer braking distance.<br /> <br /> This paper proposes an interesting, novel model prediction algorithm, using LSTM_RNN. However, since motion prediction in autonomous driving has great real-life impacts, I do believe that the evaluations of the algorithm should be more thorough. For example, more traditional motion planning algorithms such as multi-modal estimation and Kalman filters should be used as benchmarks. Moreover, the experiment results are based on Korean driving conditions only. Eastern and Western drivers can have very different driving patterns, so that should be addressed in the discussion section of the paper as well.<br /> <br /> The paper mentions that in the future, this research plans to learn the real life behaviour of automated vehicles. Seeing a possible improvement in road safety due to this research will be very interesting.<br /> <br /> This predictor is also possible to be applied in the traffic control system.<br /> <br /> This prediction model should consider various conditions that could happen in an intersection. However, normal prediction may not work when there is a traffic jam or in some crowded time periods like rush hours.<br /> <br /> It would be better that the author could provide more comparison between the LSTN-RNN algorithm and other traditional algorithm such as RNN or just LSTM.<br /> <br /> The paper has really good results for what they aimed to achieve. However for the future work it would also be nice to have various climates/weathers to be included in the Seoul dataset. I think it's also important to consider it as different climates/weather (such as snowy roads, or rain) would introduce more noisier data (camera's image processing) and the human drivers behaviour would change as well to adapt to the new environment.<br /> <br /> The summary explains the whole process well, but is missing the small details among the steps. It would be better to explain concepts such as RNN, modelling procedure for first time users.<br /> <br /> == Reference ==<br />  E. Choi, Crash Factors in Intersection-Related Crashes: An On-Scene Perspective (No. Dot HS 811 366), U.S. DOT Nat. Highway Traffic Safety Admin., Washington, DC, USA, 2010.<br /> <br />  D. J. Phillips, T. A. Wheeler, and M. J. Kochenderfer, “Generalizable intention prediction of human drivers at intersections,” in Proc. IEEE Intell. Veh. Symp. (IV), Los Angeles, CA, USA, 2017, pp. 1665–1670.<br /> <br />  B. Kim, C. M. Kang, J. Kim, S. H. Lee, C. C. Chung, and J. W. Choi, “Probabilistic vehicle trajectory prediction over occupancy grid map via recurrent neural network,” in Proc. IEEE 20th Int. Conf. Intell. Transp. Syst. (ITSC), Yokohama, Japan, 2017, pp. 399–404.<br /> <br />  E. Strigel, D. Meissner, F. Seeliger, B. Wilking, and K. Dietmayer, “The Ko-PER intersection laserscanner and video dataset,” in Proc. 17th Int. IEEE Conf. Intell. Transp. Syst. (ITSC), Qingdao, China, 2014, pp. 1900–1901.<br /> <br />  Henggang Cui, Thi Nguyen, Fang-Chieh Chou, Tsung-Han Lin, Jeff Schneider, David Bradley, Nemanja Djuric: “Deep Kinematic Models for Kinematically Feasible Vehicle Trajectory Predictions”, 2019; [http://arxiv.org/abs/1908.00219 arXiv:1908.00219].<br /> <br /> Schulz, Jens &amp; Hubmann, Constantin &amp; Morin, Nikolai &amp; Löchner, Julian &amp; Burschka, Darius. (2019). Learning Interaction-Aware Probabilistic Driver Behavior Models from Urban Scenarios. 10.1109/IVS.2019.8814080.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Evaluating_Machine_Accuracy_on_ImageNet&diff=49219 Evaluating Machine Accuracy on ImageNet 2020-12-05T17:23:48Z <p>Sh68lee: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Siyuan Xia, Jiaxiang Liu, Jiabao Dong, Yipeng Du<br /> <br /> == Introduction == <br /> ImageNet is the most influential data set in machine learning with images and corresponding labels over 1000 classes. This paper intends to explore the causes for performance differences between human experts and machine learning models, more specifically, CNN, on ImageNet. <br /> <br /> Firstly, some images could belong to multiple classes. As a result, it is possible to underestimate the performance if we assign each image with only one label, which is what is being done in the top-1 metric. Therefore, we adopt both top-1 and top-5 metrics where the performances of models, unlike human labelers, are linearly correlated in both cases.<br /> <br /> Secondly, in contrast to the uniform performance of models in classes, humans tend to achieve better performances on inanimate objects. Human labelers achieve similar overall accuracies as the models, which indicates spaces of improvements on specific classes for machines.<br /> <br /> Lastly, the setup of drawing training and test sets from the same distribution may favor models over human labelers. That is, the accuracy of multi-class prediction from models drops when the testing set is drawn from a different distribution than the training set, ImageNetV2. But this shift in distribution does not cause a problem for human labelers.<br /> <br /> == Experiment Setup ==<br /> === Overview ===<br /> There are four main phases to the experiment, which are (i) initial multilabel annotation, (ii) human labeler training, (iii) human labeler evaluation, and (iv) final annotation overview. The five authors of the paper are the participants in the experiments. <br /> <br /> A brief overview of the four phases is as follows:<br /> [[File:Experiment Set Up.png |800px| center]]<br /> <br /> === Initial multi-label annotation ===<br /> Three labelers A, B, and C provided multi-label annotations for a subset from the ImageNet validation set, and all images from the ImageNetV2 test sets. These experiences give A, B, and C extensive experience with the ImageNet dataset. <br /> <br /> === Human Labeler Training === <br /> All five labelers trained on labeling a subset of the remaining ImageNet images. &quot;Training&quot; the human labelers consisted of teaching the humans the distinctions between very similar classes in the training set. For example, there are 118 classes of &quot;dog&quot; within ImageNet and typical human participants will not have working knowledge of the names of each breed of dog seen even if they can recognize and distinguish that breed from others. Local members of the American Kennel Club were even contacted to help with dog breed classification. To do this labelers were trained on class-specific tasks for groups like dogs, insects, monkeys beaver and others. They were also given immediate feedback on whether they were correct and then were asked where they thought they needed more training to improve. Unlike the two annotators in (Russakovsky et al., 2015), who had insufficient training data, the labelers in this experiment had to 100 training images per class while labeling. This allowed the labelers to really understand the finer details of each class. <br /> <br /> === Human Labeler Evaluation ===<br /> Class-balanced random samples, which contains 1,000 images from the 20,000 annotated images are generated from both the ImageNet validation set and ImageNetV2. Five participants labeled these images over 28 days.<br /> <br /> === Final annotation Review ===<br /> All labelers reviewed the additional annotations generated in the human labeler evaluation phase.<br /> <br /> == Multi-label annotations==<br /> [[File:Categories Multilabel.png|800px|center]]<br /> &lt;div align=&quot;center&quot;&gt;Figure 3&lt;/div&gt;<br /> <br /> ===Top-1 accuracy===<br /> With Top-1 accuracy being the standard accuracy measure used in classification studies, it measures the proportions of examples for which the predicted label matches the single target label. As many images often contain more than one object for classification, for example, Figure 3a contains a desk, laptop, keyboard, space bar, and more. With Figure 3b showing a centered prominent figure yet labeled otherwise (people vs picket fence), it can be seen how a single target label is inaccurate for such a task since identifying the main objects in the image does not suffice due to its overly stringent and punishes predictions that are the main image yet does not match its label.<br /> ===Top-5 accuracy===<br /> With Top-5 considers a classification correct if the object label is in the top 5 predicted labels, it partially resolves the problem with Top-1 labeling yet it is still not ideal since it can trivialize class distinctions. For instance, within the dataset, five turtle classes are given which is difficult to distinguish under such classification evaluations.<br /> ===Multi-label accuracy===<br /> The paper then proposes that for every image, the image shall have a set of target labels and a prediction; if such prediction matches one of the labels, it will be considered as correct labeling. Due to the above-discussed limitations of Top-1 and Top-5 metrics, the paper claims it is necessary for rigorous accuracy evaluation on the dataset. <br /> <br /> ===Types of Multi-label annotations===<br /> ====Multiple objects or organisms====<br /> For the images containing more than one object or organism that corresponds to ImageNet, the paper proposed to add an additional target label for each entity in the image. With the discussed image in Figure 3b, the class groom, bow tie, suit, gown, and hoopskirt are all present in the foreground which is then subsequently added to the set of labels.<br /> ====Synonym or subset relations====<br /> For similar classes, the paper considers them as under the same bigger class, that is, for two similarly labeled images, classification is considered correct if the produced label matches either one of the labels. For instance, warthog, African elephant, and Indian element all have prominent tusks, they will be considered subclasses of the tusker, Figure 3c shows a modification of labels to contain tusker as a correct label.<br /> ====Unclear Image====<br /> In certain cases such as Figure 3d, there is a distinctive difficulty to determine whether a label was correct due to ambiguities in the class hierarchy.<br /> ===Collecting multi-label annotations===<br /> Participants reviewed all predictions made by the models on the dataset ImageNet and ImageNet-V2, the participants then categorized every unique prediction made by the models on the dataset into correct and incorrect labels in order to allow all images to have multiple correct labels to satisfy the above-listed method.<br /> ===The multi-label accuracy metric===<br /> One prediction is only correct if and only if it was marked correct by the expert reviewers during the annotation stage. As discussed in the experiment setup section, after human labelers have completed labeling, a second annotation stage is conducted. In Figure 4, a comparison of Top-1, Top-5, and multi-label accuracies showed higher Top-1 and Top-5 accuracy corresponds with higher multi-label accuracy as expected. With multi-label accuracies measures consistently higher than Top-1 yet lower than Top-5 which shows a high correlation between the three metrics, the paper concludes that multi-label metrics measures a semantically more meaningful notion of accuracy compared to its counterparts.<br /> <br /> == Human Accuracy Measurement Process ==<br /> === Bias Control ===<br /> Since three participants participated in the initial round of annotation, they did not look at the data for six months, and two additional annotators are introduced in the final evaluation phase to ensure fairness of the experiment. <br /> <br /> === Human Labeler Training ===<br /> The three main difficulties encountered during human labeler training are fine-grained distinctions, class unawareness, and insufficient training images. Thus, three training regimens are provided to address the problems listed above, respectively. First, labelers will be assigned extra training tasks with immediate feedbacks on similar classes. Second, labelers will be provided access to search for specific classes during labeling. Finally, the training set will contain a reasonable amount of images for each class.<br /> <br /> === Labeling Guide ===<br /> A labeling guide is constructed to distill class analysis learned during training into discriminative traits that could be used as a reference during the final labeling evaluation.<br /> <br /> === Final Evaluation and Review ===<br /> Two samples, each containing 1000 images, are sampled from ImageNet and ImageNetV2, respectively, They are sampled in a class-balanced manner and shuffled together. Over 28 days, all five participants labeled all images. They spent a median of 26 seconds per image. After labeling is completed, an additional multi-label annotation session was conducted, in which human predictions for all images are manually reviewed. Comparing to the initial round of labeling, 37% of the labels changes due to participants' greater familiarity with the classes.<br /> <br /> == Main Results ==<br /> [[File:Evaluating Machine Accuracy on ImageNet Figure 1.png | center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1&lt;/div&gt;<br /> <br /> ===Comparison of Human and Machine Accuracies on Image Net===<br /> From Figure 1, we can see that the difference in accuracies between the datasets is within 1% for all human participants. As hypothesized, human testers indeed performed better than the automated models on both datasets. It's worth noticing that labelers D and E, who did not participate in the initial annotation period, actually performed better than the best automated model.<br /> ===Comparison of Human and Machine Accuracies on Image Net===<br /> Based on the results shown in Figure 1, we can see that the confidence interval of the best 4 human participants and 4 best model overlap; however, with a p-value of 0.037 using the McNemar's paired test, it rejects the hypothesis that the FixResNeXt model and Human E labeler have the same accuracy with respect to the ImageNet validation dataset. Figure 1 also shows that the confidence intervals of the labeling accuracies for human labelers C, D, E do not overlap with the confidence interval of the best model with respect to ImageNet-V2 and with the McNemar's test yielding a p-value of &lt;math&gt;2\times 10^{-4}&lt;/math&gt;, it is clear that the hypothesis human and machined models have same robustness to model distribution shifts ought to be rejected.<br /> <br /> == Other Observations ==<br /> <br /> [[File: Results_Summary_Table.png| 800px|center]]<br /> <br /> === Difficult Images ===<br /> <br /> The experiment also shed some light on images that are difficult to label. 10 images were misclassified by all of the human labelers. Among those 10 images, there was 1 image of a monkey and 9 of dogs. In addition, 27 images, with 19 in object classes and 8 in organism classes, were misclassified by all 72 machine learning models in this experiment. Only 2 images were labeled wrong by all human labelers and models. Both images contained dogs. Researchers also noted that difficult images for models are mostly images of objects and exclusively images of animals for human labelers.<br /> <br /> === Accuracies without dogs ===<br /> <br /> As previously discussed in the paper, machine learning models tend to outperform human labelers when classifying the 118 dog classes. To better understand to what extent does models outperform human labelers, researchers computed the accuracies again by excluding all the dog classes. Results showed a 0.6% increase in accuracy on the ImageNet images using the best model and a 1.1% increase on the ImageNet V2 images. In comparison, the mean increases in accuracy for human labelers are 1.9% and 1.8% on the ImageNet and ImageNet V2 images respectively. Researchers also conducted a simulation to demonstrate that the increase in human labeling accuracy on non-dog images is significant. This simulation was done by bootstrapping to estimate the changes in accuracy when only using data for the non-dog classes, and simulation results show smaller increases than in the experiment. <br /> <br /> In conclusion, it's more difficult for human labelers to classify images with dogs than it is for machine learning models.<br /> <br /> === Accuracies on objects ===<br /> Researchers also computed machine and human labelers' accuracies on a subset of data with only objects, as opposed to organisms, to better illustrate the differences in performance. This test involved 590 object classes. As shown in the table above, there is a 3.3% and 3.4% increase in mean accuracies for human labelers on the ImageNet and ImageNet V2 images. In contrast, there is a 0.5% decrease in accuracy for the best model on both ImageNet and ImageNet V2. This indicates that human labelers are much better at classifying objects than these models are.<br /> <br /> === Accuracies on fast images ===<br /> Unlike the CNN models, human labelers spent different amounts of time on different images, spanning from several seconds to 40 minutes. To further analyze the images that take human labelers less time to classify, researchers took a subset of images with median labeling time spent by human labelers of at most 60 seconds. These images were referred to as &quot;fast images&quot;. There are 756 and 714 fast images from ImageNet and ImageNet V2 respectively, out of the total 2000 images used for evaluation. Accuracies of models and humans on the fast images increased significantly, especially for humans. <br /> <br /> This result suggests that human labelers know when an image is difficult to label and would spend more time on it. It also shows that the models are more likely to correctly label images that human labelers can label relatively quickly.<br /> <br /> == Related Work ==<br /> <br /> === Human accuracy on ImageNet ===<br /> <br /> Russakovsky et al. (2015) studied two trained human labelers' accuracies on 1500 and 258 images in the context of the ImageNet challenge. The top-5 accuracy of the labeler who labeled 1500 images was the well-known human baseline on ImageNet. <br /> <br /> As introduced before, the researchers went beyond by using multi-label accuracy, using more labelers, and focusing on robustness to small distribution shifts. Although the researchers had some different findings, some results are also consistent with results from (Russakovsky et al., 2015). An example is that both experiments indicated that it takes human labelers around one minute to label an image. The time distribution also has a long tail, due to the difficult images as mentioned before.<br /> <br /> === Human performance in computer vision broadly ===<br /> There are many examples of recent studies about humans in the area of computer vision, such as investigating human robustness to synthetic distribution change (Geirhos et al., 2017) and studying what characteristics do humans use to recognize objects (Geirhos et al., 2018). Other examples include the adversarial examples constructed to fool both machines and time-limited humans (Elsayed et al., 2018) and illustrating foreground/background objects' effects on human and machine performance (Zhu et al., 2016). <br /> <br /> === Multi-label annotations ===<br /> Stock &amp; Cissé (2017) also studied ImageNet's multi-label nature, which aligns with the researchers' study in this paper. According to Stock &amp; Cissé (2017), the top-1 accuracy measure could underestimate multi-label by up to 13.2%.<br /> <br /> === ImageNet inconsistencies and label error ===<br /> Researches have found and recorded some incorrectly labeled images from ImageNet and ImageNet V2 during this study. Earlier studies (Van Horn et al., 2015) also shown that at least 4% of the birds in ImageNet are misclassified. This work also noted that the inconsistent taxonomic structure in birds' classes could lead to weak class boundaries. Researchers also noted that the majority of the fine-grained organism classes also had similar taxonomic issues.<br /> <br /> === Distribution shift ===<br /> There has been an increasing amount of studies in this area. One focus of the studies is distributionally robust optimization (DRO), which finds the model that has the smallest worst-case expected error over a set of probability distributions. Another focus is on finding the model with the lowest error rates on adversarial examples. Work in both areas has been productive, but none was shown to resolve the drop in accuracies between ImageNet and ImageNet V2. A recent [https://papers.nips.cc/paper/2019/file/8558cb408c1d76621371888657d2eb1d-Paper.pdf paper] also discusses quantifying uncertainty under a distribution shift, in other words whether the output of probabilistic deep learning models should or should not be trusted.<br /> <br /> == Conclusion and Future Work ==<br /> <br /> === Conclusion ===<br /> Researchers noted that in order to achieve truly reliable machine learning, researchers need a deeper understanding of the range of parameters where the model still remain robust. Techniques from Combinatorics and sensitivity analysis, in particular, might yield fruitful results. This study has provided valuable insights into the desired robustness properties by comparing model performance to human performance. This is especially evident given the results of the experiment which show humans drastically outperforming machine learning in many cases and proposes the question of how much accuracy one is willing to give up in exchange for efficiency. The results have shown that current performance benchmarks are not addressing the robustness to small and natural distribution shifts, which are easily handled by humans.<br /> <br /> === Future work ===<br /> Other than improving the robustness of models, researchers should consider investigating if less-trained human labelers can achieve a similar level of robustness to distributional shifts. In addition, researchers can study the robustness to temporal changes, which is another form of natural distribution shift (Gu et al., 2019; Shankar et al., 2019). Also, Convolutional Neural Network can be a candidate to improve the accuracy of classifying images.<br /> <br /> == Critiques ==<br /> <br /> # Table 1 simply showed a difference in ImageNet multi-label accuracy yet does not give an explicit reason as to why such a difference is present. Although the paper suggested the distribution shift has caused the difference, it does not give other factors to concretely explain why the distribution shift was the cause.<br /> # With the recommendation to future machine evaluations, the paper proposed to &quot;Report performances on dogs, other animals, and inanimate objects separately.&quot;. Despite its intentions, it is narrowly specific and requires further generalization for it to be convincing. <br /> # With choosing human subjects as samplers, no further information was given as to how they are chosen nor there are any background information was given. As it is a classification problem involving many classes as specific to species, a biology student would give far more accurate results than a computer science student or a math student. <br /> # As explaining the importance of multi-label metrics using comparison to Top-5 metric, the turtle example falls within the overall similarity (simony) classification of the multi-label evaluation metric, as such, if the Top-5 evaluation suggests any one of the turtle species were selected, the algorithm is considered to produce a correct prediction which is the intention. The example does not convey the necessity of changing to the proposed metric over the Top-5 metric. <br /> # With the definition in the paper regarding multi-label metrics, it is hard to see why expanding the label set is different from a traditional Top-5 metric or rather necessary, ergo does not yield the claim which the proposed metric is necessary for rigorous accuracy evaluation on ImageNet.<br /> # When discussing the main results, the paper discusses the hypothesis on distribution shift having no effects on human and machine model accuracies; the presentation is poor at best with no clear centric to what they are trying to convey to how (in detail) they resulted in such claims.<br /> # In the experiment setup of the presentation, there are a lot of key terms without detailed description. For example, Human labeler training using a subset of the remaining 30,000 unannotated images in the ImageNet validation set, labelers A, B, C, D, and E underwent extensive training to understand the intricacies of fine-grained class distinctions in the ImageNet class hierarchy. Authors should clarify each key term in the presentation otherwise readers are hard to follow.<br /> # Not sure how the human samplers were determined and simply picking several people will have really high bias because the sample is too small and they have different background which will definitely affect the results a lot. Also, it will be better if there are more comparisons between the model introduced and other models.<br /> # Given the low amount of human participants, it is hard to take the results seriously (there is too much variance). Also it's not exactly clear how the authors determined that the multi-label accuracy metric measures a semantically more meaningful notion of accuracy compared to its counterparts. For example, one of the issues with top-5 accuracy that they mention is: &quot;For instance, within the dataset, five turtle classes are given which is difficult to distinguish under such classification evaluations.&quot; But it's not clear how multi-label accuracy would be better in this instance.<br /> # It is unclear how well the human labeler can perform labeling after training. So the final result is not that trust-worthy.<br /> # In this experiment set up, label annotators are the same as participants of the experiments. Even if there's a break between the annotating and evaluating human labeler evaluation, the impact of the break in reducing bias is not clear. One potential human labeling data is google's &quot;I'm not a robot&quot; verification test. One variation of the verification test asks users to select all the photos from 9 images that are related to a certain keyword. This allows for a more accurate measurement of human performance vs ImageNet performance. In addition, it's going to reduce the biases from the small number of experiment participants.<br /> # Following Table 2, the authors appear to try and claim that the model is better than the human labelers, simply because the model experienced a better increase in classification following the removal of dog photos then the human labeler did, however, a quick look at the table shows that most human labelers still performed better than the best model. The authors should be making the claim that human labelers are better at labeling dogs than the modal, but are still better overall after removing the dogs dataset.<br /> # The reason why human labeler outperforms CNN could be human had much more training. It would be more convincing if the paper could provide a metric in order to measure human labelers' training data set size.<br /> # Actually, in the multi-label case, it is vague to determine whether the machine learning model or the human labellers were giving the correct label. The structure of the dataset is pretty essential in training a network, in which data with uncertain label (even determined by human) should be avoided.<br /> # I believe the authors needed to include more information about how they determined the samples such as human samplers, and also more details on how to define unclear images.<br /> # It would be more convincing if the author could provide the criteria of being human samplers and unclear images, and the accuracy of the human labeler.<br /> # The summary only explains some model components but does not thoroughly goes through the big picture of the model; data-preprocessing, training, and prediction procedures. It would be nice to know the details as well.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=48554 Improving neural networks by preventing co-adaption of feature detectors 2020-12-01T01:12:30Z <p>Sh68lee: /* CNN */</p> <hr /> <div>== Presented by ==<br /> Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim<br /> <br /> = Introduction =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden units being present during training. Hence there are fewer co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; Reuters Corpus Volume; CIFAR-10; and ImageNet.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with mini-batches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by the decaying factor &lt;math&gt;f&lt;/math&gt; = 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross-validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation of 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist2.png|center|400px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors. This was reduced to about 130 errors with 0.5 dropout and different L2 constraints for each hidden unit input weight. By omitting a random 20% of the input pixels in addition to the aforementioned changes, the number of errors was further reduced to 110. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> TIMIT dataset includes voice samples of 630 American English speakers varying across 8 different dialects. It is often used to evaluate the performance of automatic speech recognition systems. Using Kaldi, the dataset was pre-processed to extract input features in the form of log filter bank responses.<br /> <br /> === Pre-training and Training ===<br /> <br /> For pretraining, they pretrained their neural network with a deep belief network and the first layer was built using Restricted Boltzmann Machine (RBM). Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged.<br /> <br /> Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> <br /> === Classification Test and Performance ===<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input.<br /> <br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Thus, neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters Corpus Volume =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias a.k.a weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. The figure above gives a visual representation of a Convolutional Neural Network. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. When looking at the image example, green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + \epsilon &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90 minutes and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> === CIFAR-10 Dataset ===<br /> <br /> Removing incorrect labels, The CIFAR-10 dataset is a subset of the Tiny Images dataset with 10 classes. It contains 5000 training images and 1000 testing images for each class. The dataset has 32 x 32 color images searched from the web and the images are labeled with the noun used to search the image.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> === Models for CIFAR-10 ===<br /> <br /> Two models, one with dropout and one without dropout, were built to test the performance of dropout on CIFAR-10. All models have CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers. A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> <br /> Additional changes were made with the model with dropout. The model with dropout enables us to use more parameters because dropout forces a strong regularization on the network. Thus, a fourth weight layer is added to take the input from the previous pooling layer. This fourth weight layer is locally connected, but not convolutional, and contains 16 banks of filters of size 3 × 3 with 50% dropout. Lastly, the softmax layer takes its input from this fourth weight layer.<br /> <br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. The model with one additional locally-connected layer and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset was the error rate of 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error rate using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. When applying 50% dropout to the 6th layer, the error rate was brought down to 42.4%.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the model without dropout had a similar approach, but there was a serious issue with overfitting): <br /> <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. This could reduce the network’s capacity to overfit the training data and helped generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, four corners, and their horizontal reflections).<br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> = Critiques =<br /> It is a very brilliant idea to dropout half of the neurons to reduce co-adaptations. It is mentioned that for fully connected layers, dropout in all hidden layers works better than dropout in only one hidden layer. There is another paper Dropout: A Simple Way to Prevent Neural Networks from<br /> Overfitting[https://www.cs.toronto.edu/~hinton/absps/JMLRdropout.pdf] gives a more detailed explanation.<br /> <br /> It will be interesting to see how this paper could be used to prevent overfitting of LSTMs.<br /> <br /> = Conclusion =<br /> <br /> The authors have shown a consistent improvement by the models trained with dropout in classifying objects in the following datasets: MNIST; TIMIT; Reuters Corpus Volume I; CIFAR-10; and ImageNet.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat441F21&diff=48325 stat441F21 2020-11-30T05:17:02Z <p>Sh68lee: /* Paper presentation */</p> <hr /> <div><br /> <br /> == [[F20-STAT 441/841 CM 763-Proposal| Project Proposal ]] ==<br /> <br /> &lt;!--[https://goo.gl/forms/apurag4dr9kSR76X2 Your feedback on presentations]--&gt;<br /> <br /> = Record your contributions here [https://docs.google.com/spreadsheets/d/10CHiJpAylR6kB9QLqN7lZHN79D9YEEW6CDTH27eAhbQ/edit?usp=sharing]=<br /> <br /> Use the following notations:<br /> <br /> P: You have written a summary/critique of the paper.<br /> <br /> T: You had a technical contribution on a paper (excluding the paper that you present).<br /> <br /> E: You had an editorial contribution on a paper (excluding the paper that you present).<br /> <br /> =Paper presentation=<br /> {| class=&quot;wikitable&quot;<br /> <br /> {| border=&quot;1&quot; cellpadding=&quot;3&quot;<br /> |-<br /> |width=&quot;60pt&quot;|Date<br /> |width=&quot;250pt&quot;|Name <br /> |width=&quot;15pt&quot;|Paper number <br /> |width=&quot;700pt&quot;|Title<br /> |width=&quot;15pt&quot;|Link to the paper<br /> |width=&quot;30pt&quot;|Link to the summary<br /> |width=&quot;30pt&quot;|Link to the video<br /> |-<br /> |Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&amp;t=539]<br /> |-<br /> |Week of Nov 16 ||Sharman Bharat, Li Dylan,Lu Leonie, Li Mingdao || 1|| Risk prediction in life insurance industry using supervised learning algorithms || [https://rdcu.be/b780J Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Bsharman Summary] ||<br /> [https://www.youtube.com/watch?v=TVLpSFYgF0c&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Delaney Smith, Mohammad Assem Mahmoud || 2|| Influenza Forecasting Framework based on Gaussian Processes || [https://proceedings.icml.cc/static/paper_files/icml/2020/1239-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes Summary]|| [https://www.youtube.com/watch?v=HZG9RAHhpXc&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Tatianna Krikella, Swaleh Hussain, Grace Tompkins || 3|| Processing of Missing Data by Neural Networks || [http://papers.nips.cc/paper/7537-processing-of-missing-data-by-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Gtompkin Summary] || [https://learn.uwaterloo.ca/d2l/ext/rp/577051/lti/framedlaunch/6ec1ebea-5547-46a2-9e4f-e3dc9d79fd54]<br /> |-<br /> |Week of Nov 16 ||Jonathan Chow, Nyle Dharani, Ildar Nasirov ||4 ||Streaming Bayesian Inference for Crowdsourced Classification ||[https://papers.nips.cc/paper/9439-streaming-bayesian-inference-for-crowdsourced-classification.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification Summary] || [https://www.youtube.com/watch?v=UgVRzi9Ubws]<br /> |-<br /> |Week of Nov 16 || Matthew Hall, Johnathan Chalaturnyk || 5|| Neural Ordinary Differential Equations || [https://papers.nips.cc/paper/7892-neural-ordinary-differential-equations.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs Summary]||<br /> |-<br /> |Week of Nov 16 || Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun || 6|| Adversarial Attacks on Copyright Detection Systems || Paper [https://proceedings.icml.cc/static/paper_files/icml/2020/1894-Paper.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems Summary] || [https://www.youtube.com/watch?v=bQI9S6bCo8o]<br /> |-<br /> |Week of Nov 16 || Casey De Vera, Solaiman Jawad || 7|| IPBoost – Non-Convex Boosting via Integer Programming || [https://arxiv.org/pdf/2002.04679.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost Summary] || [https://www.youtube.com/watch?v=4DhJDGC4pyI&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Yuxin Wang, Evan Peters, Yifan Mou, Sangeeth Kalaichanthiran || 8|| What Game Are We Playing? End-to-end Learning in Normal and Extensive Form Games || [https://arxiv.org/pdf/1805.02777.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=what_game_are_we_playing Summary] || [https://www.youtube.com/watch?v=9qJoVxo3hnI&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Yuchuan Wu || 9|| || || ||<br /> |-<br /> |Week of Nov 16 || Zhou Zeping, Siqi Li, Yuqin Fang, Fu Rao || 10|| A survey of neural network-based cancer prediction models from microarray data || [https://www.sciencedirect.com/science/article/pii/S0933365717305067 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Y93fang Summary] || [https://youtu.be/B8pPUU8ypO0]<br /> |-<br /> |Week of Nov 23 ||Jinjiang Lian, Jiawen Hou, Yisheng Zhu, Mingzhe Huang || 11|| DROCC: Deep Robust One-Class Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/6556-Paper.pdf paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou Summary] || [https://www.youtube.com/watch?v=tvCEvvy54X8&amp;ab_channel=JJLian]<br /> |-<br /> |Week of Nov 23 || Bushra Haque, Hayden Jones, Michael Leung, Cristian Mustatea || 12|| Combine Convolution with Recurrent Networks for Text Classification || [https://arxiv.org/pdf/2006.15795.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat Summary] || [https://www.youtube.com/watch?v=or5RTxDnZDo]<br /> |-<br /> |Week of Nov 23 || Taohao Wang, Zeren Shen, Zihao Guo, Rui Chen || 13|| Large Scale Landmark Recognition via Deep Metric Learning || [https://arxiv.org/pdf/1908.10192.pdf paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang Summary] || [https://www.youtube.com/watch?v=K9NypDNPLJo Video]<br /> |-<br /> |Week of Nov 23 || Qianlin Song, William Loh, Junyue Bai, Phoebe Choi || 14|| Task Understanding from Confusing Multi-task Data || [https://proceedings.icml.cc/static/paper_files/icml/2020/578-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data Summary] || [https://youtu.be/i_5PQdfuH-Y]<br /> |-<br /> |Week of Nov 23 || Rui Gong, Xuetong Wang, Xinqi Ling, Di Ma || 15|| Semantic Relation Classification via Convolution Neural Network|| [https://www.aclweb.org/anthology/S18-1127.pdf paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification——via_Convolution_Neural_Network Summary]|| [https://www.youtube.com/watch?v=m9o3NuMUKkU&amp;ab_channel=DiMa video]<br /> |-<br /> |Week of Nov 23 || Xiaolan Xu, Robin Wen, Yue Weng, Beizhen Chang || 16|| Graph Structure of Neural Networks || [https://proceedings.icml.cc/paper/2020/file/757b505cfd34c64c85ca5b5690ee5293-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Graph_Structure_of_Neural_Networks Summary] || [https://youtu.be/x9eUgEwntcs Video]<br /> |-<br /> |Week of Nov 23 ||Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty || 17|| Superhuman AI for multiplayer poker || [https://www.cs.cmu.edu/~noamb/papers/19-Science-Superhuman.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker Summary]|| [https://www.youtube.com/watch?v=kazqcOwbtTI Video]<br /> |-<br /> |Week of Nov 23 ||Guanting Pan, Haocheng Chang, Zaiwei Zhang || 18|| Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence || [https://arxiv.org/pdf/1809.10770.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence Summary] || [https://www.youtube.com/watch?v=aAwjaos_Hus Video]<br /> |-<br /> |Week of Nov 23 || Jerry Huang, Daniel Jiang, Minyan Dai || 19|| Neural Speed Reading Via Skim-RNN ||[https://arxiv.org/pdf/1711.02085.pdf?fbclid=IwAR3EeFsKM_b5p9Ox7X9mH-1oI3U3oOKPBy3xUOBN0XvJa7QW2ZeJJ9ypQVo Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN Summary]|| [https://youtu.be/vOENmt9jgVE Video]<br /> |-<br /> |Week of Nov 23 ||Ruixian Chin, Yan Kai Tan, Jason Ong, Wen Cheen Chiew || 20|| DivideMix: Learning with Noisy Labels as Semi-supervised Learning || [https://openreview.net/pdf?id=HJgExaVtwr Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan Summary]|| [https://www.youtube.com/watch?v=48xYZXifjS0&amp;ab_channel=SeakraChin]<br /> |-<br /> |Week of Nov 30 || Banno Dion, Battista Joseph, Kahn Solomon || 21|| Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks || [https://www.sciencedirect.com/science/article/pii/S1877050919310646] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN#Evaluation_of_Music_Recommendation_System: Summary] || [https://youtu.be/eGUV3zwLwqQ]<br /> |-<br /> |Week of Nov 30 || Isaac Ellmen, Dorsa Mohammadrezaei, Emilee Carson || 22|| A universal SNP and small-indel variant caller using deep neural networks||[https://www.nature.com/articles/nbt.4235.epdf?author_access_token=q4ZmzqvvcGBqTuKyKgYrQ9RgN0jAjWel9jnR3ZoTv0NuM3saQzpZk8yexjfPUhdFj4zyaA4Yvq0LWBoCYQ4B9vqPuv8e2HHy4vShDgEs8YxI_hLs9ov6Y1f_4fyS7kGZ Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=A_universal_SNP_and_small-indel_variant_caller_using_deep_neural_networks Summary] ||<br /> |-<br /> |Week of Nov 30 || Daniel Fagan, Cooper Brooke, Maya Perelman || 23|| Efficient kNN Classification With Different Number of Nearest Neighbors || [https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=7898482 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Dfagan Summary]||<br /> |-<br /> |Week of Nov 30 || Karam Abuaisha, Evan Li, Jason Pu, Nicholas Vadivelu || 24|| Being Bayesian about Categorical Probability || [https://proceedings.icml.cc/static/paper_files/icml/2020/3560-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Being_Bayesian_about_Categorical_Probability Summary] || [https://drive.google.com/file/d/1I0uYF2xEMuNVtaEhPb_vZ6bxSKMi0gUh/view?usp=sharing]<br /> |-<br /> |Week of Nov 30 || Anas Mahdi Will Thibault Jan Lau Jiwon Yang || 25|| Loss Function Search for Face Recognition<br /> || [https://proceedings.icml.cc/static/paper_files/icml/2020/245-Paper.pdf] paper || Summary [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition] || [https://youtu.be/i3dXnK9HGSQ]<br /> |-<br /> |Week of Nov 30 ||Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee || 26|| Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms || [https://arxiv.org/pdf/1912.07618.pdf?fbclid=IwAR0RwATSn4CiT3qD9LuywYAbJVw8YB3nbex8Kl19OCExIa4jzWaUut3oVB0 Paper] || Summary [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&amp;fbclid=IwAR1Tad2DAM7LT6NXXuSYDZtHHBvN0mjZtDdCOiUFFq_XwVcQxG3hU-3XcaE] || [https://www.youtube.com/watch?v=kiYbAmd_3IA]<br /> |-<br /> |Week of Nov 30 || Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim || 27|| Improving neural networks by preventing co-adaption of feature detectors || [https://arxiv.org/pdf/1207.0580.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors Summary] || [https://youtu.be/SV5UOM3QwiA Video]<br /> |-<br /> |Week of Nov 30 || Yawen Wang, Danmeng Cui, ZiJie Jiang, Mingkang Jiang, Haotian Ren, Haris Bin Zahid || 28|| A Brief Survey of Text Mining: Classification, Clustering and Extraction Techniques || [https://arxiv.org/pdf/1707.02919.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Describtion_of_Text_Mining Summary] ||<br /> |-<br /> |Week of Nov 30 || Qing Guo, XueGuang Ma, James Ni, Yuanxin Wang || 29|| Mask R-CNN || [https://arxiv.org/pdf/1703.06870.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Mask_RCNN Summary] || [https://youtu.be/NgcSMXNDNuU]<br /> |-<br /> |Week of Nov 30 || Junyi Yang, Jill Yu Chieh Wang, Yu Min Wu, Calvin Li || 30|| Research paper classifcation systems based on TF‑IDF and LDA schemes || [https://hcis-journal.springeropen.com/articles/10.1186/s13673-019-0192-7?fbclid=IwAR3swO-eFrEbj1BUQfmomJazxxeFR6SPgr6gKayhs38Y7aBG-zX1G3XWYRM Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Research_Papers_Classification_System Summary] || [https://youtu.be/Ug-5H4B5xkQ]<br /> |-<br /> |Week of Nov 30 || Daniel Zhang, Jacky Yao, Scholar Sun, Russell Parco, Ian Cheung || 31 || Speech2Face: Learning the Face Behind a Voice || [https://arxiv.org/pdf/1905.09773.pdf?utm_source=thenewstack&amp;utm_medium=website&amp;utm_campaign=platform Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Speech2Face:_Learning_the_Face_Behind_a_Voice Summary] || [https://youtu.be/lNQAbMxOj4w]<br /> |-<br /> |Week of Nov 30 || Siyuan Xia, Jiaxiang Liu, Jiabao Dong, Yipeng Du || 32 || Evaluating Machine Accuracy on ImageNet || [https://proceedings.icml.cc/static/paper_files/icml/2020/6173-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Evaluating_Machine_Accuracy_on_ImageNet Summary] ||<br /> |-<br /> |Week of Nov 30 || Mushi Wang, Siyuan Qiu, Yan Yu || 33 || Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn Intersections || [https://ieeexplore.ieee.org/abstract/document/8957421 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Surround_Vehicle_Motion_Prediction Summary] ||</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat441F21&diff=48324 stat441F21 2020-11-30T05:16:41Z <p>Sh68lee: /* Paper presentation */</p> <hr /> <div><br /> <br /> == [[F20-STAT 441/841 CM 763-Proposal| Project Proposal ]] ==<br /> <br /> &lt;!--[https://goo.gl/forms/apurag4dr9kSR76X2 Your feedback on presentations]--&gt;<br /> <br /> = Record your contributions here [https://docs.google.com/spreadsheets/d/10CHiJpAylR6kB9QLqN7lZHN79D9YEEW6CDTH27eAhbQ/edit?usp=sharing]=<br /> <br /> Use the following notations:<br /> <br /> P: You have written a summary/critique of the paper.<br /> <br /> T: You had a technical contribution on a paper (excluding the paper that you present).<br /> <br /> E: You had an editorial contribution on a paper (excluding the paper that you present).<br /> <br /> =Paper presentation=<br /> {| class=&quot;wikitable&quot;<br /> <br /> {| border=&quot;1&quot; cellpadding=&quot;3&quot;<br /> |-<br /> |width=&quot;60pt&quot;|Date<br /> |width=&quot;250pt&quot;|Name <br /> |width=&quot;15pt&quot;|Paper number <br /> |width=&quot;700pt&quot;|Title<br /> |width=&quot;15pt&quot;|Link to the paper<br /> |width=&quot;30pt&quot;|Link to the summary<br /> |width=&quot;30pt&quot;|Link to the video<br /> |-<br /> |Sep 15 (example)||Ri Wang || ||Sequence to sequence learning with neural networks.||[http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Going_Deeper_with_Convolutions Summary] || [https://youtu.be/JWozRg_X-Vg?list=PLehuLRPyt1HzXDemu7K4ETcF0Ld_B5adG&amp;t=539]<br /> |-<br /> |Week of Nov 16 ||Sharman Bharat, Li Dylan,Lu Leonie, Li Mingdao || 1|| Risk prediction in life insurance industry using supervised learning algorithms || [https://rdcu.be/b780J Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Bsharman Summary] ||<br /> [https://www.youtube.com/watch?v=TVLpSFYgF0c&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Delaney Smith, Mohammad Assem Mahmoud || 2|| Influenza Forecasting Framework based on Gaussian Processes || [https://proceedings.icml.cc/static/paper_files/icml/2020/1239-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes Summary]|| [https://www.youtube.com/watch?v=HZG9RAHhpXc&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Tatianna Krikella, Swaleh Hussain, Grace Tompkins || 3|| Processing of Missing Data by Neural Networks || [http://papers.nips.cc/paper/7537-processing-of-missing-data-by-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Gtompkin Summary] || [https://learn.uwaterloo.ca/d2l/ext/rp/577051/lti/framedlaunch/6ec1ebea-5547-46a2-9e4f-e3dc9d79fd54]<br /> |-<br /> |Week of Nov 16 ||Jonathan Chow, Nyle Dharani, Ildar Nasirov ||4 ||Streaming Bayesian Inference for Crowdsourced Classification ||[https://papers.nips.cc/paper/9439-streaming-bayesian-inference-for-crowdsourced-classification.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification Summary] || [https://www.youtube.com/watch?v=UgVRzi9Ubws]<br /> |-<br /> |Week of Nov 16 || Matthew Hall, Johnathan Chalaturnyk || 5|| Neural Ordinary Differential Equations || [https://papers.nips.cc/paper/7892-neural-ordinary-differential-equations.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs Summary]||<br /> |-<br /> |Week of Nov 16 || Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun || 6|| Adversarial Attacks on Copyright Detection Systems || Paper [https://proceedings.icml.cc/static/paper_files/icml/2020/1894-Paper.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems Summary] || [https://www.youtube.com/watch?v=bQI9S6bCo8o]<br /> |-<br /> |Week of Nov 16 || Casey De Vera, Solaiman Jawad || 7|| IPBoost – Non-Convex Boosting via Integer Programming || [https://arxiv.org/pdf/2002.04679.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost Summary] || [https://www.youtube.com/watch?v=4DhJDGC4pyI&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Yuxin Wang, Evan Peters, Yifan Mou, Sangeeth Kalaichanthiran || 8|| What Game Are We Playing? End-to-end Learning in Normal and Extensive Form Games || [https://arxiv.org/pdf/1805.02777.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=what_game_are_we_playing Summary] || [https://www.youtube.com/watch?v=9qJoVxo3hnI&amp;feature=youtu.be]<br /> |-<br /> |Week of Nov 16 || Yuchuan Wu || 9|| || || ||<br /> |-<br /> |Week of Nov 16 || Zhou Zeping, Siqi Li, Yuqin Fang, Fu Rao || 10|| A survey of neural network-based cancer prediction models from microarray data || [https://www.sciencedirect.com/science/article/pii/S0933365717305067 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Y93fang Summary] || [https://youtu.be/B8pPUU8ypO0]<br /> |-<br /> |Week of Nov 23 ||Jinjiang Lian, Jiawen Hou, Yisheng Zhu, Mingzhe Huang || 11|| DROCC: Deep Robust One-Class Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/6556-Paper.pdf paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou Summary] || [https://www.youtube.com/watch?v=tvCEvvy54X8&amp;ab_channel=JJLian]<br /> |-<br /> |Week of Nov 23 || Bushra Haque, Hayden Jones, Michael Leung, Cristian Mustatea || 12|| Combine Convolution with Recurrent Networks for Text Classification || [https://arxiv.org/pdf/2006.15795.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat Summary] || [https://www.youtube.com/watch?v=or5RTxDnZDo]<br /> |-<br /> |Week of Nov 23 || Taohao Wang, Zeren Shen, Zihao Guo, Rui Chen || 13|| Large Scale Landmark Recognition via Deep Metric Learning || [https://arxiv.org/pdf/1908.10192.pdf paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang Summary] || [https://www.youtube.com/watch?v=K9NypDNPLJo Video]<br /> |-<br /> |Week of Nov 23 || Qianlin Song, William Loh, Junyue Bai, Phoebe Choi || 14|| Task Understanding from Confusing Multi-task Data || [https://proceedings.icml.cc/static/paper_files/icml/2020/578-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data Summary] || [https://youtu.be/i_5PQdfuH-Y]<br /> |-<br /> |Week of Nov 23 || Rui Gong, Xuetong Wang, Xinqi Ling, Di Ma || 15|| Semantic Relation Classification via Convolution Neural Network|| [https://www.aclweb.org/anthology/S18-1127.pdf paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification——via_Convolution_Neural_Network Summary]|| [https://www.youtube.com/watch?v=m9o3NuMUKkU&amp;ab_channel=DiMa video]<br /> |-<br /> |Week of Nov 23 || Xiaolan Xu, Robin Wen, Yue Weng, Beizhen Chang || 16|| Graph Structure of Neural Networks || [https://proceedings.icml.cc/paper/2020/file/757b505cfd34c64c85ca5b5690ee5293-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Graph_Structure_of_Neural_Networks Summary] || [https://youtu.be/x9eUgEwntcs Video]<br /> |-<br /> |Week of Nov 23 ||Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty || 17|| Superhuman AI for multiplayer poker || [https://www.cs.cmu.edu/~noamb/papers/19-Science-Superhuman.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker Summary]|| [https://www.youtube.com/watch?v=kazqcOwbtTI Video]<br /> |-<br /> |Week of Nov 23 ||Guanting Pan, Haocheng Chang, Zaiwei Zhang || 18|| Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence || [https://arxiv.org/pdf/1809.10770.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence Summary] || [https://www.youtube.com/watch?v=aAwjaos_Hus Video]<br /> |-<br /> |Week of Nov 23 || Jerry Huang, Daniel Jiang, Minyan Dai || 19|| Neural Speed Reading Via Skim-RNN ||[https://arxiv.org/pdf/1711.02085.pdf?fbclid=IwAR3EeFsKM_b5p9Ox7X9mH-1oI3U3oOKPBy3xUOBN0XvJa7QW2ZeJJ9ypQVo Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN Summary]|| [https://youtu.be/vOENmt9jgVE Video]<br /> |-<br /> |Week of Nov 23 ||Ruixian Chin, Yan Kai Tan, Jason Ong, Wen Cheen Chiew || 20|| DivideMix: Learning with Noisy Labels as Semi-supervised Learning || [https://openreview.net/pdf?id=HJgExaVtwr Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan Summary]|| [https://www.youtube.com/watch?v=48xYZXifjS0&amp;ab_channel=SeakraChin]<br /> |-<br /> |Week of Nov 30 || Banno Dion, Battista Joseph, Kahn Solomon || 21|| Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks || [https://www.sciencedirect.com/science/article/pii/S1877050919310646] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Music_Recommender_System_Based_using_CRNN#Evaluation_of_Music_Recommendation_System: Summary] || [https://youtu.be/eGUV3zwLwqQ]<br /> |-<br /> |Week of Nov 30 || Isaac Ellmen, Dorsa Mohammadrezaei, Emilee Carson || 22|| A universal SNP and small-indel variant caller using deep neural networks||[https://www.nature.com/articles/nbt.4235.epdf?author_access_token=q4ZmzqvvcGBqTuKyKgYrQ9RgN0jAjWel9jnR3ZoTv0NuM3saQzpZk8yexjfPUhdFj4zyaA4Yvq0LWBoCYQ4B9vqPuv8e2HHy4vShDgEs8YxI_hLs9ov6Y1f_4fyS7kGZ Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=A_universal_SNP_and_small-indel_variant_caller_using_deep_neural_networks Summary] ||<br /> |-<br /> |Week of Nov 30 || Daniel Fagan, Cooper Brooke, Maya Perelman || 23|| Efficient kNN Classification With Different Number of Nearest Neighbors || [https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=7898482 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Dfagan Summary]||<br /> |-<br /> |Week of Nov 30 || Karam Abuaisha, Evan Li, Jason Pu, Nicholas Vadivelu || 24|| Being Bayesian about Categorical Probability || [https://proceedings.icml.cc/static/paper_files/icml/2020/3560-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Being_Bayesian_about_Categorical_Probability Summary] || [https://drive.google.com/file/d/1I0uYF2xEMuNVtaEhPb_vZ6bxSKMi0gUh/view?usp=sharing]<br /> |-<br /> |Week of Nov 30 || Anas Mahdi Will Thibault Jan Lau Jiwon Yang || 25|| Loss Function Search for Face Recognition<br /> || [https://proceedings.icml.cc/static/paper_files/icml/2020/245-Paper.pdf] paper || Summary [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Loss_Function_Search_for_Face_Recognition] || [https://youtu.be/i3dXnK9HGSQ]<br /> |-<br /> |Week of Nov 30 ||Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee || 26|| Deep Learning for Cardiologist-level Myocardial Infarction Detection in Electrocardiograms || [https://arxiv.org/pdf/1912.07618.pdf?fbclid=IwAR0RwATSn4CiT3qD9LuywYAbJVw8YB3nbex8Kl19OCExIa4jzWaUut3oVB0 Paper] || Summary [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&amp;fbclid=IwAR1Tad2DAM7LT6NXXuSYDZtHHBvN0mjZtDdCOiUFFq_XwVcQxG3hU-3XcaE] || [https://www.youtube.com/watch?v=kiYbAmd_3IA]<br /> |-<br /> |Week of Nov 30 || Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim || 27|| Improving neural networks by preventing co-adaption of feature detectors || [https://arxiv.org/pdf/1207.0580.pdf paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors Summary] || [https://youtu.be/SV5UOM3QwiA Video]<br /> |-<br /> |Week of Nov 30 || Yawen Wang, Danmeng Cui, ZiJie Jiang, Mingkang Jiang, Haotian Ren, Haris Bin Zahid || 28|| A Brief Survey of Text Mining: Classification, Clustering and Extraction Techniques || [https://arxiv.org/pdf/1707.02919.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Describtion_of_Text_Mining Summary] ||<br /> |-<br /> |Week of Nov 30 || Qing Guo, XueGuang Ma, James Ni, Yuanxin Wang || 29|| Mask R-CNN || [https://arxiv.org/pdf/1703.06870.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Mask_RCNN Summary] || [https://youtu.be/NgcSMXNDNuU]<br /> |-<br /> |Week of Nov 30 || Junyi Yang, Jill Yu Chieh Wang, Yu Min Wu, Calvin Li || 30|| Research paper classifcation systems based on TF‑IDF and LDA schemes || [https://hcis-journal.springeropen.com/articles/10.1186/s13673-019-0192-7?fbclid=IwAR3swO-eFrEbj1BUQfmomJazxxeFR6SPgr6gKayhs38Y7aBG-zX1G3XWYRM Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Research_Papers_Classification_System Summary] || [https://youtu.be/Ug-5H4B5xkQ]<br /> |-<br /> |Week of Nov 30 || Daniel Zhang, Jacky Yao, Scholar Sun, Russell Parco, Ian Cheung || 31 || Speech2Face: Learning the Face Behind a Voice || [https://arxiv.org/pdf/1905.09773.pdf?utm_source=thenewstack&amp;utm_medium=website&amp;utm_campaign=platform Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Speech2Face:_Learning_the_Face_Behind_a_Voice Summary] || [https://youtu.be/lNQAbMxOj4w]<br /> |-<br /> |Week of Nov 30 || Siyuan Xia, Jiaxiang Liu, Jiabao Dong, Yipeng Du || 32 || Evaluating Machine Accuracy on ImageNet || [https://proceedings.icml.cc/static/paper_files/icml/2020/6173-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Evaluating_Machine_Accuracy_on_ImageNet Summary] ||<br /> |-<br /> |Week of Nov 30 || Mushi Wang, Siyuan Qiu, Yan Yu || 33 || Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn Intersections || [https://ieeexplore.ieee.org/abstract/document/8957421 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Surround_Vehicle_Motion_Prediction Summary] ||</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47573 Improving neural networks by preventing co-adaption of feature detectors 2020-11-29T03:24:44Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim<br /> <br /> = Introduction =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden units being present during training. Hence there are fewer co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; Reuters Corpus Volume; CIFAR-10; and ImageNet.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with mini-batches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross-validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation of 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist2.png|center|400px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. <br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> <br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters Corpus Volume =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. When looking at the image example, green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + \epsilon &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90 minutes and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> === CIFAR-10 Dataset ===<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images are labeled with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> === Models for CIFAR-10 ===<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. Two models both have CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers. A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> <br /> Additional changes were made with the model with dropout. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. This fourth weight layer is locally connected but not convolutional and contains 16 banks of filters of size 3 × 3 with 50% dropout. Lastly, the softmax layer takes its input from this fourth weight layer.<br /> <br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset was the error rate of 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, the error rate of 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> = Conclusion =<br /> <br /> The authors have shown a consistent improvement by the models trained with dropout in classifying objects in the following datasets: MNIST; TIMIT; Reuters Corpus Volume I; CIFAR-10; and ImageNet.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47572 Improving neural networks by preventing co-adaption of feature detectors 2020-11-29T03:19:19Z <p>Sh68lee: /* CNN */</p> <hr /> <div>== Presented by ==<br /> Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim<br /> <br /> = Introduction =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden units being present during training. Hence there are fewer co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; Reuters Corpus Volume; CIFAR-10; and ImageNet.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with mini-batches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross-validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation of 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist2.png|center|400px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. <br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> <br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters Corpus Volume =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. When looking at the image example, green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90 minutes and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> === CIFAR-10 Dataset ===<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images are labeled with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> === Models for CIFAR-10 ===<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. Two models both have CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers. A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> <br /> Additional changes were made with the model with dropout. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. This fourth weight layer is locally connected but not convolutional and contains 16 banks of filters of size 3 × 3 with 50% dropout. Lastly, the softmax layer takes its input from this fourth weight layer.<br /> <br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset was the error rate of 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, the error rate of 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> = Conclusion =<br /> <br /> The authors have shown a consistent improvement by the models trained with dropout in classifying objects in the following datasets: MNIST; TIMIT; Reuters Corpus Volume I; CIFAR-10; and ImageNet.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47570 Improving neural networks by preventing co-adaption of feature detectors 2020-11-29T03:08:30Z <p>Sh68lee: /* Local Response Normalization */</p> <hr /> <div>== Presented by ==<br /> Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim<br /> <br /> = Introduction =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden units being present during training. Hence there are fewer co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; Reuters Corpus Volume; CIFAR-10; and ImageNet.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with mini-batches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross-validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation of 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist2.png|center|400px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. <br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> <br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters Corpus Volume =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90 minutes and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> <br /> = CIFAR-10 =<br /> <br /> === CIFAR-10 Dataset ===<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images are labeled with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> === Models for CIFAR-10 ===<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. Two models both have CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers. A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> <br /> Additional changes were made with the model with dropout. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. This fourth weight layer is locally connected but not convolutional and contains 16 banks of filters of size 3 × 3 with 50% dropout. Lastly, the softmax layer takes its input from this fourth weight layer.<br /> <br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset was the error rate of 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, the error rate of 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> = Conclusion =<br /> <br /> The authors have shown a consistent improvement by the models trained with dropout in classifying objects in the following datasets: MNIST; TIMIT; Reuters Corpus Volume I; CIFAR-10; and ImageNet.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47568 Improving neural networks by preventing co-adaption of feature detectors 2020-11-29T03:08:03Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Stan Lee, Seokho Lim, Kyle Jung, Dae Hyun Kim<br /> <br /> = Introduction =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden units being present during training. Hence there are fewer co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; Reuters Corpus Volume; CIFAR-10; and ImageNet.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with mini-batches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross-validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation of 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist2.png|center|400px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. <br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> <br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters Corpus Volume =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> local response norm.png<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90 minutes and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> <br /> = CIFAR-10 =<br /> <br /> === CIFAR-10 Dataset ===<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images are labeled with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> === Models for CIFAR-10 ===<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. Two models both have CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers. A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> <br /> Additional changes were made with the model with dropout. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. This fourth weight layer is locally connected but not convolutional and contains 16 banks of filters of size 3 × 3 with 50% dropout. Lastly, the softmax layer takes its input from this fourth weight layer.<br /> <br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset was the error rate of 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, the error rate of 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> = Conclusion =<br /> <br /> The authors have shown a consistent improvement by the models trained with dropout in classifying objects in the following datasets: MNIST; TIMIT; Reuters Corpus Volume I; CIFAR-10; and ImageNet.</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47243 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T06:16:40Z <p>Sh68lee: /* CNN */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=3|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> local response norm.png<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|800px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47242 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T06:15:59Z <p>Sh68lee: /* Local Response Normalization */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation:<br /> [[File:local response norm.png|upright=2|center|]] where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> local response norm.png<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet Dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet Dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|800px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47240 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T06:15:07Z <p>Sh68lee: /* Local Response Normalization */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> local response norm.png<br /> <br /> [[File:local response norm.png|thumb|upright=2|center|alt=text|Figure 3: An RNN and it’s unfolded counterpart]]<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images may contain multiple objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''An ambiguous example to classify:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|800px|center]] <br /> <br /> [[File:layer2.png|600px|center]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:local_response_norm.png&diff=47236 File:local response norm.png 2020-11-28T06:12:54Z <p>Sh68lee: </p> <hr /> <div></div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47233 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T06:06:37Z <p>Sh68lee: /* CNN */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In the following figure, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. <br /> <br /> [[File:reuters_figure.png|700px|center]]<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. [[File:cnnbigpicture.jpeg|thumb|upright=2|center|alt=text|Figure: Overview of Convolutional Neural Network]] There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px|center]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px|center]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used and it was found that dropout was very effective. Also, it was demonstrated that using non-convolutional higher layers with the number of parameters worked well with dropout, but it had a negative impact to the performance without dropout.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47228 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T06:01:06Z <p>Sh68lee: /* CNN */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure: Bank of neurons]]<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described below.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47227 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:59:48Z <p>Sh68lee: /* Pooling */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|center|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. The following figure visualizes the result.<br /> [[File:mnist_figure.png|center|500px]]<br /> A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:maxandavgpooling.jpeg|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> [[File:CIFAR-10.png|thumb|upright=2|center|alt=text|Figure 4: CIFAR-10 Sample Dataset]]<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described below.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =<br /> <br /> Training with dropout improved the performance...</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:maxandavgpooling.jpeg&diff=47226 File:maxandavgpooling.jpeg 2020-11-28T05:59:24Z <p>Sh68lee: </p> <hr /> <div></div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:cnnbigpicture.jpeg&diff=47225 File:cnnbigpicture.jpeg 2020-11-28T05:58:09Z <p>Sh68lee: </p> <hr /> <div></div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47212 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:50:20Z <p>Sh68lee: /* Pooling */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure: Max pooling and Average pooling]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47211 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:49:30Z <p>Sh68lee: /* Pooling */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:bankofneurons.gif|thumb|upright=2|center|alt=text|Figure 3: An RNN and it’s unfolded counterpart]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:bankofneurons.gif&diff=47210 File:bankofneurons.gif 2020-11-28T05:48:52Z <p>Sh68lee: </p> <hr /> <div></div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47209 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:46:24Z <p>Sh68lee: /* Pooling */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:example.png|thumb|upright=2|center|alt=text|Figure 3: An RNN and it’s unfolded counterpart]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47208 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:45:40Z <p>Sh68lee: /* Pooling */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution &lt;math&gt;N(0, 0.01)&lt;/math&gt;. Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by &lt;math&gt;(1-momentum)&lt;/math&gt; and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, &lt;math&gt;p&lt;/math&gt; was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to &lt;math&gt;log(p/(1 − p))&lt;/math&gt;. Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> [[File:Example.jpg]]<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47205 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:39:58Z <p>Sh68lee: /* Learning */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^{-2}&lt;/math&gt; or &lt;math&gt;10^{-3}&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47204 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:39:38Z <p>Sh68lee: /* Learning */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of &lt;math&gt;10^-2&lt;/math&gt; or &lt;math&gt;10^-3&lt;/math&gt;. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47203 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:39:06Z <p>Sh68lee: /* Local Response Normalization */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt; and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47202 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:38:52Z <p>Sh68lee: /* Local Response Normalization */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (&lt;math&gt;L1&lt;/math&gt;,and &lt;math&gt;L2&lt;/math&gt;)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001&lt;/math&gt;, and &lt;math&gt;β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47200 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:38:18Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. &lt;math&gt;L&lt;/math&gt; denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and &lt;math&gt;\frac{dE}{dw}&lt;/math&gt; is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001, and β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47198 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:37:53Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. L denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;/math&gt; is the learning rate and \frac{dE}{dw} is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;/math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with &lt;math&gt;N = 9, α = 0.001, and β = 0.75&lt;/math&gt; are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47196 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:37:29Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate &lt;math&gt;\epsilon&lt;/math&gt; was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, &lt;math&gt;l&lt;/math&gt;, and they found from cross validation that the results were the best when &lt;math&gt;l&lt;/math&gt; = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of &lt;math&gt;p&lt;/math&gt; was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by &lt;math&gt;1 – p&lt;/math&gt;. L denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight &lt;math&gt;w&lt;/math&gt; is $$v_{i+1} = 0.9v_i + &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$ where &lt;math&gt;i&lt;/math&gt; is the iteration index, &lt;math&gt;v&lt;/math&gt; is a momentum variable, &lt;math&gt;\epsilon&lt;math&gt; is the learning rate and \frac{dE}{dw} is the average over the &lt;math&gt;i&lt;/math&gt;th batch of the derivative of the objective with respect to &lt;math&gt;w_i&lt;math&gt;. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with N = 9, α = 0.001,'' and ''β = 0.75'' are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47190 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:32:46Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate ''ε'' was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, ''l'', and they found from cross validation that the results were the best when ''l'' = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, ''p'', called momentum, was used to accelerate learning. The initial value of ''p'' was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by 1 – ''p''. L denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight w is $$v_{i+1} = 0.9v_i + \epsilon &lt;\frac{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$, where i is the iteration index, v is a momentum variable, e is the learning rate and dE/dw is the average over the ith batch of the derivative of the objective with respect to w_i. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with N = 9, α = 0.001, and β = 0.75 are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ------<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47187 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:32:02Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate ε was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, l, and they found from cross validation that the results were the best when l = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, p, called momentum, was used to accelerate learning. The initial value of p was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by 1 – p. L denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight w is $$v_{i+1} = 0.9v_i + \epsilon &lt;\diff{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$, where i is the iteration index, v is a momentum variable, e is the learning rate and dE/dw is the average over the ith batch of the derivative of the objective with respect to w_i. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.<br /> <br /> They implemented two different models for CIFAR-10, one with dropout and the other without. The one with dropout enables us to use more parameters because dropout forces a strong regularization on the network, and a fourth weight layer is added to take the input from the previous pooling layer. We add a fourth weight layer that is locally connected but not convolutional and this layer contains 16 banks of filters of size 3 × 3 (50% dropout). And then, the softmax layer takes its input from this fourth weight layer.<br /> <br /> The one without dropout is a CNN with three convolutional layers each with a pooling layer. The max-pooling method is performed by the pooling layer which follows the first convolutional layer, and the average-pooling method is performed by remaining 2 pooling layers. The first and second pooling layers with N = 9, α = 0.001, and β = 0.75 are followed by response normalization layers.<br /> <br /> A ten-unit softmax layer, which is used to output a probability distribution over class labels, is connected with the upper-most pooling layer. Using filter size of 5×5, all convolutional layers have 64 filter banks.<br /> Thus, with a neural network with 3 convolutional hidden layers with 3 max-pooling layers, the classification error achieved 16.6% to beat 18.5% from the best published error rate without using transformed data. Then, adding one locally-connected layer after these 6 layers and dropout at the last hidden layer produced the error rate of 15.6%.<br /> <br /> = ImageNet =<br /> <br /> ===ImageNet dataset===<br /> <br /> ImageNet is a dataset of millions of high-resolution labeled images in thousands of categories which were collected from the web and labelled by human labellers using MTerk tool (Amazon’s Mechanical Turk crowd-sourcing tool). Because this dataset has millions of labeled images in thousands of categories, it is very difficult to have perfect accuracy on this dataset even for humans because the ImageNet images contain multiple instances of ImageNet objects and there are a large number of object classes. ImageNet and CIFAR-10 are very similar, but the scale of ImageNet is about 20 times bigger (1,300,000 vs 60,000). The size of ImageNet is about 1.3 million training images, 50,000 validation images, and 150,000 testing images. They used resized images of 256 x 256 pixels for their experiments.<br /> <br /> '''Example of ambiguous image to label:'''<br /> <br /> [[File:imagenet1.png|200px]]<br /> <br /> When this paper was written, the best score on this dataset is 45.7% by High-dimensional signature compression for large-scale image classification (J. Sanchez, F. Perronnin, CVPR11 (2011)). The authors of this paper could achieve a comparable performance of 48.6% error using a single neural network with five convolutional hidden layers with a max-pooling layer in between, followed by two globally connected layers and a final 1000-way softmax layer. Also, 42.4% could be achieved by using 50% dropout in the 6th hidden layer.<br /> <br /> '''ImageNet dataset:'''<br /> <br /> [[File:imagenet2.png|400px]]<br /> <br /> It was demonstrated that making a large number of decisions was important for the architecture of the net design for the speech recognition (TIMIT) and object recognition datasets (CIFAR-10 and ImageNet). A separate validation set which evaluated the performance of a large number of different architectures was used to make those decisions, and then they chose the best performance architecture with dropout on the validation set so that they could apply it to the real test set.<br /> <br /> ------<br /> <br /> ===Models for ImageNet===<br /> <br /> The models for ImageNet with dropout (the one without dropout had a similar approach, but there was a serious issue with overfitting): <br /> They used a convolutional neural network trained by 224×224 patches randomly extracted from the 256 × 256 images. It can reduce the network’s capacity to overfit the training data and helps generalization as a form of data augmentation. The method of averaging the prediction of the net on ten 224 × 224 patches of the 256 × 256 input image was used for a testing (patched at the center, the four corner patches, and their horizontal reflections). <br /> <br /> To maximize the performance on the validation set, this complicated network architecture was used as described below. They could show that dropout is a helpful factor for very complex neural nets that have been developed by the joint efforts of many groups over many years to be really good at object recognition. Using non-convolutional higher layers with a lot of parameters leads to a big improvement with dropout, but makes things worse without dropout. Training with dropout improved the performance even for a complicated model as described above.<br /> <br /> [[File:modelh2.png|700px]] [[File:layer2.png|500px]]<br /> <br /> = Conclusion =</div> Sh68lee http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Improving_neural_networks_by_preventing_co-adaption_of_feature_detectors&diff=47185 Improving neural networks by preventing co-adaption of feature detectors 2020-11-28T05:31:50Z <p>Sh68lee: /* Training */</p> <hr /> <div>== Presented by ==<br /> Kyle Jung, Dae Hyun Kim, Seokho Lim, Stan Lee<br /> <br /> = Introduction to Dropout &amp; Dataset =<br /> In this paper, Hinton et al. introduces a novel way to improve neural networks’ performance. By omitting neurons in hidden layers with a probability of 0.5, each hidden unit is prevented from relying on other hidden unit being present during training, hence there are less co-adaptations among them on the training data. Called “dropout,” this process is also an efficient alternative to training many separate networks and average their predictions on the test set.<br /> They used the standard, stochastic gradient descent algorithm and separated training data into mini-batches. An upper bound was set on the L2 norm of incoming weight vector for each hidden neuron, which was normalized if its size exceeds the bound. They found that using a constraint, instead of a penalty, forced model to do a more thorough search of the weight-space, when coupled with the very large learning rate that decays during training. <br /> Their dropout models included all of the hidden neurons, and their outgoing weights were halved to account for the chances of omission. The models were shown to result in lower test error rates on several datasets: MNIST; TIMIT; CIFAR-10; ImageNet; and Reuters Corpus Volume.<br /> <br /> = MNIST =<br /> The MNIST dataset contains 70,000 digit images of size 28 x 28. To see the impact of dropout, they used 4 different neural networks (784-800-800-10, 784-1200-1200-10, 784-2000-2000-10, 784-1200-1200-1200-10), using the same dropout rates as 50% for hidden neurons and 20% for visible neurons. Stochastic gradient descent was used with minibatches of size 100 and a cross-entropy objective function as the loss function. Weights were updated after each minibatch, and training was done for 3000 epochs. An exponentially decaying learning rate ε was used, with the initial value set as 10.0, and it was multiplied by 0.998 at the end of each epoch. At each hidden layer, the incoming weight vector for each hidden neuron was set an upper bound of its length, l, and they found from cross validation that the results were the best when l = 15. Initial weights values were pooled from a normal distribution with mean 0 and standard deviation 0.01. To update weights, an additional variable, p, called momentum, was used to accelerate learning. The initial value of p was 0.5, and it increased linearly to the final value 0.99 during the first 500 epochs, remaining unchanged after. Also, when updating weights, the learning rate was multiplied by 1 – p. L denotes the gradient of loss function.<br /> <br /> [[File:weights_mnist.png|700px]]<br /> <br /> The best published result for a standard feedforward neural network was 160 errors, and it was reduced to about 130 errors with dropout. By omitting a random 20% of the input pixels, it was further reduced to 110 errors. A publicly available pre-trained deep belief net resulted in 118 errors, and it was reduced to 92 errors when the model was fine-tuned with dropout. Another publicly available model was a deep Boltzmann machine, and it resulted in 103, 97, 94, 93 and 88 when the model was fine-tuned using standard backpropagation and was unrolled. They were reduced to 83, 79, 78, 78, and 77 when the model was fine-tuned with dropout – the mean of 79 errors was a record for models that do not use prior knowledge or enhanced training sets.<br /> <br /> = TIMIT = <br /> <br /> Consisting of recordings of 630 speakers of 8 dialects of American English each reading 10 phonetically-rich sentences, the TIMIT is a standard dataset used for evaluation of automatic speech recognition systems. The objective is to convert a given speech signal into a transcription sequence of phones. Hidden Markov Models (HMMs) is an acoustic model that is typically used to deal with variance and determines a level of fit from coefficients of input to each state of HMMs. Recent results show that mapping feedforward neural networks with an acoustic input coupled with a probability distribution over HMM states perform better than the traditional Gaussian mixture models on speech recognition datasets including TIMIT.<br /> <br /> A Neural network was constructed to output the classification error rate on the test set of TIMIT dataset. They have built the neural network with four fully-connected hidden layers with 4000 neurons per layer. The output layer distinguishes distinct classes from one hundred 185 softmax output neurons that are merged into 39 classes. After constructing the neural network, 21 adjacent frames with an advance of 10ms per frame was given as an input. The results show that applying dropout with 50% of hidden units on various neural networks exceed classification performance from the neural networks without dropout. The decoder, a network that knows transition probabilities between HMM states, runs the Viterbi algorithm on class probabilities for each frame from the output of the neural network to predict the best single sequence of HMM states. The classification error achieved 19.7% with dropout and 22.7% without dropout.<br /> <br /> === Pre-training ===<br /> <br /> Deep Belief Network was used to pretrain the neural network. Since the inputs are real-valued, Gaussian RBM was used for pretraining the first layer. Initializing visible biases with zero, weights were sampled from random numbers that followed normal distribution N(0, 0.01). Each visible neuron’s variance was set to 1.0 and remained unchanged during training. Minimizing Contrastive Divergence (CD) was used to facilitate learning. Since momentum is used to speed up learning, it was initially set to 0.5 and increased linearly to 0.9 over 20 epochs. The average gradient had 0.001 of a learning rate which was then multiplied by (1-momentum) and L2 weight decay was set to 0.001. After setting up the hyperparameters, the model was done training after 100 epochs. Binary RBMs were used for training all subsequent layers with a learning rate of 0.01. Then, p was set as the mean activation of a neuron in the data set and the visible bias of each neuron was initialized to log(p/(1 − p)). Training each layer with 50 epochs, all remaining hyper-parameters were the same as those for the Gaussian RBM.<br /> <br /> === Dropout tuning ===<br /> <br /> The initial weights were set in a neural network from the pretrained RBMs. To finetune the network with dropout-backpropagation, momentum was initially set to 0.5 and increased linearly up to 0.9 over 10 epochs. The model had a small constant learning rate of 1.0 and it was used to apply to the average gradient on a minibatch. The model also retained all other hyperparameters the same as the model from MNIST dropout finetuning. The model required approximately 200 epochs to converge. For comparison purpose, they also finetuned the same network with standard backpropagation with a learning rate of 0.1 with the same hyperparameters.<br /> Comparing the performance of dropout with standard backpropagation on several network architectures and input representations, dropout consistently achieved lower error and cross-entropy. Results showed that it significantly controls overfitting, making the method robust to choices of network architecture. It also allowed much larger nets to be trained and removed the need for early stopping. Neural network architectures with dropout are not very sensitive to the choice of learning rate and momentum.<br /> <br /> = Reuters =<br /> Reuters Corpus Volume I archives 804,414 news documents that belong to 103 topics. Under four major themes - corporate/industrial, economics, government/social, and markets – they belonged to 63 classes. After removing 11 classes with no data and one class with insufficient data, they are left with 50 classes and 402,738 documents. The documents were divided into training and test sets equally and randomly, with each document representing the 2000 most frequent words in the dataset, excluding stopwords.<br /> <br /> They trained two neural networks, with size 2000-2000-1000-50, one using dropout and backpropagation, and the other using standard backpropagation. The training hyperparameters are the same as that in MNIST, but training was done for 500 epochs.<br /> <br /> In Figure 7, we see the significant improvements by the model with dropout in the test set error. On the right side, we see that the learning with dropout also proceeds smoother. ********(figure must be added)<br /> <br /> = CNN =<br /> <br /> Feed-forward neural networks consist of several layers of neurons where each neuron in a layer applies a linear filter to the input image data and is passed on to the neurons in the next layer. When calculating the neuron’s output, scalar bias aka weights is applied to the filter with nonlinear activation function as parameters of the network that are learned by training data. There are several differences between Convolutional Neural networks and ordinary neural networks. First, CNN’s neurons are organized topographically into a bank and laid out on a 2D grid, so it reflects the organization of dimensions of the input data. Secondly, neurons in CNN apply filters which are local, and which are centered at the neuron’s location in the topographic organization. Meaning that useful metrics or clues to identify the object in an input image which can be found by examining local neighborhoods of the image. Next, all neurons in a bank apply the same filter at different locations in the input image. By looking at the image example. Green is an input to one neuron bank, yellow is filter bank, and pink is the output of one neuron bank (convolved feature). A bank of neurons in a CNN applies a convolution operation, aka filters, to its input where a single layer in a CNN typically has multiple banks of neurons, each performing a convolution with a different filter. The resulting neuron banks become distinct input channels into the next layer. The whole process reduces the net’s representational capacity, but also reduces the capacity to overfit.<br /> <br /> === Pooling ===<br /> <br /> Pooling layer summarizes the activities of local patches of neurons in the convolutional layer by subsampling the output of a convolutional layer. Pooling is useful for extracting dominant features, to decrease the computational power required to process the data through dimensionality reduction. The procedure of pooling goes on like this; output from convolutional layers is divided into sections called pooling units and they are laid out topographically, connected to a local neighborhood of other pooling units from the same convolutional output. Then, each pooling unit is computed with some function which could be maximum and average. Maximum pooling returns the maximum value from the section of the image covered by the pooling unit while average pooling returns the average of all the values inside the pooling unit (see example). In result, there are fewer total pooling units than convolutional unit outputs from the previous layer, this is due to larger spacing between pixels on pooling layers. Using the max-pooling function reduces the effect of outliers and improves generalization.<br /> <br /> === Local Response Normalization === <br /> <br /> This network includes local response normalization layers which are implemented in lateral form and used on neurons with unbounded activations and permits the detection of high-frequency features with a big neuron response. This regularizer encourages competition among neurons belonging to different banks. Normalization is done by dividing the activity of a neuron in bank &lt;math&gt;i&lt;/math&gt; at position &lt;math&gt;(x,y)&lt;/math&gt; by the equation below, where the sum runs over &lt;math&gt;N&lt;/math&gt; ‘adjacent’ banks of neurons at the same position as in the topographic organization of neuron bank. The constants, &lt;math&gt;N&lt;/math&gt;, &lt;math&gt;alpha&lt;/math&gt; and &lt;math&gt;betas&lt;/math&gt; are hyper-parameters whose values are determined using a validation set. This technique is replaced by better techniques such as the combination of dropout and regularization methods (L1,and L2)<br /> <br /> === Neuron nonlinearities ===<br /> <br /> All of the neurons for this model use the max-with-zero nonlinearity where output within a neuron is computed as &lt;math&gt; a^{i}_{x,y} = max(0, z^i_{x,y})&lt;/math&gt; where &lt;math&gt; z^i_{x,y} &lt;/math&gt; is the total input to the neuron. The reason they use nonlinearity is because it has several advantages over traditional saturating neuron models, such as significant reduction in training time required to reach a certain error rate. Another advantage is that nonlinearity reduces the need for contrast-normalization and data pre-processing since neurons do not saturate- meaning activities simply scale up little by little with usually large input values. For this model’s only pre-processing step, they subtract the mean activity from each pixel and the result is a centered data.<br /> <br /> === Objective function ===<br /> <br /> The objective function of their network maximizes the multinomial logistic regression objective which is the same as minimizing the average cross-entropy across training cases between the true label and the model’s predicted label.<br /> <br /> === Weight Initialization === <br /> <br /> It’s important to note that if a neuron always receives a negative value during training, it will not learn because its output is uniformly zero under the max-with-zero nonlinearity. Hence, the weights in their model were sampled from a zero-mean normal distribution with a high enough variance. High variance in weights will set a certain number of neurons with positive values for learning to happen, and in practice, it’s necessary to try out several candidates for variances until a working initialization is found. In their experiment, setting a positive constant, or 1, as biases of the neurons in the hidden layers was helpful in finding it.<br /> <br /> === Training ===<br /> <br /> In this model, a batch size of 128 samples and momentum of 0.9, we train our model using stochastic gradient descent. The update rule for weight w is $$v_{i+1} = 0.9v_i + \epsilon &lt;\diffp{dE}{dw_i}&gt; i$$ $$w_{i+1} = w_i + v_{i+1}$$, where i is the iteration index, v is a momentum variable, e is the learning rate and dE/dw is the average over the ith batch of the derivative of the objective with respect to w_i. The whole training process on CIFAR-10 takes roughly 90minuts and ImageNet takes 4 days with dropout and two days without.<br /> <br /> === Learning ===<br /> To determine the learning rate for the network, it is a must to start with an equal learning rate for each layer which produces the largest reduction in the objective function with power of ten. Usually, it is in the order of 10^-2 or 10^-3. In this case, they reduce the learning rate twice by a factor of ten before termination of training.<br /> <br /> = CIFAR-10 =<br /> <br /> Models for CIFAR-10:<br /> <br /> CIFAR-10 is a popular object recognition dataset with size 32 x 32 color images searched from the web. It contains 10 classes and the images were labels with the noun used to search the image. It has images of 6000 train images and 1000 test images of a single dominant object from the label name for each 10 classes.&l