http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Z47shen&feedformat=atom statwiki - User contributions [US] 2021-10-19T08:50:11Z User contributions MediaWiki 1.28.3 http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification%E2%80%94%E2%80%94via_Convolution_Neural_Network&diff=48220 Semantic Relation Classification——via Convolution Neural Network 2020-11-30T03:12:17Z <p>Z47shen: /* Critiques */</p> <hr /> <div><br /> <br /> <br /> == Presented by ==<br /> Rui Gong, Xinqi Ling, Di Ma,Xuetong Wang<br /> <br /> == Introduction ==<br /> A Semantic Relation can imply a relation between different words and a relation between different sentences or phrases. For example, the pair of words &quot;white&quot; and &quot;snowy&quot; can be synonyms, while &quot;white&quot; and &quot;black&quot; can be opposites. It can be used for recommendation systems like YouTube, and understanding sentiment analysis. The study of semantic analysis involves determining the exact meaning of a text. For example, the word &quot;date&quot;, can have different meanings in different contexts, like a calendar &quot;date&quot;, a &quot;date&quot; fruit, or a romantic &quot;date&quot;. <br /> <br /> One of the emerging trends of natural language technologies is their use for the humanities and sciences (Gbor et al., 2018). SemEval 2018 Task 7 mainly solves the problem of relation extraction and classification of two entities in the same sentence into 6 potential relations. The 6 relations are USAGE, RESULT, MODEL-FEATURE, PART WHOLE, TOPIC, and COMPARE.<br /> <br /> SemEval 2018 Task 7 extracted data from 350 scientific paper abstracts, which has 1228 and 1248 annotated sentences for two tasks, respectively. For each data, an example sentence was chosen with its right and left sentences, as well as an indicator showing whether the relation is reserved, then a prediction is made. <br /> <br /> Three models were used for the prediction: Linear Classifiers, Long Short-Term Memory(LSTM), and Convolutional Neural Networks (CNN). In the end, the prediction based on the CNN model was ultimately submitted since it performed the best among all models. By using the learned custom word embedding function, the research team added a variant of negative sampling, thereby improving performance and surpassing ordinary CNN.<br /> <br /> == Previous Work ==<br /> SemEval 2010 Task 8 (Hendrickx et al., 2010) explored the classification of natural language relations and studied the 9 relations between word pairs. However, it is not designed for scientific text analysis, and their challenge differs from the challenge of this paper in its generalizability; this paper’s relations are specific to ACL papers (e.g. MODEL-FEATURE), whereas the 2010 relations are more general, and might necessitate more common-sense knowledge than the 2018 relations. Xu et al. (2015a) and Santos et al. (2015) both applied CNN with negative sampling to finish task7. The 2017 SemEval Task 10 also featured relation extraction within scientific publications.<br /> <br /> == Algorithm ==<br /> <br /> [[File:CNN.png|800px|center]]<br /> <br /> This is the architecture of CNN. We first transform a sentence via Feature embeddings. Basically, we transform each sentence into continuous word embeddings:<br /> <br /> $$<br /> (e^{w_i})<br />$$<br /> <br /> And word position embeddings:<br /> $$<br /> (e^{wp_i}): e_i = [e^{w_i}, e^{wp_i}]<br />$$<br /> <br /> In the word embeddings, we got a vocabulary ‘V’, and we will make an embedding word matrix based on the position of the word in the vocabulary. This matrix is trainable and needs to be initialized by pre-trained embedding vectors.<br /> <br /> In the word position embeddings, we first need to input some words named ‘entities,’ and they are the key for the machine to determine the sentence’s relation. During this process, if we have two entities, we will use the relative position of them in the sentence to make the<br /> embeddings. We will output two vectors, and one of them keeps track of the first entity relative position in the sentence ( we will make the entity recorded as 0, the former word recorded as -1 and the next one 1, etc. ). And the same procedure for the second entity. Finally, we will get two vectors concatenated as the position embedding. For example, in the sentence &quot;the black '''cat''' jumped&quot;, the position embedding of &quot;'''cat'''&quot; is -2,-1,0,1.<br /> <br /> <br /> <br /> After the embeddings, the model will transform the embedded sentence into a fix-sized representation of the whole sentence via the convolution layer. Finally, after the max-pooling to reduce the dimension of the output of the layers, we will get a score for each relation class via a linear transformation.<br /> <br /> <br /> After featurizing all words in the sentence. The sentence of length N can be expressed as a vector of length &lt;math&gt; N &lt;/math&gt;, which looks like <br /> $$e=[e_{1},e_{2},\ldots,e_{N}]$$<br /> and each entry represents a token of the word. Also, to apply <br /> convolutional neural network, the subsets of features<br /> $$e_{i:i+j}=[e_{i},e_{i+1},\ldots,e_{i+j}]$$<br /> are given to a weight matrix &lt;math&gt; W\in\mathbb{R}^{(d^{w}+2d^{wp})\times k}&lt;/math&gt; to <br /> produce a new feature, defiend as <br /> $$c_{i}=\text{tanh}(W\cdot e_{i:i+k-1}+bias)$$<br /> This process is applied to all subsets of features with length &lt;math&gt; k &lt;/math&gt; starting <br /> from the first one. Then a mapped feature factor is produced:<br /> $$c=[c_{1},c_{2},\ldots,c_{N-k+1}]$$<br /> <br /> <br /> The max pooling operation is used, the &lt;math&gt; \hat{c}=max\{c\} &lt;/math&gt; was picked.<br /> With different weight filter, different mapped feature vectors can be obtained. Finally, the original <br /> sentence &lt;math&gt; e &lt;/math&gt; can be converted into a new representation &lt;math&gt; r_{x} &lt;/math&gt; with a fixed length. For example, if there are 5 filters,<br /> then there are 5 features (&lt;math&gt; \hat{c} &lt;/math&gt;) picked to create &lt;math&gt; r_{x} &lt;/math&gt; for each &lt;math&gt; x &lt;/math&gt;.<br /> <br /> Then, the score vector <br /> $$s(x)=W^{classes}r_{x}$$<br /> is obtained which represented the score for each class, given &lt;math&gt; x &lt;/math&gt;'s entities' relation will be classified as <br /> the one with the highest score. The &lt;math&gt; W^{classes} &lt;/math&gt; here is the model being trained.<br /> <br /> To improve the performance, “Negative Sampling&quot; was used. Given the trained data point <br /> &lt;math&gt; \tilde{x} &lt;/math&gt;, and its correct class &lt;math&gt; \tilde{y} &lt;/math&gt;. Let &lt;math&gt; I=Y\setminus\{\tilde{y}\} &lt;/math&gt; represent the <br /> incorrect labels for &lt;math&gt; x &lt;/math&gt;. Basically, the distance between the correct score and the positive margin, and the negative <br /> distance (negative margin plus the second largest score) should be minimized. So the loss function is <br /> $$L=\log(1+e^{\gamma(m^{+}-s(x)_{y})})+\log(1+e^{\gamma(m^{-}-\mathtt{max}_{y'\in I}(s(x)_{y'}))})$$<br /> with margins &lt;math&gt; m_{+} &lt;/math&gt;, &lt;math&gt; m_{-} &lt;/math&gt;, and penalty scale factor &lt;math&gt; \gamma &lt;/math&gt;.<br /> The whole training is based on ACL anthology corpus and there are 25,938 papers with 136,772,370 tokens in total, <br /> and 49,600 of them are unique.<br /> <br /> == Results ==<br /> In machine learning, the most important part is to tune the hyper-parameters. Unlike traditional hyper-parameter optimization, there are some<br /> modifications to the model to increase performance on the test set. There are 5 modifications that we can apply:<br /> <br /> '''1.''' Merged Training Sets. It combined two training sets to increase the data set<br /> size and it improves the equality between classes to get better predictions.<br /> <br /> '''2.''' Reversal Indicate Features. It added a binary feature.<br /> <br /> '''3.''' Custom ACL Embeddings. It embedded a word vector to an ACL-specific<br /> corps.<br /> <br /> '''4.''' Context words. Within the sentence, it varies in size on a context window<br /> around the entity-enclosed text.<br /> <br /> '''5.''' Ensembling. It used different early stop and random initializations to improve<br /> the predictions.<br /> <br /> These modifications performances well on the training data and they are shown<br /> in table 3.<br /> <br /> [[File:table3.PNG|center]]<br /> <br /> <br /> <br /> As we can see the best choice for this model is ensembling as the random initialization made the data more natural and avoided the overfit.<br /> During the training process, there are some methods such that they can only<br /> increase the score on the cross-validation test sets but hurt the performance on<br /> the overall macro-F1 score. Thus, these methods were eventually ruled out.<br /> <br /> <br /> [[File:table4.PNG|center]]<br /> <br /> There are six submissions in total. Three for each training set and the result<br /> is shown in figure 2.<br /> <br /> The best submission for the training set 1.1 is the third submission which does not<br /> use a separate cross-validation dataset. Instead, a constant number of<br /> training epochs are run with cross-validation based on the training data.<br /> <br /> This compares to the other submissions in which 10% of the training data are<br /> removed to form the validation set (both with and without stratification).<br /> Predictions for these are made when the model has the highest validation accuracy. <br /> <br /> The best submission for the training set 1.2 is the submission which<br /> extracted 10% of the training data to form the validation dataset. Predictions are<br /> made when maximum accuracy is reached on the validation data.<br /> <br /> All in all, early stopping cannot always be based on the accuracy of the validation set<br /> since it cannot guarantee to get better performance on the real test set. Thus,<br /> we have to try new approaches and combine them to see the prediction<br /> results. Also, doing stratification will certainly improve the performance of<br /> the test data.<br /> <br /> == Conclusions ==<br /> Throughout the process, we have experimented with linear classifiers, sequential random forest, LSTM, and CNN models with various variations applied, such as two models of attention, negative sampling, entity embedding or sentence-only embedding, etc. <br /> <br /> Among all variations, vanilla CNN with negative sampling and ACL-embedding, without attention, has significantly better performance than all others. Attention-based pooling, up-sampling, and data augmentation are also tested, but they barely perform positive increment on the behavior.<br /> <br /> == Critiques == <br /> <br /> - Applying this in news apps might be beneficial to improve readability by highlighting specific important sections.<br /> <br /> - The data set come from 350 scientist papers, this could be more explained by the author on how those paper are selected and why those paper are important to discuss.<br /> <br /> - In the section of previous work, the author mentioned 9 natural language relationships between the word pairs. Among them, 6 potential relationships are USAGE, RESULT, MODEL-FEATURE, PART WHOLE, TOPIC, and COMPARE. It would help the readers to better understand if all 9 relationships are listed in the summary.<br /> <br /> -This topic is interesting and this application might be helpful for some educational websites to improve their website to help readers focus on the important points. I think it will be nice to use Latex to type the equation in the sentence rather than center the equation on the next line. I think it will be interesting to discuss applying this way to other languages such as Chinese, Japanese, etc.<br /> <br /> - It would be a good idea if the authors can provide more details regarding ACL Embeddings and Context words modifications. Scores generated using these two modifications are quite close to the highest Ensembling modification generated score, which makes it a valid consideration to examine these two modifications in detail. <br /> <br /> - This paper is dealing with a similar problem as 'Neural Speed Reading Via Skim-RNN', num 19 paper summary. It will be an interesting approach to compare these two models' performance based on the same dataset.<br /> <br /> - I think it would be highly practical to implement this system as a page-rank system for search engines (such as google, bing, or other platforms like Facebook, Instagram, etc.) by finding the most prevalent information available in a search query and then matching the search to the related text which can be found on webpages. This could also be implemented in search bars on specific websites or locations as well.<br /> <br /> - It would be interesting to see in the future how the model would behave if data not already trained was used. This pre-trained data as mentioned in the paper had noise included. Using cleaner data would give better results maybe.<br /> <br /> - The selection of the training dataset, i.e. the abstracts of scientific papers, is an excellent idea since the abstracts usually contain more information than the body. But it may be also a good idea to train the model with the conclusions. Other than that, the result of applying the model to the body part of the scientific papers may show some interesting features of the model.<br /> <br /> - From Table4 we find that comparing with using a fixed number of training periods, early stopping based on the accuracy of the validation set does not guarantee better test set performance. The label ratio of the validation set is layered according to the training set, which helps to improve the performance of the test set. Whether it is beneficial to add entity embedding as an additional feature could be an interesting point of discussion.<br /> <br /> == References ==<br /> Diederik P Kingma and Jimmy Ba. 2014. Adam: A<br /> method for stochastic optimization. arXiv preprint<br /> arXiv:1412.6980.<br /> <br /> DragomirR. Radev, Pradeep Muthukrishnan, Vahed<br /> Qazvinian, and Amjad Abu-Jbara. 2013. The ACL<br /> anthology network corpus. Language Resources<br /> and Evaluation, pages 1–26.<br /> <br /> Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey<br /> Dean. 2013a. Efficient estimation of word<br /> representations in vector space. arXiv preprint<br /> arXiv:1301.3781.<br /> <br /> Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado,<br /> and Jeff Dean. 2013b. Distributed representations<br /> of words and phrases and their compositionality.<br /> In Advances in neural information processing<br /> systems, pages 3111–3119.<br /> <br /> Kata Gbor, Davide Buscaldi, Anne-Kathrin Schumann, Behrang QasemiZadeh, Hafa Zargayouna,<br /> and Thierry Charnois. 2018. Semeval-2018 task 7:Semantic relation extraction and classification in scientific papers. <br /> In Proceedings of the 12th International Workshop on Semantic Evaluation (SemEval2018), New Orleans, LA, USA, June 2018.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification%E2%80%94%E2%80%94via_Convolution_Neural_Network&diff=48219 Semantic Relation Classification——via Convolution Neural Network 2020-11-30T03:11:56Z <p>Z47shen: /* Critiques */</p> <hr /> <div><br /> <br /> <br /> == Presented by ==<br /> Rui Gong, Xinqi Ling, Di Ma,Xuetong Wang<br /> <br /> == Introduction ==<br /> A Semantic Relation can imply a relation between different words and a relation between different sentences or phrases. For example, the pair of words &quot;white&quot; and &quot;snowy&quot; can be synonyms, while &quot;white&quot; and &quot;black&quot; can be opposites. It can be used for recommendation systems like YouTube, and understanding sentiment analysis. The study of semantic analysis involves determining the exact meaning of a text. For example, the word &quot;date&quot;, can have different meanings in different contexts, like a calendar &quot;date&quot;, a &quot;date&quot; fruit, or a romantic &quot;date&quot;. <br /> <br /> One of the emerging trends of natural language technologies is their use for the humanities and sciences (Gbor et al., 2018). SemEval 2018 Task 7 mainly solves the problem of relation extraction and classification of two entities in the same sentence into 6 potential relations. The 6 relations are USAGE, RESULT, MODEL-FEATURE, PART WHOLE, TOPIC, and COMPARE.<br /> <br /> SemEval 2018 Task 7 extracted data from 350 scientific paper abstracts, which has 1228 and 1248 annotated sentences for two tasks, respectively. For each data, an example sentence was chosen with its right and left sentences, as well as an indicator showing whether the relation is reserved, then a prediction is made. <br /> <br /> Three models were used for the prediction: Linear Classifiers, Long Short-Term Memory(LSTM), and Convolutional Neural Networks (CNN). In the end, the prediction based on the CNN model was ultimately submitted since it performed the best among all models. By using the learned custom word embedding function, the research team added a variant of negative sampling, thereby improving performance and surpassing ordinary CNN.<br /> <br /> == Previous Work ==<br /> SemEval 2010 Task 8 (Hendrickx et al., 2010) explored the classification of natural language relations and studied the 9 relations between word pairs. However, it is not designed for scientific text analysis, and their challenge differs from the challenge of this paper in its generalizability; this paper’s relations are specific to ACL papers (e.g. MODEL-FEATURE), whereas the 2010 relations are more general, and might necessitate more common-sense knowledge than the 2018 relations. Xu et al. (2015a) and Santos et al. (2015) both applied CNN with negative sampling to finish task7. The 2017 SemEval Task 10 also featured relation extraction within scientific publications.<br /> <br /> == Algorithm ==<br /> <br /> [[File:CNN.png|800px|center]]<br /> <br /> This is the architecture of CNN. We first transform a sentence via Feature embeddings. Basically, we transform each sentence into continuous word embeddings:<br /> <br /> $$<br /> (e^{w_i})<br />$$<br /> <br /> And word position embeddings:<br /> $$<br /> (e^{wp_i}): e_i = [e^{w_i}, e^{wp_i}]<br />$$<br /> <br /> In the word embeddings, we got a vocabulary ‘V’, and we will make an embedding word matrix based on the position of the word in the vocabulary. This matrix is trainable and needs to be initialized by pre-trained embedding vectors.<br /> <br /> In the word position embeddings, we first need to input some words named ‘entities,’ and they are the key for the machine to determine the sentence’s relation. During this process, if we have two entities, we will use the relative position of them in the sentence to make the<br /> embeddings. We will output two vectors, and one of them keeps track of the first entity relative position in the sentence ( we will make the entity recorded as 0, the former word recorded as -1 and the next one 1, etc. ). And the same procedure for the second entity. Finally, we will get two vectors concatenated as the position embedding. For example, in the sentence &quot;the black '''cat''' jumped&quot;, the position embedding of &quot;'''cat'''&quot; is -2,-1,0,1.<br /> <br /> <br /> <br /> After the embeddings, the model will transform the embedded sentence into a fix-sized representation of the whole sentence via the convolution layer. Finally, after the max-pooling to reduce the dimension of the output of the layers, we will get a score for each relation class via a linear transformation.<br /> <br /> <br /> After featurizing all words in the sentence. The sentence of length N can be expressed as a vector of length &lt;math&gt; N &lt;/math&gt;, which looks like <br /> $$e=[e_{1},e_{2},\ldots,e_{N}]$$<br /> and each entry represents a token of the word. Also, to apply <br /> convolutional neural network, the subsets of features<br /> $$e_{i:i+j}=[e_{i},e_{i+1},\ldots,e_{i+j}]$$<br /> are given to a weight matrix &lt;math&gt; W\in\mathbb{R}^{(d^{w}+2d^{wp})\times k}&lt;/math&gt; to <br /> produce a new feature, defiend as <br /> $$c_{i}=\text{tanh}(W\cdot e_{i:i+k-1}+bias)$$<br /> This process is applied to all subsets of features with length &lt;math&gt; k &lt;/math&gt; starting <br /> from the first one. Then a mapped feature factor is produced:<br /> $$c=[c_{1},c_{2},\ldots,c_{N-k+1}]$$<br /> <br /> <br /> The max pooling operation is used, the &lt;math&gt; \hat{c}=max\{c\} &lt;/math&gt; was picked.<br /> With different weight filter, different mapped feature vectors can be obtained. Finally, the original <br /> sentence &lt;math&gt; e &lt;/math&gt; can be converted into a new representation &lt;math&gt; r_{x} &lt;/math&gt; with a fixed length. For example, if there are 5 filters,<br /> then there are 5 features (&lt;math&gt; \hat{c} &lt;/math&gt;) picked to create &lt;math&gt; r_{x} &lt;/math&gt; for each &lt;math&gt; x &lt;/math&gt;.<br /> <br /> Then, the score vector <br /> $$s(x)=W^{classes}r_{x}$$<br /> is obtained which represented the score for each class, given &lt;math&gt; x &lt;/math&gt;'s entities' relation will be classified as <br /> the one with the highest score. The &lt;math&gt; W^{classes} &lt;/math&gt; here is the model being trained.<br /> <br /> To improve the performance, “Negative Sampling&quot; was used. Given the trained data point <br /> &lt;math&gt; \tilde{x} &lt;/math&gt;, and its correct class &lt;math&gt; \tilde{y} &lt;/math&gt;. Let &lt;math&gt; I=Y\setminus\{\tilde{y}\} &lt;/math&gt; represent the <br /> incorrect labels for &lt;math&gt; x &lt;/math&gt;. Basically, the distance between the correct score and the positive margin, and the negative <br /> distance (negative margin plus the second largest score) should be minimized. So the loss function is <br /> $$L=\log(1+e^{\gamma(m^{+}-s(x)_{y})})+\log(1+e^{\gamma(m^{-}-\mathtt{max}_{y'\in I}(s(x)_{y'}))})$$<br /> with margins &lt;math&gt; m_{+} &lt;/math&gt;, &lt;math&gt; m_{-} &lt;/math&gt;, and penalty scale factor &lt;math&gt; \gamma &lt;/math&gt;.<br /> The whole training is based on ACL anthology corpus and there are 25,938 papers with 136,772,370 tokens in total, <br /> and 49,600 of them are unique.<br /> <br /> == Results ==<br /> In machine learning, the most important part is to tune the hyper-parameters. Unlike traditional hyper-parameter optimization, there are some<br /> modifications to the model to increase performance on the test set. There are 5 modifications that we can apply:<br /> <br /> '''1.''' Merged Training Sets. It combined two training sets to increase the data set<br /> size and it improves the equality between classes to get better predictions.<br /> <br /> '''2.''' Reversal Indicate Features. It added a binary feature.<br /> <br /> '''3.''' Custom ACL Embeddings. It embedded a word vector to an ACL-specific<br /> corps.<br /> <br /> '''4.''' Context words. Within the sentence, it varies in size on a context window<br /> around the entity-enclosed text.<br /> <br /> '''5.''' Ensembling. It used different early stop and random initializations to improve<br /> the predictions.<br /> <br /> These modifications performances well on the training data and they are shown<br /> in table 3.<br /> <br /> [[File:table3.PNG|center]]<br /> <br /> <br /> <br /> As we can see the best choice for this model is ensembling as the random initialization made the data more natural and avoided the overfit.<br /> During the training process, there are some methods such that they can only<br /> increase the score on the cross-validation test sets but hurt the performance on<br /> the overall macro-F1 score. Thus, these methods were eventually ruled out.<br /> <br /> <br /> [[File:table4.PNG|center]]<br /> <br /> There are six submissions in total. Three for each training set and the result<br /> is shown in figure 2.<br /> <br /> The best submission for the training set 1.1 is the third submission which does not<br /> use a separate cross-validation dataset. Instead, a constant number of<br /> training epochs are run with cross-validation based on the training data.<br /> <br /> This compares to the other submissions in which 10% of the training data are<br /> removed to form the validation set (both with and without stratification).<br /> Predictions for these are made when the model has the highest validation accuracy. <br /> <br /> The best submission for the training set 1.2 is the submission which<br /> extracted 10% of the training data to form the validation dataset. Predictions are<br /> made when maximum accuracy is reached on the validation data.<br /> <br /> All in all, early stopping cannot always be based on the accuracy of the validation set<br /> since it cannot guarantee to get better performance on the real test set. Thus,<br /> we have to try new approaches and combine them to see the prediction<br /> results. Also, doing stratification will certainly improve the performance of<br /> the test data.<br /> <br /> == Conclusions ==<br /> Throughout the process, we have experimented with linear classifiers, sequential random forest, LSTM, and CNN models with various variations applied, such as two models of attention, negative sampling, entity embedding or sentence-only embedding, etc. <br /> <br /> Among all variations, vanilla CNN with negative sampling and ACL-embedding, without attention, has significantly better performance than all others. Attention-based pooling, up-sampling, and data augmentation are also tested, but they barely perform positive increment on the behavior.<br /> <br /> == Critiques == <br /> <br /> - Applying this in news apps might be beneficial to improve readability by highlighting specific important sections.<br /> <br /> - The data set come from 350 scientist papers, this could be more explained by the author on how those paper are selected and why those paper are important to discuss.<br /> <br /> - In the section of previous work, the author mentioned 9 natural language relationships between the word pairs. Among them, 6 potential relationships are USAGE, RESULT, MODEL-FEATURE, PART WHOLE, TOPIC, and COMPARE. It would help the readers to better understand if all 9 relationships are listed in the summary.<br /> <br /> -This topic is interesting and this application might be helpful for some educational websites to improve their website to help readers focus on the important points. I think it will be nice to use Latex to type the equation in the sentence rather than center the equation on the next line. I think it will be interesting to discuss applying this way to other languages such as Chinese, Japanese, etc.<br /> <br /> - It would be a good idea if the authors can provide more details regarding ACL Embeddings and Context words modifications. Scores generated using these two modifications are quite close to the highest Ensembling modification generated score, which makes it a valid consideration to examine these two modifications in detail. <br /> <br /> - This paper is dealing with a similar problem as 'Neural Speed Reading Via Skim-RNN', num 19 paper summary. It will be an interesting approach to compare these two models' performance based on the same dataset.<br /> <br /> - I think it would be highly practical to implement this system as a page-rank system for search engines (such as google, bing, or other platforms like Facebook, Instagram, etc.) by finding the most prevalent information available in a search query and then matching the search to the related text which can be found on webpages. This could also be implemented in search bars on specific websites or locations as well.<br /> <br /> - It would be interesting to see in the future how the model would behave if data not already trained was used. This pre-trained data as mentioned in the paper had noise included. Using cleaner data would give better results maybe.<br /> <br /> - The selection of the training dataset, i.e. the abstracts of scientific papers, is an excellent idea since the abstracts usually contain more information than the body. But it may be also a good idea to train the model with the conclusions. Other than that, the result of applying the model to the body part of the scientific papers may show some interesting features of the model.<br /> <br /> -From Table4 we find that comparing with using a fixed number of training periods, early stopping based on the accuracy of the validation set does not guarantee better test set performance. The label ratio of the validation set is layered according to the training set, which helps to improve the performance of the test set. Whether it is beneficial to add entity embedding as an additional feature could be an interesting point of discussion.<br /> <br /> == References ==<br /> Diederik P Kingma and Jimmy Ba. 2014. Adam: A<br /> method for stochastic optimization. arXiv preprint<br /> arXiv:1412.6980.<br /> <br /> DragomirR. Radev, Pradeep Muthukrishnan, Vahed<br /> Qazvinian, and Amjad Abu-Jbara. 2013. The ACL<br /> anthology network corpus. Language Resources<br /> and Evaluation, pages 1–26.<br /> <br /> Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey<br /> Dean. 2013a. Efficient estimation of word<br /> representations in vector space. arXiv preprint<br /> arXiv:1301.3781.<br /> <br /> Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado,<br /> and Jeff Dean. 2013b. Distributed representations<br /> of words and phrases and their compositionality.<br /> In Advances in neural information processing<br /> systems, pages 3111–3119.<br /> <br /> Kata Gbor, Davide Buscaldi, Anne-Kathrin Schumann, Behrang QasemiZadeh, Hafa Zargayouna,<br /> and Thierry Charnois. 2018. Semeval-2018 task 7:Semantic relation extraction and classification in scientific papers. <br /> In Proceedings of the 12th International Workshop on Semantic Evaluation (SemEval2018), New Orleans, LA, USA, June 2018.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan&diff=48207 User:Yktan 2020-11-30T02:58:35Z <p>Z47shen: /* Critiques/ Insights */</p> <hr /> <div><br /> == Introduction ==<br /> <br /> Much of the success in training deep neural networks (DNNs) is due to the collection of large datasets with human-annotated labels. However, human annotation is both a time-consuming and expensive task, especially for data that requires expertise such as medical data. Furthermore, certain datasets will be noisy due to the biases introduced by different annotators. Data obtained in large quantities through searching for images in search engines and data downloaded from social media sites (in a manner abiding by privacy and copyright laws) are especially noisy, since the labels are generally inferred from tags to save on human-annotation cost. <br /> <br /> There are a few existing approaches to use datasets with noisy labels. In learning with noisy labels (LNL), most methods take a loss correction approach. Other LNL methods estimate a noise transition matrix and employ it to correct the loss function. An example of a popular loss correction approach is the bootstrapping loss approach. Another approach to reducing annotation cost is semi-supervised learning (SSL), where the training data consists of labeled and unlabeled samples.<br /> <br /> This paper introduces DivideMix, which combines approaches from LNL and SSL. One unique thing about DivideMix is that it discards sample labels that are highly likely to be noisy and leverages these noisy samples as unlabeled data instead. This prevents the model from overfitting and improves generalization performance. Key contributions of this work are:<br /> 1) Co-divide, which trains two networks simultaneously, aims to improve generalization and avoiding confirmation bias.<br /> 2) During the SSL phase, an improvement is made on an existing method (MixMatch) by combining it with another method (MixUp).<br /> 3) Significant improvements to state-of-the-art results on multiple conditions are experimentally shown while using DivideMix. Extensive ablation study and qualitative results are also shown to examine the effect of different components.<br /> <br /> == Motivation ==<br /> <br /> While much has been achieved in training DNNs with noisy labels and SSL methods individually, not much progress has been made in exploring their underlying connections and building on top of the two approaches simultaneously. <br /> <br /> Existing LNL methods aim to correct the loss function by:<br /> &lt;ol&gt;<br /> &lt;li&gt; Treating all samples equally and correcting loss explicitly or implicitly through relabelling of the noisy samples<br /> &lt;li&gt; Reweighting training samples or separating clean and noisy samples, which results in correction of the loss function<br /> &lt;/ol&gt;<br /> <br /> A few examples of LNL methods include:<br /> &lt;ol&gt;<br /> &lt;li&gt; Estimating the noise transition matrix, which denotes the probability of clean labels flipping to noisy labels, to correct the loss function<br /> &lt;li&gt; Leveraging the predictions from DNNs to correct labels and using them to modify the loss<br /> &lt;li&gt; Reweighting samples so that noisy labels contribute less to the loss<br /> &lt;/ol&gt;<br /> <br /> However, these methods all have downsides: it is very challenging to correctly estimate the noise transition matrix in the first method; for the second method, DNNs tend to overfit to datasets with high noise ratio; and for the third method, we need to be able to identify clean samples, which has also proven to be challenging.<br /> <br /> On the other hand, SSL methods mostly leverage unlabeled data using regularization to improve model performance. A recently proposed method, MixMatch, incorporates the two classes of regularization. These classes are consistency regularization which enforces the model to produce consistent predictions on augmented input data, and entropy minimization which encourages the model to give high-confidence predictions on unlabeled data, as well as MixUp regularization. <br /> <br /> DivideMix partially adopts LNL in that it removes the labels that are highly likely to be noisy by using co-divide to avoid the confirmation bias problem. It then utilizes the noisy samples as unlabeled data and adopts an improved version of MixMatch (SSL) which accounts for the label noise during the label co-refinement and co-guessing phase. By incorporating SSL techniques into LNL and taking the best of both worlds, DivideMix aims to produce highly promising results in training DNNs by better addressing the confirmation bias problem, more accurately distinguishing and utilizing noisy samples, and performing well under high levels of noise.<br /> <br /> == Model Architecture and Algorithm ==<br /> <br /> DivideMix leverages semi-supervised learning to achieve effective modeling. The sample is first split into a labeled set and an unlabeled set. This is achieved by fitting a Gaussian Mixture Model as a per-sample loss distribution. The unlabeled set is made up of data points with discarded labels deemed noisy. Then, to avoid confirmation bias, which is typical when a model is self-training, two models are being trained simultaneously to filter error for each other. This is done by dividing the data using one model and then training the other model. This algorithm, known as Co-divide, keeps the two networks from converging when training, which avoids the bias from occurring. Being diverged also offers the two networks distinct abilities to filter different types of error, making the model more robust to noise. Figure 1 describes the algorithm in graphical form.<br /> <br /> [[File:ModelArchitecture.PNG | center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Model Architecture of DivideMix&lt;/div&gt;<br /> <br /> For each epoch, the network divides the dataset into a labeled set consisting of clean data, and an unlabeled set consisting of noisy data, which is then used as training data for the other network, where training is done in mini-batches. For each batch of the labelled samples, co-refinement is performed by using the ground truth label &lt;math&gt; y_b &lt;/math&gt;, the predicted label &lt;math&gt; p_b &lt;/math&gt;, and the posterior is used as the weight, &lt;math&gt; w_b &lt;/math&gt;. <br /> <br /> &lt;center&gt;&lt;math&gt; \bar{y}_b = w_b y_b + (1-w_b) p_b &lt;/math&gt;&lt;/center&gt; <br /> <br /> Then, a sharpening function is implemented on this weighted sum to produce the estimate, &lt;math&gt; \hat{y}_b &lt;/math&gt;. Using all these predicted labels, the unlabeled samples will then be assigned a &quot;co-guessed&quot; label, which should produce a more accurate prediction.<br /> &lt;math&gt; \hat{y}_b=Sharpen(\bar{y}_b,T)={\bar{y}^{c{\frac{1}{T}}}_b}/{\sum_{c=1}^C\bar{y}^{c{\frac{1}{T}}}_b} &lt;/math&gt;, for c = 1, 2,....., C.<br /> Having calculated all these labels, MixMatch is applied to the combined mini-batch of labeled, &lt;math&gt; \hat{X} &lt;/math&gt; and unlabeled data, &lt;math&gt; \hat{U} &lt;/math&gt;, where, for a pair of samples and their labels, one new sample and new label is produced. More specifically, for a pair of samples &lt;math&gt; (x_1,x_2) &lt;/math&gt; and their labels &lt;math&gt; (p_1,p_2) &lt;/math&gt;, the mixed sample &lt;math&gt; (x',p') &lt;/math&gt; is:<br /> <br /> &lt;center&gt;<br /> &lt;math&gt;<br /> \begin{alignat}{2}<br /> <br /> \lambda &amp;\sim Beta(\alpha, \alpha) \\<br /> \lambda ' &amp;= max(\lambda, 1 - \lambda) \\<br /> x' &amp;= \lambda ' x_1 + (1 - \lambda ' ) x_2 \\<br /> p' &amp;= \lambda ' p_1 + (1 - \lambda ' ) p_2 \\<br /> <br /> \end{alignat}<br /> &lt;/math&gt;<br /> &lt;/center&gt; <br /> <br /> MixMatch transforms &lt;math&gt; \hat{X} &lt;/math&gt; and &lt;math&gt; \hat{U} &lt;/math&gt; into &lt;math&gt; X' &lt;/math&gt; and &lt;math&gt; U' &lt;/math&gt;. Then, the loss on &lt;math&gt; X' &lt;/math&gt;, &lt;math&gt; L_X &lt;/math&gt; (Cross-entropy loss) and the loss on &lt;math&gt; U' &lt;/math&gt;, &lt;math&gt; L_U &lt;/math&gt; (Mean Squared Error) are calculated. A regularization term, &lt;math&gt; L_{reg} &lt;/math&gt;, is introduced to regularize the model's average output across all samples in the mini-batch. Then, the total loss is calculated as:<br /> <br /> &lt;center&gt;&lt;math&gt; L = L_X + \lambda_u L_U + \lambda_r L_{reg} &lt;/math&gt;&lt;/center&gt; <br /> <br /> where &lt;math&gt; \lambda_r &lt;/math&gt; is set to 1, and &lt;math&gt; \lambda_u &lt;/math&gt; is used to control the unsupervised loss.<br /> <br /> Lastly, the stochastic gradient descent formula is updated with the calculated loss, &lt;math&gt; L &lt;/math&gt;, and the estimated parameters, &lt;math&gt; \boldsymbol{ \theta } &lt;/math&gt;.<br /> <br /> The full algorithm is shown below. [[File:dividemix.jpg|600px| | center]]<br /> &lt;div align=&quot;center&quot;&gt;Algorithm1: DivideMix. Line 4-8: co-divide; Line 17-18: label co-refinement; Line 20: co-guessing.&lt;/div&gt;<br /> <br /> The when the model is warmed up, it is trained on all data using standard cross-entropy to initially converge the model, but with a regulatory negative entropy term &lt;math&gt;\mathcal{H} = -\sum_{c}\text{p}^\text{c}_\text{model}(x;\theta)\log(\text{p}^\text{c}_\text{model}(x;\theta))&lt;/math&gt;, where &lt;math&gt;\text{p}^\text{c}_\text{model}&lt;/math&gt; is the softmax output probability for class c. This term penalizes confident predictions during the warm up to prevent overfitting to noise during the warm up, which can happen when there is asymmetric noise.<br /> <br /> == Results ==<br /> '''Applications'''<br /> <br /> The method was validated using four benchmark datasets: CIFAR-10, CIFAR100 (Krizhevsky &amp; Hinton, 2009) which contain 50K training images and 10K test images of size 32 × 32), Clothing1M (Xiao et al., 2015), and WebVision (Li et al., 2017a).<br /> Two types of label noise are used in the experiments: symmetric and asymmetric.<br /> An 18-layer PreAct Resnet (He et al., 2016) is trained using SGD with a momentum of 0.9, a weight decay of 0.0005, and a batch size of 128. The network is trained for 300 epochs. The initial learning rate was set to 0.02 and reduced by a factor of 10 after 150 epochs. Before applying the Co-divide and MixMatch strategies, the models were first independently trained over the entire dataset using cross-entropy loss during a &quot;warm-up&quot; period. Initially, training the models in this way prepares a more regular distribution of losses to improve upon in subsequent epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100. For all CIFAR experiments, we use the same hyperparameters M = 2, T = 0.5, and α = 4. τ is set as 0.5 except for 90% noise ratio when it is set as 0.6.<br /> <br /> <br /> '''Comparison of State-of-the-Art Methods'''<br /> <br /> The effectiveness of DivideMix was shown by comparing the test accuracy with the most recent state-of-the-art methods: <br /> Meta-Learning (Li et al., 2019) proposes a gradient-based method to find model parameters that are more noise-tolerant; <br /> Joint-Optim (Tanaka et al., 2018) and P-correction (Yi &amp; Wu, 2019) jointly optimize the sample labels and the network parameters;<br /> M-correction (Arazo et al., 2019) models sample loss with BMM and apply MixUp.<br /> The following are the results on CIFAR-10 and CIFAR-100 with different levels of symmetric label noise ranging from 20% to 90%. Both the best test accuracy across all epochs and the averaged test accuracy over the last 10 epochs were recorded in the following table:<br /> <br /> <br /> [[File:divideMixtable1.PNG | center]]<br /> <br /> From table 1, the author noticed that none of these methods can consistently outperform others across different datasets. M-correction excels at symmetric noise, whereas Meta-Learning performs better for asymmetric noise. DivideMix outperforms state-of-the-art methods by a large margin across all noise ratios. The improvement is substantial (∼10% of accuracy) for the more challenging CIFAR-100 with high noise ratios.<br /> <br /> DivideMix was compared with the state-of-the-art methods with the other two datasets: Clothing1M and WebVision. It also shows that DivideMix consistently outperforms state-of-the-art methods across all datasets with different types of label noise. For WebVision, DivideMix achieves more than 12% improvement in top-1 accuracy. <br /> <br /> <br /> '''Ablation Study'''<br /> <br /> The effect of removing different components to provide insights into what makes DivideMix successful. We analyze the results in Table 5 as follows.<br /> <br /> <br /> [[File:DivideMixtable5.PNG | center]]<br /> <br /> The authors combined self-divide with the original MixMatch as a naive baseline for using SLL in LNL.<br /> They also find that both label refinement and input augmentation are beneficial for DivideMix. ''Label refinement'' is important for high noise ratio due because samples that are noisier would be incorrectly divided into the labeled set. ''Augmentation'' upgrades model performance by creating more reliable predictions and by achieving consistent regularization. In addition, the performance drop was seen in the ''DivideMix w/o co-training'' highlights the disadvantage of self-training; the model still has dataset division, label refinement and label guessing, but they are all performed by the same model.<br /> <br /> == Conclusion ==<br /> <br /> This paper provides a new and effective algorithm for learning with noisy labels by leveraging SSL. The DivideMix method trains two networks simultaneously and utilizes co-guessing and co-labeling effectively, therefore it is a robust approach to dealing with noise in datasets. Also, the DivideMix method has also been tested using various datasets with the results consistently being one of the best when compared to the state-of-the-art methods through extensive experiments.<br /> <br /> Future work of DivideMix is to create an adaptation for other applications such as Natural Language Processing, and incorporating the ideas of SSL and LNL into DivideMix architecture.<br /> <br /> == Critiques/ Insights ==<br /> <br /> 1. While combining both models makes the result better, the author did not show the relative time increase using this new combined methodology, which is very crucial considering training a large amount of data, especially for images. In addition, it seems that the author did not perform much on hyperparameters tuning for the combined model.<br /> <br /> 2. There is an interesting insight, which is when the noise ratio increases from 80% to 90%, the accuracy of DivideMix drops dramatically in both datasets.<br /> <br /> 3. There should be a further explanation of why the learning rate drops by a factor of 10 after 150 epochs.<br /> <br /> 4. It would be interesting to see the effectiveness of this method in other domains such as NLP. I am not aware of noisy training datasets available in NLP, but surely this is an important area to focus on, as much of the available data is collected from noisy sources from the web.<br /> <br /> 5. The paper implicitly assumes that a Gaussian mixture model (GMM) is sufficiently capable of identifying noise. Given the nature of a GMM, it would work well for noise that is distributed by a Gaussian distribution but for all other noise, it would probably be only asymptotic. The paper should present theoretical results on the noise that are Exponential, Rayleigh, etc. This is particularly important because the experiments were done on massive datasets, but they do not directly address the case when there are not many data points. <br /> <br /> 6. Comparing the training result on these benchmark datasets makes the algorithm quite comprehensive. This is a very insightful idea to maintain two networks to avoid bias from occurring.<br /> <br /> 7. The current benchmark accuracy for CIFAR-10 is 99.7, CIFAR-100 is 96.08 using EffNet-L2 in 2020. In 2019, CIFAR-10 is 99.37, CIFAR-100 is 93.51 using BiT-L.(based on paperswithcode.com) As there exists better methods, it would be nice to know why the authors chose these state-of-the-art methods to compare the test accuracy.<br /> <br /> 8. Another interesting observation is that DivideMix seems to maintain a similar accuracy while some methods give unstable results. That shows the reliability of the proposed algorithm.<br /> <br /> 9. It would be interesting to see if the drop in accuracy from increasing the noise ratio to 90% is a result of a low porportion or low number of clean labels. That is, would increasing the size of the training set but keeping the noise ratio at 90% result in increased accuracy?<br /> <br /> 10. For Ablation Study part, the paper also introduced a study on the Robustness of Testing Marking Methods Noise, including AUC for classification of clean/noisy samples of CIFAR-10 training data. And it shows that the method can effectively separate clean and noisy samples as training proceeds.<br /> <br /> == References ==<br /> Eric Arazo, Diego Ortego, Paul Albert, Noel E. O’Connor, and Kevin McGuinness. Unsupervised<br /> label noise modeling and loss correction. In ICML, pp. 312–321, 2019.<br /> <br /> David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin<br /> Raffel. Mixmatch: A holistic approach to semi-supervised learning. NeurIPS, 2019.<br /> <br /> Yifan Ding, Liqiang Wang, Deliang Fan, and Boqing Gong. A semi-supervised two-stage approach<br /> to learning from noisy labels. In WACV, pp. 1215–1224, 2018.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=48132 Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence 2020-11-30T02:06:19Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Guanting(Tony) Pan, Zaiwei(Zara) Zhang, Haocheng(Beren) Chang<br /> <br /> == Introduction == <br /> With the development of mobile devices and location-acquisition technologies, accessing real-time location information is becoming easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) like Yelp and Foursquare have become an important part of human’s life. People can share their experiences in locations, such as restaurants and parks, on the Internet. These locations can be seen as a Point-of-Interest (POI) in software such as Maps on our phone. These large amounts of user-POI interaction data can provide a service, which is called personalized POI recommendation, to give recommendations to users that the location they might be interested in. These large amounts of data can be used to train a model through Machine Learning methods(i.e., Classification, Clustering, etc.) to predict a POI that users might be interested in. The POI recommendation system still faces some challenging issues: (1) the difficulty of modeling complex user-POI interactions from sparse implicit feedback; (2) the difficulty of incorporating geographic background information. In order to meet these challenges, this paper will introduce a novel autoencoder-based model to learn non-linear user-POI relations, which is called SAE-NAD. SAE stands for the self-attentive encoder, while NAD stands for the neighbor-aware decoder. Autoencoder is an unsupervised learning technique that we implement in the neural network model for representation learning, meaning that our neural network will contain a &quot;bottleneck&quot; layer that produces a compressed knowledge representation of the original input. This method will include machine learning knowledge that we learned in this course.<br /> <br /> == Previous Work == <br /> <br /> In the previous works, the method is just equally treating users checked in POIs. The drawback of equally treating users checked in POIs is that valuable information about the similarity between users is not utilized, thus reducing the power of such recommenders. However, the SAE adaptively differentiates the user preference degrees in multiple aspects.<br /> <br /> There are some other personalized POI recommendation methods that can be used. Some famous software (e.g., Netflix) uses model-based methods that are built on matrix factorization (MF). For example, ranked based Geographical Factorization Method in  adopted weighted regularized MF to serve people on POI. Machine learning is popular in this area. POI recommendation is an important topic in the domain of recommender systems . This paper also described related work in Personalized location recommendation and attention mechanism in the recommendation.<br /> <br /> == Motivation == <br /> This paper reviews encoder and decoder. A single hidden-layer autoencoder is an unsupervised neural network, which consists of two parts: an encoder and a decoder. The encoder has one activation function that maps the input data to the latent space. The decoder also has one activation function mapping the representations in the latent space to the reconstruction space. And here is the formula:<br /> <br /> [[File: formula.png|center]](Note: a is the activation function)<br /> <br /> The proposed method uses a two-layer neural network to compute the score matrix in the architecture of the SAE. The NAD adopts the RBF kernel to make checked-in POIs exert more influence on nearby unvisited POIs. To train this model, Network training is required.<br /> <br /> This paper will use the datasets in the real world, which are from Gowalla, Foursquare , and Yelp. These datasets would be used to train by using the method introduced in this paper and compare the performance of SAE-NAD with other POI recommendation methods. Three groups of methods are used to compare with the proposed method, which are traditional MF methods for implicit feedback, Classical POI recommendation methods, and Deep learning-based methods. Specifically, the Deep learning-based methods contain a DeepAE which is a three-hidden-layer autoencoder with a weighted loss function, we can connect this to the material in this course.<br /> <br /> Autoencoder (AE) due to their ability to represent complex data have become very useful in recommendation systems. The primary reason it is used is because with deep neural network and with non-linear activation function it effectively captures the non-linear and non-trivial relationships between users and POI's.<br /> <br /> == Methodology == <br /> <br /> === Notations ===<br /> <br /> Here are the notations used in this paper. It will be helpful when trying to understand the structure and equations in the algorithm.<br /> [[File:notations.JPG|500px|x300px|center]]<br /> <br /> === Structure ===<br /> <br /> The structure of the network in this paper includes a self-attentive encoder as the input layer(yellow), and a neighbor-aware decoder as the output layer(green).<br /> <br /> [[File:1.JPG|1200px|x600px]]<br /> <br /> === Self-Attentive Encoder ===<br /> <br /> The self-attentive encoder is the input layer. It transfers the preference vector &lt;math&gt;x_u&lt;/math&gt; to hidden representation &lt;math&gt;A_u&lt;/math&gt; using weight matrix &lt;math&gt;W^1&lt;/math&gt; and the activation function &lt;math&gt;softmax&lt;/math&gt; and &lt;math&gt;tanh&lt;/math&gt;. The 0's and 1's in &lt;math&gt;x_u&lt;/math&gt; indicates whether the user has been to a certain POI. The weight matrix &lt;math&gt;W_a&lt;/math&gt; assigns different weights on various features of POIs. &lt;math&gt;A_u&lt;/math&gt; is the importance score matrix, where each column is a POI, and each row is the importance level of the &lt;math&gt;n&lt;/math&gt; checked in POIs in one aspect.<br /> <br /> [[File:encoder.JPG|center]]<br /> <br /> &lt;math&gt;\mathbf{Z}_u^{(1)} = \mathbf{A}_u \cdot (\mathbf{W}^{(1)}[L_u])^\top&lt;/math&gt; is the multiplication of the importance score matrix and the POI embeddings, and represents the user from &lt;math&gt;d_a&lt;/math&gt; aspects. &lt;math&gt;\mathbf{Z}_u^{(1)}&lt;/math&gt; is a &lt;math&gt;d_a \times H_1&lt;/math&gt; matrix. The aggregation layer then combines multiple aspects that represent the user into one, so that it fits into the Neighbor-Aware decoder: &lt;math&gt;\mathbf{z}_u^{(1)} = a_t(\mathbf{Z}_u^{(1)\top}\mathbf{w}_t + \mathbf{b}_t)&lt;/math&gt;.<br /> <br /> === Neighbor-Aware Decoder ===<br /> <br /> POI recommendation uses the geographical clustering phenomenon, which increases the weight of the unvisited POIs that surrounds the visited POIs. Also, an aggregation layer is added to the network to aggregate users’ representations from different aspects into one aspect. This means that a person who has visited a location are very likely to return to this location again in the future, so the user is recommended POIs surrounding this area. An example would be someone who has been to the UW plaza and bought Lazeez are very likely to return to the plaza, therefore the person is recommended to try Mr. Panino's Beijing House.<br /> <br /> [[File:decoder.JPG|center]]<br /> <br /> === Objective Function ===<br /> <br /> By minimizing the objective function, the partial derivatives with respect to all the parameters can be computed by gradient descent with backpropagation. After that, the training is complete.<br /> <br /> [[File:objective_function.JPG|center]]<br /> <br /> <br /> == Comparative analysis ==<br /> <br /> === Metrics introduction ===<br /> To obtain a comprehensive evaluation of the effectiveness of the model, the authors performed a thorough comparison between the proposed model and the existing major POI recommendation methods. These methods can be further broken down into three categories: traditional matrix factorization methods for implicit feedback, classical POI recommendation methods, and deep learning-based methods. Here, three key evaluation metrics were introduced as Precison@k, Recall@k, and MAP@k. Through comparing all models on three datasets using the above metrics, it is concluded that the proposed model achieved the best performance.<br /> <br /> To better understand the comparison results, it is critical for one to understand the meanings behind each evaluation metrics. Suppose the proposed model generated k recommended POIs for the user. The first metric, Precison@k, measures the percentage of the recommended POIs which the user has visited. Recall@k is also associated with the user’s behavior. However, it will measure the percentage of recommended POIs in all POIs which have been visited by the user. Lastly, MAP@k represents the mean average precision at k, where average precision is the average of precision values at all k ranks, where relevant POIs are found.<br /> <br /> === Model Comparison ===<br /> Among all models in the comparison group, RankGeoFM, IRNMF, and PACE produced the best results. Nonetheless, these models are still incomparable to our proposed model. The reasons are explained in details as follows:<br /> <br /> Both RankGeoFM and IRNMF incorporate geographical influence into their ranking models, which is significant for generating POI recommendations. However, they are not capable of capturing non-linear interactions between users and POIs. In comparison, the proposed model, while incorporating geographical influence, adopts a deep neural structure which enables it to measure non-linear and complex interactions. As a result, it outperforms the two methods in the comparison group.<br /> <br /> Moreover, compared to PACE, which is a deep learning-based method, the proposed model offers a more precise measurement of geographical influence. Though PACE is able to capture complex interactions, it models the geographical influence by a context graph, which fails to incorporate user reachability into the modeling process. In contrast, the proposed model is able to capture geographical influence directly through its neighbor-aware decoder, which allows it to achieve better performance than the PACE model.<br /> <br /> [[File:model_comparison.JPG|center]]<br /> <br /> == Conclusion ==<br /> In summary, the proposed model, namely SAE-NAD, clearly showed its advantages compared to many state-of-the-art baseline methods. Its self-attentive encoder effectively discriminates user preferences on check-in POIs, and its neighbor-aware decoder measures geographical influence precisely through differentiating user reachability on unvisited POIs. By leveraging these two components together, it can generate recommendations that are highly relevant to its users.<br /> <br /> == Critiques ==<br /> Besides developing the model and conducting a detailed analysis, the authors also did very well in constructing this paper. The paper is well-written and has a highly logical structure. Definitions, notations, and metrics are introduced and explained clearly, which enables readers to follow through the analysis easily. Last but not least, both the abstract and the conclusion of this paper are strong. The abstract concisely reported the objectives and outcomes of the experiment, whereas the conclusion is succinct and precise.<br /> <br /> This idea would have many applications, such as suggesting new restaurants to customers in the food delivery service app. Would the improvement in accuracy outweigh the increased complexity of the model when it comes to use in industry?<br /> <br /> It would be nice if the author could if the authors can describe the extensive experiments on the real-world datasets, with different baseline methods and evaluation metrics, to demonstrate the effectiveness of the proposed model. Moreover, show the comparison result in tables vs other methodologies, both in terms of accuracy and time-efficiency. In addition, the drawbacks of this new methodology are unknown to the readers. In other words, how does this compare to the already established recommendation systems found in large scale applications utilize by companies like Netflix? Why use the proposed method over something simpler such as matrix factorization or collaborative filtering? <br /> <br /> It would also be nice if the authors provided some more ablation on the various components of the proposed method. Even after reading some of their experiments, we do not have a clear understanding of how important each component is to the recommendation quality.<br /> <br /> It is recommended that the author can present how the encoder and the decoder help in the process by comparing different models with or without encoder and decoder.<br /> <br /> It would have been better if the author included all figures to explain the sensitivity of parameters more elaborately. In the paper he only included plots showing effects on Gowalla and Foursquare datasets but not other datasets.<br /> <br /> Some additional explanations can be inserted in the Objective Function part. From the paper, we can find &lt;math&gt;\lambda&lt;/math&gt; is the regularization parameter and &lt;math&gt;W_a&lt;/math&gt; and &lt;math&gt;w_t&lt;/math&gt; are the learned parameters in the attention layer and aggregation layer.<br /> <br /> == References ==<br />  Defu Lian, Cong Zhao, Xing Xie, Guangzhong Sun, Enhong Chen, and Yong Rui. 2014. GeoMF: joint geographical modeling and matrix factorization for point-of-interest recommendation. In KDD. ACM, 831–840.<br /> <br />  Eunjoon Cho, Seth A. Myers, and Jure Leskovec. 2011. Friendship and mobility: user movement in location-based social networks. In KDD. ACM, 1082–1090.<br /> <br />  Yiding Liu, Tuan-Anh Pham, Gao Cong, and Quan Yuan. 2017. An Experimental Evaluation of Point-of-interest Recommendation in Location-based Social Networks. PVLDB 10, 10 (2017), 1010–1021.<br /> <br />  Jie Bao, Yu Zheng, David Wilkie, and Mohamed F. Mokbel. 2015. Recommendations in location-based social networks: a survey. GeoInformatica 19, 3 (2015), 525–565.<br /> <br />  Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. 2017. Neural Collaborative Filtering. In WWW. ACM, 173–182.<br /> <br />  Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br /> <br />  Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667.  Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br /> <br />  Yong Liu,WeiWei, Aixin Sun, and Chunyan Miao. 2014. Exploiting Geographical<br /> Neighborhood Characteristics for Location Recommendation. In CIKM. ACM,<br /> 739–748<br /> <br />  Xutao Li, Gao Cong, Xiaoli Li, Tuan-Anh Nguyen Pham, and Shonali Krishnaswamy.<br /> 2015. Rank-GeoFM: A Ranking based Geographical Factorization<br /> Method for Point of Interest Recommendation. In SIGIR. ACM, 433–442.<br /> <br />  Carl Yang, Lanxiao Bai, Chao Zhang, Quan Yuan, and Jiawei Han. 2017. Bridging<br /> Collaborative Filtering and Semi-Supervised Learning: A Neural Approach for<br /> POI Recommendation. In KDD. ACM, 1245–1254.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=48128 Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence 2020-11-30T02:04:22Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Guanting(Tony) Pan, Zaiwei(Zara) Zhang, Haocheng(Beren) Chang<br /> <br /> == Introduction == <br /> With the development of mobile devices and location-acquisition technologies, accessing real-time location information is becoming easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) like Yelp and Foursquare have become an important part of human’s life. People can share their experiences in locations, such as restaurants and parks, on the Internet. These locations can be seen as a Point-of-Interest (POI) in software such as Maps on our phone. These large amounts of user-POI interaction data can provide a service, which is called personalized POI recommendation, to give recommendations to users that the location they might be interested in. These large amounts of data can be used to train a model through Machine Learning methods(i.e., Classification, Clustering, etc.) to predict a POI that users might be interested in. The POI recommendation system still faces some challenging issues: (1) the difficulty of modeling complex user-POI interactions from sparse implicit feedback; (2) the difficulty of incorporating geographic background information. In order to meet these challenges, this paper will introduce a novel autoencoder-based model to learn non-linear user-POI relations, which is called SAE-NAD. SAE stands for the self-attentive encoder, while NAD stands for the neighbor-aware decoder. Autoencoder is an unsupervised learning technique that we implement in the neural network model for representation learning, meaning that our neural network will contain a &quot;bottleneck&quot; layer that produces a compressed knowledge representation of the original input. This method will include machine learning knowledge that we learned in this course.<br /> <br /> == Previous Work == <br /> <br /> In the previous works, the method is just equally treating users checked in POIs. The drawback of equally treating users checked in POIs is that valuable information about the similarity between users is not utilized, thus reducing the power of such recommenders. However, the SAE adaptively differentiates the user preference degrees in multiple aspects.<br /> <br /> There are some other personalized POI recommendation methods that can be used. Some famous software (e.g., Netflix) uses model-based methods that are built on matrix factorization (MF). For example, ranked based Geographical Factorization Method in  adopted weighted regularized MF to serve people on POI. Machine learning is popular in this area. POI recommendation is an important topic in the domain of recommender systems . This paper also described related work in Personalized location recommendation and attention mechanism in the recommendation.<br /> <br /> == Motivation == <br /> This paper reviews encoder and decoder. A single hidden-layer autoencoder is an unsupervised neural network, which consists of two parts: an encoder and a decoder. The encoder has one activation function that maps the input data to the latent space. The decoder also has one activation function mapping the representations in the latent space to the reconstruction space. And here is the formula:<br /> <br /> [[File: formula.png|center]](Note: a is the activation function)<br /> <br /> The proposed method uses a two-layer neural network to compute the score matrix in the architecture of the SAE. The NAD adopts the RBF kernel to make checked-in POIs exert more influence on nearby unvisited POIs. To train this model, Network training is required.<br /> <br /> This paper will use the datasets in the real world, which are from Gowalla, Foursquare , and Yelp. These datasets would be used to train by using the method introduced in this paper and compare the performance of SAE-NAD with other POI recommendation methods. Three groups of methods are used to compare with the proposed method, which are traditional MF methods for implicit feedback, Classical POI recommendation methods, and Deep learning-based methods. Specifically, the Deep learning-based methods contain a DeepAE which is a three-hidden-layer autoencoder with a weighted loss function, we can connect this to the material in this course.<br /> <br /> Autoencoder (AE) due to their ability to represent complex data have become very useful in recommendation systems. The primary reason it is used is because with deep neural network and with non-linear activation function it effectively captures the non-linear and non-trivial relationships between users and POI's.<br /> <br /> == Methodology == <br /> <br /> === Notations ===<br /> <br /> Here are the notations used in this paper. It will be helpful when trying to understand the structure and equations in the algorithm.<br /> [[File:notations.JPG|500px|x300px|center]]<br /> <br /> === Structure ===<br /> <br /> The structure of the network in this paper includes a self-attentive encoder as the input layer(yellow), and a neighbor-aware decoder as the output layer(green).<br /> <br /> [[File:1.JPG|1200px|x600px]]<br /> <br /> === Self-Attentive Encoder ===<br /> <br /> The self-attentive encoder is the input layer. It transfers the preference vector &lt;math&gt;x_u&lt;/math&gt; to hidden representation &lt;math&gt;A_u&lt;/math&gt; using weight matrix &lt;math&gt;W^1&lt;/math&gt; and the activation function &lt;math&gt;softmax&lt;/math&gt; and &lt;math&gt;tanh&lt;/math&gt;. The 0's and 1's in &lt;math&gt;x_u&lt;/math&gt; indicates whether the user has been to a certain POI. The weight matrix &lt;math&gt;W_a&lt;/math&gt; assigns different weights on various features of POIs. &lt;math&gt;A_u&lt;/math&gt; is the importance score matrix, where each column is a POI, and each row is the importance level of the &lt;math&gt;n&lt;/math&gt; checked in POIs in one aspect.<br /> <br /> [[File:encoder.JPG|center]]<br /> <br /> &lt;math&gt;\mathbf{Z}_u^{(1)} = \mathbf{A}_u \cdot (\mathbf{W}^{(1)}[L_u])^\top&lt;/math&gt; is the multiplication of the importance score matrix and the POI embeddings, and represents the user from &lt;math&gt;d_a&lt;/math&gt; aspects. &lt;math&gt;\mathbf{Z}_u^{(1)}&lt;/math&gt; is a &lt;math&gt;d_a \times H_1&lt;/math&gt; matrix. The aggregation layer then combines multiple aspects that represent the user into one, so that it fits into the Neighbor-Aware decoder: &lt;math&gt;\mathbf{z}_u^{(1)} = a_t(\mathbf{Z}_u^{(1)\top}\mathbf{w}_t + \mathbf{b}_t)&lt;/math&gt;.<br /> <br /> === Neighbor-Aware Decoder ===<br /> <br /> POI recommendation uses the geographical clustering phenomenon, which increases the weight of the unvisited POIs that surrounds the visited POIs. Also, an aggregation layer is added to the network to aggregate users’ representations from different aspects into one aspect. This means that a person who has visited a location are very likely to return to this location again in the future, so the user is recommended POIs surrounding this area. An example would be someone who has been to the UW plaza and bought Lazeez are very likely to return to the plaza, therefore the person is recommended to try Mr. Panino's Beijing House.<br /> <br /> [[File:decoder.JPG|center]]<br /> <br /> === Objective Function ===<br /> <br /> By minimizing the objective function, the partial derivatives with respect to all the parameters can be computed by gradient descent with backpropagation. After that, the training is complete.<br /> <br /> [[File:objective_function.JPG|center]]<br /> <br /> <br /> == Comparative analysis ==<br /> <br /> === Metrics introduction ===<br /> To obtain a comprehensive evaluation of the effectiveness of the model, the authors performed a thorough comparison between the proposed model and the existing major POI recommendation methods. These methods can be further broken down into three categories: traditional matrix factorization methods for implicit feedback, classical POI recommendation methods, and deep learning-based methods. Here, three key evaluation metrics were introduced as Precison@k, Recall@k, and MAP@k. Through comparing all models on three datasets using the above metrics, it is concluded that the proposed model achieved the best performance.<br /> <br /> To better understand the comparison results, it is critical for one to understand the meanings behind each evaluation metrics. Suppose the proposed model generated k recommended POIs for the user. The first metric, Precison@k, measures the percentage of the recommended POIs which the user has visited. Recall@k is also associated with the user’s behavior. However, it will measure the percentage of recommended POIs in all POIs which have been visited by the user. Lastly, MAP@k represents the mean average precision at k, where average precision is the average of precision values at all k ranks, where relevant POIs are found.<br /> <br /> === Model Comparison ===<br /> Among all models in the comparison group, RankGeoFM, IRNMF, and PACE produced the best results. Nonetheless, these models are still incomparable to our proposed model. The reasons are explained in details as follows:<br /> <br /> Both RankGeoFM and IRNMF incorporate geographical influence into their ranking models, which is significant for generating POI recommendations. However, they are not capable of capturing non-linear interactions between users and POIs. In comparison, the proposed model, while incorporating geographical influence, adopts a deep neural structure which enables it to measure non-linear and complex interactions. As a result, it outperforms the two methods in the comparison group.<br /> <br /> Moreover, compared to PACE, which is a deep learning-based method, the proposed model offers a more precise measurement of geographical influence. Though PACE is able to capture complex interactions, it models the geographical influence by a context graph, which fails to incorporate user reachability into the modeling process. In contrast, the proposed model is able to capture geographical influence directly through its neighbor-aware decoder, which allows it to achieve better performance than the PACE model.<br /> <br /> [[File:model_comparison.JPG|center]]<br /> <br /> == Conclusion ==<br /> In summary, the proposed model, namely SAE-NAD, clearly showed its advantages compared to many state-of-the-art baseline methods. Its self-attentive encoder effectively discriminates user preferences on check-in POIs, and its neighbor-aware decoder measures geographical influence precisely through differentiating user reachability on unvisited POIs. By leveraging these two components together, it can generate recommendations that are highly relevant to its users.<br /> <br /> == Critiques ==<br /> Besides developing the model and conducting a detailed analysis, the authors also did very well in constructing this paper. The paper is well-written and has a highly logical structure. Definitions, notations, and metrics are introduced and explained clearly, which enables readers to follow through the analysis easily. Last but not least, both the abstract and the conclusion of this paper are strong. The abstract concisely reported the objectives and outcomes of the experiment, whereas the conclusion is succinct and precise.<br /> <br /> This idea would have many applications, such as suggesting new restaurants to customers in the food delivery service app. Would the improvement in accuracy outweigh the increased complexity of the model when it comes to use in industry?<br /> <br /> It would be nice if the author could if the authors can describe the extensive experiments on the real-world datasets, with different baseline methods and evaluation metrics, to demonstrate the effectiveness of the proposed model. Moreover, show the comparison result in tables vs other methodologies, both in terms of accuracy and time-efficiency. In addition, the drawbacks of this new methodology are unknown to the readers. In other words, how does this compare to the already established recommendation systems found in large scale applications utilize by companies like Netflix? Why use the proposed method over something simpler such as matrix factorization or collaborative filtering? <br /> <br /> It would also be nice if the authors provided some more ablation on the various components of the proposed method. Even after reading some of their experiments, we do not have a clear understanding of how important each component is to the recommendation quality.<br /> <br /> It is recommended that the author can present how the encoder and the decoder help in the process by comparing different models with or without encoder and decoder.<br /> <br /> It would have been better if the author included all figures to explain the sensitivity of parameters more elaborately. In the paper he only included plots showing effects on Gowalla and Foursquare datasets but not other datasets.<br /> <br /> Some additional explanations can be inserted in the Objective Function part. From the paper, we can find &lt;/math&gt;\lambda&lt;/math&gt; is the regularization parameter and &lt;math&gt;W_a&lt;/math&gt; and &lt;math&gt;w_t&lt;/math&gt; are the learned parameters in the attention layer and aggregation layer.<br /> <br /> == References ==<br />  Defu Lian, Cong Zhao, Xing Xie, Guangzhong Sun, Enhong Chen, and Yong Rui. 2014. GeoMF: joint geographical modeling and matrix factorization for point-of-interest recommendation. In KDD. ACM, 831–840.<br /> <br />  Eunjoon Cho, Seth A. Myers, and Jure Leskovec. 2011. Friendship and mobility: user movement in location-based social networks. In KDD. ACM, 1082–1090.<br /> <br />  Yiding Liu, Tuan-Anh Pham, Gao Cong, and Quan Yuan. 2017. An Experimental Evaluation of Point-of-interest Recommendation in Location-based Social Networks. PVLDB 10, 10 (2017), 1010–1021.<br /> <br />  Jie Bao, Yu Zheng, David Wilkie, and Mohamed F. Mokbel. 2015. Recommendations in location-based social networks: a survey. GeoInformatica 19, 3 (2015), 525–565.<br /> <br />  Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. 2017. Neural Collaborative Filtering. In WWW. ACM, 173–182.<br /> <br />  Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br /> <br />  Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667.  Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br /> <br />  Yong Liu,WeiWei, Aixin Sun, and Chunyan Miao. 2014. Exploiting Geographical<br /> Neighborhood Characteristics for Location Recommendation. In CIKM. ACM,<br /> 739–748<br /> <br />  Xutao Li, Gao Cong, Xiaoli Li, Tuan-Anh Nguyen Pham, and Shonali Krishnaswamy.<br /> 2015. Rank-GeoFM: A Ranking based Geographical Factorization<br /> Method for Point of Interest Recommendation. In SIGIR. ACM, 433–442.<br /> <br />  Carl Yang, Lanxiao Bai, Chao Zhang, Quan Yuan, and Jiawei Han. 2017. Bridging<br /> Collaborative Filtering and Semi-Supervised Learning: A Neural Approach for<br /> POI Recommendation. In KDD. ACM, 1245–1254.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=48126 Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence 2020-11-30T02:04:05Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Guanting(Tony) Pan, Zaiwei(Zara) Zhang, Haocheng(Beren) Chang<br /> <br /> == Introduction == <br /> With the development of mobile devices and location-acquisition technologies, accessing real-time location information is becoming easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) like Yelp and Foursquare have become an important part of human’s life. People can share their experiences in locations, such as restaurants and parks, on the Internet. These locations can be seen as a Point-of-Interest (POI) in software such as Maps on our phone. These large amounts of user-POI interaction data can provide a service, which is called personalized POI recommendation, to give recommendations to users that the location they might be interested in. These large amounts of data can be used to train a model through Machine Learning methods(i.e., Classification, Clustering, etc.) to predict a POI that users might be interested in. The POI recommendation system still faces some challenging issues: (1) the difficulty of modeling complex user-POI interactions from sparse implicit feedback; (2) the difficulty of incorporating geographic background information. In order to meet these challenges, this paper will introduce a novel autoencoder-based model to learn non-linear user-POI relations, which is called SAE-NAD. SAE stands for the self-attentive encoder, while NAD stands for the neighbor-aware decoder. Autoencoder is an unsupervised learning technique that we implement in the neural network model for representation learning, meaning that our neural network will contain a &quot;bottleneck&quot; layer that produces a compressed knowledge representation of the original input. This method will include machine learning knowledge that we learned in this course.<br /> <br /> == Previous Work == <br /> <br /> In the previous works, the method is just equally treating users checked in POIs. The drawback of equally treating users checked in POIs is that valuable information about the similarity between users is not utilized, thus reducing the power of such recommenders. However, the SAE adaptively differentiates the user preference degrees in multiple aspects.<br /> <br /> There are some other personalized POI recommendation methods that can be used. Some famous software (e.g., Netflix) uses model-based methods that are built on matrix factorization (MF). For example, ranked based Geographical Factorization Method in  adopted weighted regularized MF to serve people on POI. Machine learning is popular in this area. POI recommendation is an important topic in the domain of recommender systems . This paper also described related work in Personalized location recommendation and attention mechanism in the recommendation.<br /> <br /> == Motivation == <br /> This paper reviews encoder and decoder. A single hidden-layer autoencoder is an unsupervised neural network, which consists of two parts: an encoder and a decoder. The encoder has one activation function that maps the input data to the latent space. The decoder also has one activation function mapping the representations in the latent space to the reconstruction space. And here is the formula:<br /> <br /> [[File: formula.png|center]](Note: a is the activation function)<br /> <br /> The proposed method uses a two-layer neural network to compute the score matrix in the architecture of the SAE. The NAD adopts the RBF kernel to make checked-in POIs exert more influence on nearby unvisited POIs. To train this model, Network training is required.<br /> <br /> This paper will use the datasets in the real world, which are from Gowalla, Foursquare , and Yelp. These datasets would be used to train by using the method introduced in this paper and compare the performance of SAE-NAD with other POI recommendation methods. Three groups of methods are used to compare with the proposed method, which are traditional MF methods for implicit feedback, Classical POI recommendation methods, and Deep learning-based methods. Specifically, the Deep learning-based methods contain a DeepAE which is a three-hidden-layer autoencoder with a weighted loss function, we can connect this to the material in this course.<br /> <br /> Autoencoder (AE) due to their ability to represent complex data have become very useful in recommendation systems. The primary reason it is used is because with deep neural network and with non-linear activation function it effectively captures the non-linear and non-trivial relationships between users and POI's.<br /> <br /> == Methodology == <br /> <br /> === Notations ===<br /> <br /> Here are the notations used in this paper. It will be helpful when trying to understand the structure and equations in the algorithm.<br /> [[File:notations.JPG|500px|x300px|center]]<br /> <br /> === Structure ===<br /> <br /> The structure of the network in this paper includes a self-attentive encoder as the input layer(yellow), and a neighbor-aware decoder as the output layer(green).<br /> <br /> [[File:1.JPG|1200px|x600px]]<br /> <br /> === Self-Attentive Encoder ===<br /> <br /> The self-attentive encoder is the input layer. It transfers the preference vector &lt;math&gt;x_u&lt;/math&gt; to hidden representation &lt;math&gt;A_u&lt;/math&gt; using weight matrix &lt;math&gt;W^1&lt;/math&gt; and the activation function &lt;math&gt;softmax&lt;/math&gt; and &lt;math&gt;tanh&lt;/math&gt;. The 0's and 1's in &lt;math&gt;x_u&lt;/math&gt; indicates whether the user has been to a certain POI. The weight matrix &lt;math&gt;W_a&lt;/math&gt; assigns different weights on various features of POIs. &lt;math&gt;A_u&lt;/math&gt; is the importance score matrix, where each column is a POI, and each row is the importance level of the &lt;math&gt;n&lt;/math&gt; checked in POIs in one aspect.<br /> <br /> [[File:encoder.JPG|center]]<br /> <br /> &lt;math&gt;\mathbf{Z}_u^{(1)} = \mathbf{A}_u \cdot (\mathbf{W}^{(1)}[L_u])^\top&lt;/math&gt; is the multiplication of the importance score matrix and the POI embeddings, and represents the user from &lt;math&gt;d_a&lt;/math&gt; aspects. &lt;math&gt;\mathbf{Z}_u^{(1)}&lt;/math&gt; is a &lt;math&gt;d_a \times H_1&lt;/math&gt; matrix. The aggregation layer then combines multiple aspects that represent the user into one, so that it fits into the Neighbor-Aware decoder: &lt;math&gt;\mathbf{z}_u^{(1)} = a_t(\mathbf{Z}_u^{(1)\top}\mathbf{w}_t + \mathbf{b}_t)&lt;/math&gt;.<br /> <br /> === Neighbor-Aware Decoder ===<br /> <br /> POI recommendation uses the geographical clustering phenomenon, which increases the weight of the unvisited POIs that surrounds the visited POIs. Also, an aggregation layer is added to the network to aggregate users’ representations from different aspects into one aspect. This means that a person who has visited a location are very likely to return to this location again in the future, so the user is recommended POIs surrounding this area. An example would be someone who has been to the UW plaza and bought Lazeez are very likely to return to the plaza, therefore the person is recommended to try Mr. Panino's Beijing House.<br /> <br /> [[File:decoder.JPG|center]]<br /> <br /> === Objective Function ===<br /> <br /> By minimizing the objective function, the partial derivatives with respect to all the parameters can be computed by gradient descent with backpropagation. After that, the training is complete.<br /> <br /> [[File:objective_function.JPG|center]]<br /> <br /> <br /> == Comparative analysis ==<br /> <br /> === Metrics introduction ===<br /> To obtain a comprehensive evaluation of the effectiveness of the model, the authors performed a thorough comparison between the proposed model and the existing major POI recommendation methods. These methods can be further broken down into three categories: traditional matrix factorization methods for implicit feedback, classical POI recommendation methods, and deep learning-based methods. Here, three key evaluation metrics were introduced as Precison@k, Recall@k, and MAP@k. Through comparing all models on three datasets using the above metrics, it is concluded that the proposed model achieved the best performance.<br /> <br /> To better understand the comparison results, it is critical for one to understand the meanings behind each evaluation metrics. Suppose the proposed model generated k recommended POIs for the user. The first metric, Precison@k, measures the percentage of the recommended POIs which the user has visited. Recall@k is also associated with the user’s behavior. However, it will measure the percentage of recommended POIs in all POIs which have been visited by the user. Lastly, MAP@k represents the mean average precision at k, where average precision is the average of precision values at all k ranks, where relevant POIs are found.<br /> <br /> === Model Comparison ===<br /> Among all models in the comparison group, RankGeoFM, IRNMF, and PACE produced the best results. Nonetheless, these models are still incomparable to our proposed model. The reasons are explained in details as follows:<br /> <br /> Both RankGeoFM and IRNMF incorporate geographical influence into their ranking models, which is significant for generating POI recommendations. However, they are not capable of capturing non-linear interactions between users and POIs. In comparison, the proposed model, while incorporating geographical influence, adopts a deep neural structure which enables it to measure non-linear and complex interactions. As a result, it outperforms the two methods in the comparison group.<br /> <br /> Moreover, compared to PACE, which is a deep learning-based method, the proposed model offers a more precise measurement of geographical influence. Though PACE is able to capture complex interactions, it models the geographical influence by a context graph, which fails to incorporate user reachability into the modeling process. In contrast, the proposed model is able to capture geographical influence directly through its neighbor-aware decoder, which allows it to achieve better performance than the PACE model.<br /> <br /> [[File:model_comparison.JPG|center]]<br /> <br /> == Conclusion ==<br /> In summary, the proposed model, namely SAE-NAD, clearly showed its advantages compared to many state-of-the-art baseline methods. Its self-attentive encoder effectively discriminates user preferences on check-in POIs, and its neighbor-aware decoder measures geographical influence precisely through differentiating user reachability on unvisited POIs. By leveraging these two components together, it can generate recommendations that are highly relevant to its users.<br /> <br /> == Critiques ==<br /> Besides developing the model and conducting a detailed analysis, the authors also did very well in constructing this paper. The paper is well-written and has a highly logical structure. Definitions, notations, and metrics are introduced and explained clearly, which enables readers to follow through the analysis easily. Last but not least, both the abstract and the conclusion of this paper are strong. The abstract concisely reported the objectives and outcomes of the experiment, whereas the conclusion is succinct and precise.<br /> <br /> This idea would have many applications, such as suggesting new restaurants to customers in the food delivery service app. Would the improvement in accuracy outweigh the increased complexity of the model when it comes to use in industry?<br /> <br /> It would be nice if the author could if the authors can describe the extensive experiments on the real-world datasets, with different baseline methods and evaluation metrics, to demonstrate the effectiveness of the proposed model. Moreover, show the comparison result in tables vs other methodologies, both in terms of accuracy and time-efficiency. In addition, the drawbacks of this new methodology are unknown to the readers. In other words, how does this compare to the already established recommendation systems found in large scale applications utilize by companies like Netflix? Why use the proposed method over something simpler such as matrix factorization or collaborative filtering? <br /> <br /> It would also be nice if the authors provided some more ablation on the various components of the proposed method. Even after reading some of their experiments, we do not have a clear understanding of how important each component is to the recommendation quality.<br /> <br /> It is recommended that the author can present how the encoder and the decoder help in the process by comparing different models with or without encoder and decoder.<br /> <br /> It would have been better if the author included all figures to explain the sensitivity of parameters more elaborately. In the paper he only included plots showing effects on Gowalla and Foursquare datasets but not other datasets.<br /> <br /> Some additional explanations can be inserted in the Objective Function part. From the paper, we can find &lt;/math&gt;lambda&lt;/math&gt; is the regularization parameter and &lt;math&gt;W_a&lt;/math&gt; and &lt;math&gt;w_t&lt;/math&gt; are the learned parameters in the attention layer and aggregation layer.<br /> <br /> == References ==<br />  Defu Lian, Cong Zhao, Xing Xie, Guangzhong Sun, Enhong Chen, and Yong Rui. 2014. GeoMF: joint geographical modeling and matrix factorization for point-of-interest recommendation. In KDD. ACM, 831–840.<br /> <br />  Eunjoon Cho, Seth A. Myers, and Jure Leskovec. 2011. Friendship and mobility: user movement in location-based social networks. In KDD. ACM, 1082–1090.<br /> <br />  Yiding Liu, Tuan-Anh Pham, Gao Cong, and Quan Yuan. 2017. An Experimental Evaluation of Point-of-interest Recommendation in Location-based Social Networks. PVLDB 10, 10 (2017), 1010–1021.<br /> <br />  Jie Bao, Yu Zheng, David Wilkie, and Mohamed F. Mokbel. 2015. Recommendations in location-based social networks: a survey. GeoInformatica 19, 3 (2015), 525–565.<br /> <br />  Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. 2017. Neural Collaborative Filtering. In WWW. ACM, 173–182.<br /> <br />  Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br /> <br />  Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667.  Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br /> <br />  Yong Liu,WeiWei, Aixin Sun, and Chunyan Miao. 2014. Exploiting Geographical<br /> Neighborhood Characteristics for Location Recommendation. In CIKM. ACM,<br /> 739–748<br /> <br />  Xutao Li, Gao Cong, Xiaoli Li, Tuan-Anh Nguyen Pham, and Shonali Krishnaswamy.<br /> 2015. Rank-GeoFM: A Ranking based Geographical Factorization<br /> Method for Point of Interest Recommendation. In SIGIR. ACM, 433–442.<br /> <br />  Carl Yang, Lanxiao Bai, Chao Zhang, Quan Yuan, and Jiawei Han. 2017. Bridging<br /> Collaborative Filtering and Semi-Supervised Learning: A Neural Approach for<br /> POI Recommendation. In KDD. ACM, 1245–1254.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=48125 Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence 2020-11-30T02:02:35Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Guanting(Tony) Pan, Zaiwei(Zara) Zhang, Haocheng(Beren) Chang<br /> <br /> == Introduction == <br /> With the development of mobile devices and location-acquisition technologies, accessing real-time location information is becoming easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) like Yelp and Foursquare have become an important part of human’s life. People can share their experiences in locations, such as restaurants and parks, on the Internet. These locations can be seen as a Point-of-Interest (POI) in software such as Maps on our phone. These large amounts of user-POI interaction data can provide a service, which is called personalized POI recommendation, to give recommendations to users that the location they might be interested in. These large amounts of data can be used to train a model through Machine Learning methods(i.e., Classification, Clustering, etc.) to predict a POI that users might be interested in. The POI recommendation system still faces some challenging issues: (1) the difficulty of modeling complex user-POI interactions from sparse implicit feedback; (2) the difficulty of incorporating geographic background information. In order to meet these challenges, this paper will introduce a novel autoencoder-based model to learn non-linear user-POI relations, which is called SAE-NAD. SAE stands for the self-attentive encoder, while NAD stands for the neighbor-aware decoder. Autoencoder is an unsupervised learning technique that we implement in the neural network model for representation learning, meaning that our neural network will contain a &quot;bottleneck&quot; layer that produces a compressed knowledge representation of the original input. This method will include machine learning knowledge that we learned in this course.<br /> <br /> == Previous Work == <br /> <br /> In the previous works, the method is just equally treating users checked in POIs. The drawback of equally treating users checked in POIs is that valuable information about the similarity between users is not utilized, thus reducing the power of such recommenders. However, the SAE adaptively differentiates the user preference degrees in multiple aspects.<br /> <br /> There are some other personalized POI recommendation methods that can be used. Some famous software (e.g., Netflix) uses model-based methods that are built on matrix factorization (MF). For example, ranked based Geographical Factorization Method in  adopted weighted regularized MF to serve people on POI. Machine learning is popular in this area. POI recommendation is an important topic in the domain of recommender systems . This paper also described related work in Personalized location recommendation and attention mechanism in the recommendation.<br /> <br /> == Motivation == <br /> This paper reviews encoder and decoder. A single hidden-layer autoencoder is an unsupervised neural network, which consists of two parts: an encoder and a decoder. The encoder has one activation function that maps the input data to the latent space. The decoder also has one activation function mapping the representations in the latent space to the reconstruction space. And here is the formula:<br /> <br /> [[File: formula.png|center]](Note: a is the activation function)<br /> <br /> The proposed method uses a two-layer neural network to compute the score matrix in the architecture of the SAE. The NAD adopts the RBF kernel to make checked-in POIs exert more influence on nearby unvisited POIs. To train this model, Network training is required.<br /> <br /> This paper will use the datasets in the real world, which are from Gowalla, Foursquare , and Yelp. These datasets would be used to train by using the method introduced in this paper and compare the performance of SAE-NAD with other POI recommendation methods. Three groups of methods are used to compare with the proposed method, which are traditional MF methods for implicit feedback, Classical POI recommendation methods, and Deep learning-based methods. Specifically, the Deep learning-based methods contain a DeepAE which is a three-hidden-layer autoencoder with a weighted loss function, we can connect this to the material in this course.<br /> <br /> Autoencoder (AE) due to their ability to represent complex data have become very useful in recommendation systems. The primary reason it is used is because with deep neural network and with non-linear activation function it effectively captures the non-linear and non-trivial relationships between users and POI's.<br /> <br /> == Methodology == <br /> <br /> === Notations ===<br /> <br /> Here are the notations used in this paper. It will be helpful when trying to understand the structure and equations in the algorithm.<br /> [[File:notations.JPG|500px|x300px|center]]<br /> <br /> === Structure ===<br /> <br /> The structure of the network in this paper includes a self-attentive encoder as the input layer(yellow), and a neighbor-aware decoder as the output layer(green).<br /> <br /> [[File:1.JPG|1200px|x600px]]<br /> <br /> === Self-Attentive Encoder ===<br /> <br /> The self-attentive encoder is the input layer. It transfers the preference vector &lt;math&gt;x_u&lt;/math&gt; to hidden representation &lt;math&gt;A_u&lt;/math&gt; using weight matrix &lt;math&gt;W^1&lt;/math&gt; and the activation function &lt;math&gt;softmax&lt;/math&gt; and &lt;math&gt;tanh&lt;/math&gt;. The 0's and 1's in &lt;math&gt;x_u&lt;/math&gt; indicates whether the user has been to a certain POI. The weight matrix &lt;math&gt;W_a&lt;/math&gt; assigns different weights on various features of POIs. &lt;math&gt;A_u&lt;/math&gt; is the importance score matrix, where each column is a POI, and each row is the importance level of the &lt;math&gt;n&lt;/math&gt; checked in POIs in one aspect.<br /> <br /> [[File:encoder.JPG|center]]<br /> <br /> &lt;math&gt;\mathbf{Z}_u^{(1)} = \mathbf{A}_u \cdot (\mathbf{W}^{(1)}[L_u])^\top&lt;/math&gt; is the multiplication of the importance score matrix and the POI embeddings, and represents the user from &lt;math&gt;d_a&lt;/math&gt; aspects. &lt;math&gt;\mathbf{Z}_u^{(1)}&lt;/math&gt; is a &lt;math&gt;d_a \times H_1&lt;/math&gt; matrix. The aggregation layer then combines multiple aspects that represent the user into one, so that it fits into the Neighbor-Aware decoder: &lt;math&gt;\mathbf{z}_u^{(1)} = a_t(\mathbf{Z}_u^{(1)\top}\mathbf{w}_t + \mathbf{b}_t)&lt;/math&gt;.<br /> <br /> === Neighbor-Aware Decoder ===<br /> <br /> POI recommendation uses the geographical clustering phenomenon, which increases the weight of the unvisited POIs that surrounds the visited POIs. Also, an aggregation layer is added to the network to aggregate users’ representations from different aspects into one aspect. This means that a person who has visited a location are very likely to return to this location again in the future, so the user is recommended POIs surrounding this area. An example would be someone who has been to the UW plaza and bought Lazeez are very likely to return to the plaza, therefore the person is recommended to try Mr. Panino's Beijing House.<br /> <br /> [[File:decoder.JPG|center]]<br /> <br /> === Objective Function ===<br /> <br /> By minimizing the objective function, the partial derivatives with respect to all the parameters can be computed by gradient descent with backpropagation. After that, the training is complete.<br /> <br /> [[File:objective_function.JPG|center]]<br /> <br /> <br /> == Comparative analysis ==<br /> <br /> === Metrics introduction ===<br /> To obtain a comprehensive evaluation of the effectiveness of the model, the authors performed a thorough comparison between the proposed model and the existing major POI recommendation methods. These methods can be further broken down into three categories: traditional matrix factorization methods for implicit feedback, classical POI recommendation methods, and deep learning-based methods. Here, three key evaluation metrics were introduced as Precison@k, Recall@k, and MAP@k. Through comparing all models on three datasets using the above metrics, it is concluded that the proposed model achieved the best performance.<br /> <br /> To better understand the comparison results, it is critical for one to understand the meanings behind each evaluation metrics. Suppose the proposed model generated k recommended POIs for the user. The first metric, Precison@k, measures the percentage of the recommended POIs which the user has visited. Recall@k is also associated with the user’s behavior. However, it will measure the percentage of recommended POIs in all POIs which have been visited by the user. Lastly, MAP@k represents the mean average precision at k, where average precision is the average of precision values at all k ranks, where relevant POIs are found.<br /> <br /> === Model Comparison ===<br /> Among all models in the comparison group, RankGeoFM, IRNMF, and PACE produced the best results. Nonetheless, these models are still incomparable to our proposed model. The reasons are explained in details as follows:<br /> <br /> Both RankGeoFM and IRNMF incorporate geographical influence into their ranking models, which is significant for generating POI recommendations. However, they are not capable of capturing non-linear interactions between users and POIs. In comparison, the proposed model, while incorporating geographical influence, adopts a deep neural structure which enables it to measure non-linear and complex interactions. As a result, it outperforms the two methods in the comparison group.<br /> <br /> Moreover, compared to PACE, which is a deep learning-based method, the proposed model offers a more precise measurement of geographical influence. Though PACE is able to capture complex interactions, it models the geographical influence by a context graph, which fails to incorporate user reachability into the modeling process. In contrast, the proposed model is able to capture geographical influence directly through its neighbor-aware decoder, which allows it to achieve better performance than the PACE model.<br /> <br /> [[File:model_comparison.JPG|center]]<br /> <br /> == Conclusion ==<br /> In summary, the proposed model, namely SAE-NAD, clearly showed its advantages compared to many state-of-the-art baseline methods. Its self-attentive encoder effectively discriminates user preferences on check-in POIs, and its neighbor-aware decoder measures geographical influence precisely through differentiating user reachability on unvisited POIs. By leveraging these two components together, it can generate recommendations that are highly relevant to its users.<br /> <br /> == Critiques ==<br /> Besides developing the model and conducting a detailed analysis, the authors also did very well in constructing this paper. The paper is well-written and has a highly logical structure. Definitions, notations, and metrics are introduced and explained clearly, which enables readers to follow through the analysis easily. Last but not least, both the abstract and the conclusion of this paper are strong. The abstract concisely reported the objectives and outcomes of the experiment, whereas the conclusion is succinct and precise.<br /> <br /> This idea would have many applications, such as suggesting new restaurants to customers in the food delivery service app. Would the improvement in accuracy outweigh the increased complexity of the model when it comes to use in industry?<br /> <br /> It would be nice if the author could if the authors can describe the extensive experiments on the real-world datasets, with different baseline methods and evaluation metrics, to demonstrate the effectiveness of the proposed model. Moreover, show the comparison result in tables vs other methodologies, both in terms of accuracy and time-efficiency. In addition, the drawbacks of this new methodology are unknown to the readers. In other words, how does this compare to the already established recommendation systems found in large scale applications utilize by companies like Netflix? Why use the proposed method over something simpler such as matrix factorization or collaborative filtering? <br /> <br /> It would also be nice if the authors provided some more ablation on the various components of the proposed method. Even after reading some of their experiments, we do not have a clear understanding of how important each component is to the recommendation quality.<br /> <br /> It is recommended that the author can present how the encoder and the decoder help in the process by comparing different models with or without encoder and decoder.<br /> <br /> It would have been better if the author included all figures to explain the sensitivity of parameters more elaborately. In the paper he only included plots showing effects on Gowalla and Foursquare datasets but not other datasets.<br /> <br /> Some additional explanations can be inserted in the Objective Function part. From the paper, we can find \lambda is the regularization parameter and Wa and wt are the learned parameters in the attention layer and aggregation layer.<br /> <br /> == References ==<br />  Defu Lian, Cong Zhao, Xing Xie, Guangzhong Sun, Enhong Chen, and Yong Rui. 2014. GeoMF: joint geographical modeling and matrix factorization for point-of-interest recommendation. In KDD. ACM, 831–840.<br /> <br />  Eunjoon Cho, Seth A. Myers, and Jure Leskovec. 2011. Friendship and mobility: user movement in location-based social networks. In KDD. ACM, 1082–1090.<br /> <br />  Yiding Liu, Tuan-Anh Pham, Gao Cong, and Quan Yuan. 2017. An Experimental Evaluation of Point-of-interest Recommendation in Location-based Social Networks. PVLDB 10, 10 (2017), 1010–1021.<br /> <br />  Jie Bao, Yu Zheng, David Wilkie, and Mohamed F. Mokbel. 2015. Recommendations in location-based social networks: a survey. GeoInformatica 19, 3 (2015), 525–565.<br /> <br />  Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. 2017. Neural Collaborative Filtering. In WWW. ACM, 173–182.<br /> <br />  Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br /> <br />  Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667.  Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br /> <br />  Yong Liu,WeiWei, Aixin Sun, and Chunyan Miao. 2014. Exploiting Geographical<br /> Neighborhood Characteristics for Location Recommendation. In CIKM. ACM,<br /> 739–748<br /> <br />  Xutao Li, Gao Cong, Xiaoli Li, Tuan-Anh Nguyen Pham, and Shonali Krishnaswamy.<br /> 2015. Rank-GeoFM: A Ranking based Geographical Factorization<br /> Method for Point of Interest Recommendation. In SIGIR. ACM, 433–442.<br /> <br />  Carl Yang, Lanxiao Bai, Chao Zhang, Quan Yuan, and Jiawei Han. 2017. Bridging<br /> Collaborative Filtering and Semi-Supervised Learning: A Neural Approach for<br /> POI Recommendation. In KDD. ACM, 1245–1254.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=48112 Superhuman AI for Multiplayer Poker 2020-11-30T01:52:28Z <p>Z47shen: /* Discussion and Critiques */</p> <hr /> <div>== Presented by == <br /> Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty<br /> <br /> == Introduction ==<br /> <br /> A superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that was built can only beat human players in two-player zero-sum games. They almost dominated most of the board games in these twenty years. The most popular AI in the board games are the chess AI deep blue and the go chess AI Alpha-go. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any ''other'' choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy. An example of this is the Prisoner's dilemma, where two individuals each have the option to testify against the other or to remain silent. Although the optimal choice is to remain silent, the individuals have an incentive to act in their own self-interest which results in a less than optimal outcome.<br /> <br /> More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. Poker is a great challenge in AI and game theory because it captures the challenges in hidden information so elegantly. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games, and having one would have surprising implications in computational complexity theory.<br /> <br /> In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.<br /> <br /> == Nash Equilibrium in Multiplayer Games ==<br /> <br /> Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games. However, the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is doing.<br /> <br /> To have a deeper understanding of Nash Equilibria we must first define some basic game theory concepts. The first one being a strategic game, in game theory a strategic game consists of a set of players, for each player a set of actions and for each player preferences (or payoffs) over the set of action profiles (set of combination of actions). With these three elements, we can model a wide variety of situations. Now a Nash Equilibrium is an action profile, with the property that no player can do better by changing their action, given that all other players' actions remain the same. A common illustration of Nash equilibria is the Prisoner's Dilemma. We also have mixed strategies and mixed strategy Nash equilibria. A mixed strategy is when instead of a player choosing an action they apply a probability distribution to their set of actions and pick randomly. Note that with mixed strategies we must look at the expected payoff of the player given the other players' strategies. Therefore a mixed strategy Nash Equilibria involves at least one player playing with a mixed strategy where no player can increase their expected payoff by changing their action, given that all other players' actions remain the same. Then we can define a pure Nash Equilibria to where no one is playing a mixed strategy. We also must be aware that a single game can have multiple pure Nash equilibria and mixed Nash equilibria. Also, Nash Equilibria are purely theoretical and depend on players acting optimally and being rational, this is not always the case with humans and we can act very irrationally. Therefore empirically we will see that games can have very unexpected outcomes and you may be able to get a better payoff if you move away from a strictly theoretical strategy and take advantage of your opponent's irrational behavior. <br /> <br /> The insufficiency with current AI systems is that they only try to achieve Nash equilibriums instead of trying to actively detect and exploit weaknesses in opponents. At the Nash equilibrium, there is no incentive for any player to change their initial strategy, so it is a stable state of the system. For example, let's consider the game of Rock-Paper-Scissors, the Nash equilibrium is to randomly pick any option with equal probability. However, we can see that this means the best strategy that the opponent can have will result in a tie. Therefore, in this example, our player cannot win in expectation. Now let's try to combine the Nash equilibrium strategy and opponent exploitation. We can initially use the Nash equilibrium strategy and then change our strategy overtime to exploit the observed weaknesses of our opponent. For example, we switch to always play Rock against our opponent who always plays Scissors. However, shifting away from the Nash equilibrium strategy opens up the possibility for our opponent to use our strategy against ourselves. For example, they notice we always play Rock and thus they will now always play Paper.<br /> <br /> Trying to approximate a Nash equilibrium is hard in theory, and in games with more than two players, it can only find a handful of possible strategies per player. Currently, existing techniques to find ways to exploit an opponent require way too many samples and are not competitive enough outside of small games. Finding a Nash equilibrium in three or more players is a great challenge. Even we can efficiently compute a Nash equilibrium in games with more than two players, it is still highly questionable if playing the Nash equilibrium strategy is a good choice. Additionally, if each player tries to find their own version of a Nash equilibrium, we could have infinitely many strategies and each player’s version of the equilibrium might not even be a Nash equilibrium.<br /> <br /> Consider the Lemonade Stand example from Figure 1 Below. We have 4 players and the goal for each player is to find a spot in the ring that is furthest away from every other player. This way, each lemonade stand can cover as much selling region as possible and generate maximum revenue. In the left circle, we have three different Nash equilibria distinguished by different colors which would benefit everyone. The right circle is an illustration of what would happen if each player decides to calculate their own Nash equilibrium.<br /> <br /> [[File:Lemonade_Example.png| 600px |center ]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Lemonade Stand Example&lt;/div&gt;<br /> <br /> From the right circle in Figure 1, we can see that when each player tries to calculate their own Nash equilibria, their own version of the equilibrium might not be a Nash equilibrium and thus they are not choosing the best possible location. This shows that attempting to find a Nash equilibrium is not the best strategy outside of two-player zero-sum games, and our goal should not be focused on finding a specific game-theoretic solution. Instead, we need to focus on observations and empirical results that consistently defeat human opponents.<br /> <br /> == Theoretical Analysis ==<br /> Pluribus uses forms of abstraction to make computations scalable. To simplify the complexity due to too many decision points, some actions are eliminated from consideration and similar decision points are grouped together and treated as identical. This process is called abstraction. Pluribus uses two kinds of abstraction: Action abstraction and information abstraction. Action abstraction reduces the number of different actions the AI needs to consider. For instance, it does not consider all bet sizes (the exact number of bets it considers varies between 1 and 14 depending on the situation). Information abstraction groups together decision points that reveal similar information. For instance, the player’s cards and revealed board cards. This is only used to reason about situations on future betting rounds, never the current betting round.<br /> <br /> Pluribus uses a built-in strategy - “Blueprint strategy”, which it gradually improves by searching in real-time in situations it finds itself in during the course of the game. In the first betting round, pluribus uses the initial blueprint strategy when the number of decision points is small. The blueprint strategy is computed using Monte Carlo Counterfactual Regret Minimization (MCCFR) algorithm. CFR is commonly used in imperfect information games AI which is trained by repeatedly playing against copies of itself, without any data of human or prior AI play used as input. For ease of computation of CFR in this context, poker is represented as a game tree. A game tree is a tree structure where each node represents either a player’s decision, a chance event, or a terminal outcome and edges represent actions taken. <br /> <br /> [[File:Screen_Shot_2020-11-17_at_11.57.00_PM.png| 600px |center ]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Kuhn Poker (Simpler form of Poker) &lt;/div&gt;<br /> <br /> At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by a player at a given time) and designates one player as the traverser of the game tree. Once that is completed, the AI reviews the decision made by the traverser at a decision point in the game and investigates whether the decision was profitable. The AI compares its decision with other actions available to the traverser at that point and also with the future hypothetical decisions that would have been made following the other available actions. To evaluate a decision, the Counterfactual Regret factor is used. This is the difference between what the traverser would have expected to receive for choosing an action and actually received on the iteration. Thus regret is a numeric value, where a positive regret indicates you regret your decision, a negative regret indicates you are happy with your decision and zero regret indicates that you are indifferent.<br /> <br /> The value of counterfactual regret for a decision is adjusted over the iterations as more scenarios or decision points are encountered. This means at the end of each iteration, the traverser’s strategy is updated so actions with higher counterfactual regret are chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converge and the average strategy is the approximated Nash equilibrium. CFR guarantees in all finite games that all counterfactual regrets grow sublinearly in the number of iterations. Pluribus uses Linear CFR in early iterations to reduce the influence of initial bad iterations i.e it assigns a weight of T to regret contributions at iteration T. This causes the influence of the first iteration to decay at a rate of &lt;math&gt;\frac{1}{\sum_{t=1}^Tt} = \frac{2}{T(T+1)}&lt;/math&gt;, compared to a rate of &lt;math&gt;\frac{1}{T}&lt;/math&gt; in the original CFR algorithm. This leads to the strategy of improving more quickly in practice.<br /> <br /> An additional feature of Pluribus is that in the subgames, instead of assuming that all players play according to a single strategy, Pluribus considers that each player may choose between k different strategies specialized to each player when a decision point is reached. This results in the searcher choosing a more balanced strategy. For instance, if a player never bluffs while holding the best possible hand then the opponents would learn that fact and always fold in that scenario. To fold in that scenario is a balanced strategy than to bet.<br /> Therefore, the blueprint strategy is produced offline for the entire game and it is gradually improved while making real-time decisions during the game.<br /> <br /> == Experimental Results ==<br /> To test how well Pluribus functions, it was tested against human players in 2 formats. The first format included 5 human players and one copy of Pluribus (5H+1AI). The 13 human participants were poker players who have won more than 1M playing professionally and were provided with cash incentives to play their best. 10,000 hands of poker were played over 12 days with the 5H+1AI format. Players were anonymized with aliases that remained consistent throughout all their games. The aliases helped the players keep track of the tendencies and types of games played by each player over the 10,000 hands. <br /> <br /> The second format includes one human player and 5 copies of Pluribus (1H+5AI). There were 2 more professional players who split another 10,000 hands of poker by playing 5000 hands each and followed the same aliasing process as the first format.<br /> The performance was measured using milli big blinds per game, mbb/game, (i.e. the initial amount of money the second player has to put in the pot) which is the standard measure in the AI field. Additionally, AIVAT was used as the variance reduction technique to control for luck in the games. Significance tests were run at a 95% significance level with one-tailed t-tests to check the profitability of Pluribus's performance.<br /> <br /> Applying AIVAT the following were the results:<br /> {| class=&quot;wikitable&quot; style=&quot;margin-left: auto; margin-right: auto; border: none;&quot;<br /> ! scope=&quot;col&quot; | Format !! scope=&quot;col&quot; | Average mbb/game !! scope=&quot;col&quot; | Standard Error in mbb/game !! scope=&quot;col&quot; | P-value of being profitable <br /> |-<br /> ! scope=&quot;row&quot; | 5H+1AI <br /> | 48 || 25 || 0.028 <br /> |-<br /> ! scope=&quot;row&quot; | 1H+5AI <br /> | 32 || 15 || 0.014<br /> |}<br /> [[File:top.PNG| 950px | x450px |left]]<br /> <br /> <br /> &lt;div align=&quot;center&quot;&gt;&quot;Figure 3. Performance of Pluribus in the 5 humans + 1 AI experiment. The dots show Pluribus's performance at the end of each day of play. (Top) The lines show the win rate (solid line) plus or minus the standard error (dashed lines). (Bottom) The lines show the cumulative number of mbbs won (solid line) plus or minus the standard error (dashed lines). The relatively steady performance of Pluribus over the course of the 10,000-hand experiment also suggests that the humans were unable to find exploitable weaknesses in the bot.&quot;&lt;/div&gt; <br /> <br /> Optimal play in Pluribus looks different from well-known poker conventions: A standard convention of “limping” in poker (calling the 'big blind' rather than folding or raising) is confirmed to be not optimal by Pluribus since it initially experimented with it but eliminated this from its strategy over its games of self-play. On the other hand, another convention of “donk betting” (starting a round by betting when someone else ended the previous round with a call) that is dismissed by players was adopted by Pluribus much more often than played by humans and is proven to be profitable.<br /> <br /> == Discussion and Critiques ==<br /> <br /> Pluribus' Blueprint strategy and Abstraction methods effectively reduce the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about144 to produce. This is in sharp contrast to all the other recent superhuman AI milestones for games. This is a great way the researchers have condensed down the problem to fit the current computational powers. <br /> <br /> Pluribus definitely shows that we can capture observational data and empirical results to construct a superhuman AI without requiring theoretical guarantees, this can be a baseline for future AI inventions and help in the research of AI. It would be interesting to use Pluribus's way of using a non-theoretical approach in more real-life problems such as autonomous driving or stock market trading.<br /> <br /> Extending this idea beyond two-player zero-sum games will have many applications in real life. For example, the emergence of strategies used by the superhuman AI that were seen as &quot;non-optimal&quot; to humans, poses interesting questions about applying such an AI to fields such as business, economics and financial markets.<br /> <br /> The summary for Superhuman AI for Multiplayer Poker is very well written, with a detailed explanation of the concept, steps, and result and with a combination of visual images. However, it seems that the experiment of the study is not well designed. For example, sample selection is not strict and well defined, this could cause selection bias introduced into the result and thus making it not generalizable.<br /> <br /> Superhuman AI, while sounding superior, is actually not uncommon. There have been many endeavours on mastering poker such as the Recursive Belief-based Learning (ReBeL) by Facebook Research. They pursued a method of reinforcement learning on a partially observable Markov decision process which was inspired by the recent successes of AlphaZero. For Pluribus to demonstrate how effective it is compared to the state-of-the-art, it should run some experiments against ReBeL.<br /> <br /> This is a very interesting topic, and this summary is clear enough for readers to understand. I think this application not only can apply in poker, maybe thinking of more applications in other areas? There are many famous AI that really changing our life. For example, AlphaGo and AlphaStar, which are developed by Google DeepMind, defeated professional gamers. Discussing more this will be interesting.<br /> <br /> One of the biggest issues when applying AI to games against humans (when not all information is known, ie, opponents' cards) is the assumption is generally made that the human players are rational players which follow a certain set of &quot;rules&quot; based on the information that they know. This could be an issue with the fact that Pluribus has trained itself by playing itself instead of humans. While the results clearly show that Pluribus has found some kind of 'optimal' method to play, it would be interesting to see if it could actually maximize its profits by learning the trends of its human opponents over time (learning on the fly with information gained each hand while it's playing). In addition to that, the paper may discuss how human action could be changed in the game when they play with Superhuman AI. We can see that playing card games require various strategy and different people can have a different set of actions in the same game and in the same situation.<br /> <br /> One interesting software called Piosolver leverages a similar tree-based algorithm presented in the paper to recommend the move that is deemed game theory optimal (GTO). In the poker world, GTO is a play-style that is based on mathematics and is considered a &quot;defensive&quot; strategy. Following the rock, paper, scissors analogy from the paper, a GTO play-style is synonymous with choosing randomly between the three options, whereas an exploitative strategy involves reading a human player's tendencies and adjusting the strategy accordingly. Piosolver is used by many professional poker players to enhance their game and gain intuition on what the best move is in certain situations.<br /> <br /> Another way to train the proposed model can be a poker game with two or more AI players. That method was used by AlphaGo to train a better model. <br /> <br /> Games with various AI players would be an interesting topic, and through comparing different AI, their shortcomes could be observed and improved. More discussions on this would be of interests.<br /> <br /> Similar to Pluribis, another [https://science.sciencemag.org/content/356/6337/508 paper] discussed a different AI program, called DeepStack, which also has defeated professional poker players at a 2-player Texas hold'em variant. However, instead of finding the Nash Equilibria, DeepStack uses recursive reasoning, decomposition, and a form of intuition that is automatically learned from self-play.<br /> <br /> AI can calculate the exact odds of a specific card or set of cards dropped on the flop. The difficulty is that in poker, the player cannot see the opponent's hand. This kind of hidden information also brings other complications (such as fraud), which is more challenging for AI at the game. At the same time, using AI to train each other is also an interesting topic.<br /> <br /> == Conclusion ==<br /> <br /> As Pluribus’s strategy was not developed with any human data and was trained only by self-play, it is an unbiased and a different perspective on how optimal play can be attained.<br /> Developing a superhuman AI for multiplayer poker is a widely recognized<br /> a milestone in this area and the major remaining milestone in computer poker.<br /> Pluribus’s success shows that despite the lack of known strong theoretical guarantees on performance in multiplayer games, there are large-scale, complex multiplayer imperfect information settings in which a carefully constructed self-play-with-search algorithm can produce superhuman strategies.<br /> <br /> == References ==<br /> <br /> Noam Brown and Tuomas Sandholm (July 11, 2019). Superhuman AI for multiplayer poker. Science 365.<br /> <br /> Osborne, Martin J.; Rubinstein, Ariel (July 12, 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br /> <br /> Justin Sermeno. (November 17, 2020). Vanilla Counterfactual Regret Minimization for Engineers. https://justinsermeno.com/posts/cfr/#:~:text=Counterfactual%20regret%20minimization%20%28CFR%29%20is%20an%20algorithm%20that,decision.%20It%20can%20be%20positive%2C%20negative%2C%20or%20zero<br /> <br /> Brown, N., Bakhtin, A., Lerer, A., &amp; Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=48111 Superhuman AI for Multiplayer Poker 2020-11-30T01:52:16Z <p>Z47shen: /* Discussion and Critiques */</p> <hr /> <div>== Presented by == <br /> Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty<br /> <br /> == Introduction ==<br /> <br /> A superintelligence is a hypothetical agent that possesses intelligence far surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that was built can only beat human players in two-player zero-sum games. They almost dominated most of the board games in these twenty years. The most popular AI in the board games are the chess AI deep blue and the go chess AI Alpha-go. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any ''other'' choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy. An example of this is the Prisoner's dilemma, where two individuals each have the option to testify against the other or to remain silent. Although the optimal choice is to remain silent, the individuals have an incentive to act in their own self-interest which results in a less than optimal outcome.<br /> <br /> More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. Poker is a great challenge in AI and game theory because it captures the challenges in hidden information so elegantly. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games, and having one would have surprising implications in computational complexity theory.<br /> <br /> In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.<br /> <br /> == Nash Equilibrium in Multiplayer Games ==<br /> <br /> Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games. However, the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is doing.<br /> <br /> To have a deeper understanding of Nash Equilibria we must first define some basic game theory concepts. The first one being a strategic game, in game theory a strategic game consists of a set of players, for each player a set of actions and for each player preferences (or payoffs) over the set of action profiles (set of combination of actions). With these three elements, we can model a wide variety of situations. Now a Nash Equilibrium is an action profile, with the property that no player can do better by changing their action, given that all other players' actions remain the same. A common illustration of Nash equilibria is the Prisoner's Dilemma. We also have mixed strategies and mixed strategy Nash equilibria. A mixed strategy is when instead of a player choosing an action they apply a probability distribution to their set of actions and pick randomly. Note that with mixed strategies we must look at the expected payoff of the player given the other players' strategies. Therefore a mixed strategy Nash Equilibria involves at least one player playing with a mixed strategy where no player can increase their expected payoff by changing their action, given that all other players' actions remain the same. Then we can define a pure Nash Equilibria to where no one is playing a mixed strategy. We also must be aware that a single game can have multiple pure Nash equilibria and mixed Nash equilibria. Also, Nash Equilibria are purely theoretical and depend on players acting optimally and being rational, this is not always the case with humans and we can act very irrationally. Therefore empirically we will see that games can have very unexpected outcomes and you may be able to get a better payoff if you move away from a strictly theoretical strategy and take advantage of your opponent's irrational behavior. <br /> <br /> The insufficiency with current AI systems is that they only try to achieve Nash equilibriums instead of trying to actively detect and exploit weaknesses in opponents. At the Nash equilibrium, there is no incentive for any player to change their initial strategy, so it is a stable state of the system. For example, let's consider the game of Rock-Paper-Scissors, the Nash equilibrium is to randomly pick any option with equal probability. However, we can see that this means the best strategy that the opponent can have will result in a tie. Therefore, in this example, our player cannot win in expectation. Now let's try to combine the Nash equilibrium strategy and opponent exploitation. We can initially use the Nash equilibrium strategy and then change our strategy overtime to exploit the observed weaknesses of our opponent. For example, we switch to always play Rock against our opponent who always plays Scissors. However, shifting away from the Nash equilibrium strategy opens up the possibility for our opponent to use our strategy against ourselves. For example, they notice we always play Rock and thus they will now always play Paper.<br /> <br /> Trying to approximate a Nash equilibrium is hard in theory, and in games with more than two players, it can only find a handful of possible strategies per player. Currently, existing techniques to find ways to exploit an opponent require way too many samples and are not competitive enough outside of small games. Finding a Nash equilibrium in three or more players is a great challenge. Even we can efficiently compute a Nash equilibrium in games with more than two players, it is still highly questionable if playing the Nash equilibrium strategy is a good choice. Additionally, if each player tries to find their own version of a Nash equilibrium, we could have infinitely many strategies and each player’s version of the equilibrium might not even be a Nash equilibrium.<br /> <br /> Consider the Lemonade Stand example from Figure 1 Below. We have 4 players and the goal for each player is to find a spot in the ring that is furthest away from every other player. This way, each lemonade stand can cover as much selling region as possible and generate maximum revenue. In the left circle, we have three different Nash equilibria distinguished by different colors which would benefit everyone. The right circle is an illustration of what would happen if each player decides to calculate their own Nash equilibrium.<br /> <br /> [[File:Lemonade_Example.png| 600px |center ]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Lemonade Stand Example&lt;/div&gt;<br /> <br /> From the right circle in Figure 1, we can see that when each player tries to calculate their own Nash equilibria, their own version of the equilibrium might not be a Nash equilibrium and thus they are not choosing the best possible location. This shows that attempting to find a Nash equilibrium is not the best strategy outside of two-player zero-sum games, and our goal should not be focused on finding a specific game-theoretic solution. Instead, we need to focus on observations and empirical results that consistently defeat human opponents.<br /> <br /> == Theoretical Analysis ==<br /> Pluribus uses forms of abstraction to make computations scalable. To simplify the complexity due to too many decision points, some actions are eliminated from consideration and similar decision points are grouped together and treated as identical. This process is called abstraction. Pluribus uses two kinds of abstraction: Action abstraction and information abstraction. Action abstraction reduces the number of different actions the AI needs to consider. For instance, it does not consider all bet sizes (the exact number of bets it considers varies between 1 and 14 depending on the situation). Information abstraction groups together decision points that reveal similar information. For instance, the player’s cards and revealed board cards. This is only used to reason about situations on future betting rounds, never the current betting round.<br /> <br /> Pluribus uses a built-in strategy - “Blueprint strategy”, which it gradually improves by searching in real-time in situations it finds itself in during the course of the game. In the first betting round, pluribus uses the initial blueprint strategy when the number of decision points is small. The blueprint strategy is computed using Monte Carlo Counterfactual Regret Minimization (MCCFR) algorithm. CFR is commonly used in imperfect information games AI which is trained by repeatedly playing against copies of itself, without any data of human or prior AI play used as input. For ease of computation of CFR in this context, poker is represented as a game tree. A game tree is a tree structure where each node represents either a player’s decision, a chance event, or a terminal outcome and edges represent actions taken. <br /> <br /> [[File:Screen_Shot_2020-11-17_at_11.57.00_PM.png| 600px |center ]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Kuhn Poker (Simpler form of Poker) &lt;/div&gt;<br /> <br /> At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by a player at a given time) and designates one player as the traverser of the game tree. Once that is completed, the AI reviews the decision made by the traverser at a decision point in the game and investigates whether the decision was profitable. The AI compares its decision with other actions available to the traverser at that point and also with the future hypothetical decisions that would have been made following the other available actions. To evaluate a decision, the Counterfactual Regret factor is used. This is the difference between what the traverser would have expected to receive for choosing an action and actually received on the iteration. Thus regret is a numeric value, where a positive regret indicates you regret your decision, a negative regret indicates you are happy with your decision and zero regret indicates that you are indifferent.<br /> <br /> The value of counterfactual regret for a decision is adjusted over the iterations as more scenarios or decision points are encountered. This means at the end of each iteration, the traverser’s strategy is updated so actions with higher counterfactual regret are chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converge and the average strategy is the approximated Nash equilibrium. CFR guarantees in all finite games that all counterfactual regrets grow sublinearly in the number of iterations. Pluribus uses Linear CFR in early iterations to reduce the influence of initial bad iterations i.e it assigns a weight of T to regret contributions at iteration T. This causes the influence of the first iteration to decay at a rate of &lt;math&gt;\frac{1}{\sum_{t=1}^Tt} = \frac{2}{T(T+1)}&lt;/math&gt;, compared to a rate of &lt;math&gt;\frac{1}{T}&lt;/math&gt; in the original CFR algorithm. This leads to the strategy of improving more quickly in practice.<br /> <br /> An additional feature of Pluribus is that in the subgames, instead of assuming that all players play according to a single strategy, Pluribus considers that each player may choose between k different strategies specialized to each player when a decision point is reached. This results in the searcher choosing a more balanced strategy. For instance, if a player never bluffs while holding the best possible hand then the opponents would learn that fact and always fold in that scenario. To fold in that scenario is a balanced strategy than to bet.<br /> Therefore, the blueprint strategy is produced offline for the entire game and it is gradually improved while making real-time decisions during the game.<br /> <br /> == Experimental Results ==<br /> To test how well Pluribus functions, it was tested against human players in 2 formats. The first format included 5 human players and one copy of Pluribus (5H+1AI). The 13 human participants were poker players who have won more than 1M playing professionally and were provided with cash incentives to play their best. 10,000 hands of poker were played over 12 days with the 5H+1AI format. Players were anonymized with aliases that remained consistent throughout all their games. The aliases helped the players keep track of the tendencies and types of games played by each player over the 10,000 hands. <br /> <br /> The second format includes one human player and 5 copies of Pluribus (1H+5AI). There were 2 more professional players who split another 10,000 hands of poker by playing 5000 hands each and followed the same aliasing process as the first format.<br /> The performance was measured using milli big blinds per game, mbb/game, (i.e. the initial amount of money the second player has to put in the pot) which is the standard measure in the AI field. Additionally, AIVAT was used as the variance reduction technique to control for luck in the games. Significance tests were run at a 95% significance level with one-tailed t-tests to check the profitability of Pluribus's performance.<br /> <br /> Applying AIVAT the following were the results:<br /> {| class=&quot;wikitable&quot; style=&quot;margin-left: auto; margin-right: auto; border: none;&quot;<br /> ! scope=&quot;col&quot; | Format !! scope=&quot;col&quot; | Average mbb/game !! scope=&quot;col&quot; | Standard Error in mbb/game !! scope=&quot;col&quot; | P-value of being profitable <br /> |-<br /> ! scope=&quot;row&quot; | 5H+1AI <br /> | 48 || 25 || 0.028 <br /> |-<br /> ! scope=&quot;row&quot; | 1H+5AI <br /> | 32 || 15 || 0.014<br /> |}<br /> [[File:top.PNG| 950px | x450px |left]]<br /> <br /> <br /> &lt;div align=&quot;center&quot;&gt;&quot;Figure 3. Performance of Pluribus in the 5 humans + 1 AI experiment. The dots show Pluribus's performance at the end of each day of play. (Top) The lines show the win rate (solid line) plus or minus the standard error (dashed lines). (Bottom) The lines show the cumulative number of mbbs won (solid line) plus or minus the standard error (dashed lines). The relatively steady performance of Pluribus over the course of the 10,000-hand experiment also suggests that the humans were unable to find exploitable weaknesses in the bot.&quot;&lt;/div&gt; <br /> <br /> Optimal play in Pluribus looks different from well-known poker conventions: A standard convention of “limping” in poker (calling the 'big blind' rather than folding or raising) is confirmed to be not optimal by Pluribus since it initially experimented with it but eliminated this from its strategy over its games of self-play. On the other hand, another convention of “donk betting” (starting a round by betting when someone else ended the previous round with a call) that is dismissed by players was adopted by Pluribus much more often than played by humans and is proven to be profitable.<br /> <br /> == Discussion and Critiques ==<br /> <br /> Pluribus' Blueprint strategy and Abstraction methods effectively reduce the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about144 to produce. This is in sharp contrast to all the other recent superhuman AI milestones for games. This is a great way the researchers have condensed down the problem to fit the current computational powers. <br /> <br /> Pluribus definitely shows that we can capture observational data and empirical results to construct a superhuman AI without requiring theoretical guarantees, this can be a baseline for future AI inventions and help in the research of AI. It would be interesting to use Pluribus's way of using a non-theoretical approach in more real-life problems such as autonomous driving or stock market trading.<br /> <br /> Extending this idea beyond two-player zero-sum games will have many applications in real life. For example, the emergence of strategies used by the superhuman AI that were seen as &quot;non-optimal&quot; to humans, poses interesting questions about applying such an AI to fields such as business, economics and financial markets.<br /> <br /> The summary for Superhuman AI for Multiplayer Poker is very well written, with a detailed explanation of the concept, steps, and result and with a combination of visual images. However, it seems that the experiment of the study is not well designed. For example, sample selection is not strict and well defined, this could cause selection bias introduced into the result and thus making it not generalizable.<br /> <br /> Superhuman AI, while sounding superior, is actually not uncommon. There have been many endeavours on mastering poker such as the Recursive Belief-based Learning (ReBeL) by Facebook Research. They pursued a method of reinforcement learning on a partially observable Markov decision process which was inspired by the recent successes of AlphaZero. For Pluribus to demonstrate how effective it is compared to the state-of-the-art, it should run some experiments against ReBeL.<br /> <br /> This is a very interesting topic, and this summary is clear enough for readers to understand. I think this application not only can apply in poker, maybe thinking of more applications in other areas? There are many famous AI that really changing our life. For example, AlphaGo and AlphaStar, which are developed by Google DeepMind, defeated professional gamers. Discussing more this will be interesting.<br /> <br /> One of the biggest issues when applying AI to games against humans (when not all information is known, ie, opponents' cards) is the assumption is generally made that the human players are rational players which follow a certain set of &quot;rules&quot; based on the information that they know. This could be an issue with the fact that Pluribus has trained itself by playing itself instead of humans. While the results clearly show that Pluribus has found some kind of 'optimal' method to play, it would be interesting to see if it could actually maximize its profits by learning the trends of its human opponents over time (learning on the fly with information gained each hand while it's playing). In addition to that, the paper may discuss how human action could be changed in the game when they play with Superhuman AI. We can see that playing card games require various strategy and different people can have a different set of actions in the same game and in the same situation.<br /> <br /> One interesting software called Piosolver leverages a similar tree-based algorithm presented in the paper to recommend the move that is deemed game theory optimal (GTO). In the poker world, GTO is a play-style that is based on mathematics and is considered a &quot;defensive&quot; strategy. Following the rock, paper, scissors analogy from the paper, a GTO play-style is synonymous with choosing randomly between the three options, whereas an exploitative strategy involves reading a human player's tendencies and adjusting the strategy accordingly. Piosolver is used by many professional poker players to enhance their game and gain intuition on what the best move is in certain situations.<br /> <br /> Another way to train the proposed model can be a poker game with two or more AI players. That method was used by AlphaGo to train a better model. <br /> <br /> Games with various AI players would be an interesting topic, and through comparing different AI, their shortcomes could be observed and improved. More discussions on this would be of interests.<br /> <br /> Similar to Pluribis, another [https://science.sciencemag.org/content/356/6337/508 paper] discussed a different AI program, called DeepStack, which also has defeated professional poker players at a 2-player Texas hold'em variant. However, instead of finding the Nash Equilibria, DeepStack uses recursive reasoning, decomposition, and a form of intuition that is automatically learned from self-play.<br /> <br /> AI can calculate the exact odds of a specific card or set of cards dropped on the flop. The difficulty is that in poker, the player cannot see the opponent's hand. This kind of hidden information also brings other complications (such as fraud), which is more challenging for AI at the game. At the same time, using AI to train each other is also an interesting topic<br /> <br /> == Conclusion ==<br /> <br /> As Pluribus’s strategy was not developed with any human data and was trained only by self-play, it is an unbiased and a different perspective on how optimal play can be attained.<br /> Developing a superhuman AI for multiplayer poker is a widely recognized<br /> a milestone in this area and the major remaining milestone in computer poker.<br /> Pluribus’s success shows that despite the lack of known strong theoretical guarantees on performance in multiplayer games, there are large-scale, complex multiplayer imperfect information settings in which a carefully constructed self-play-with-search algorithm can produce superhuman strategies.<br /> <br /> == References ==<br /> <br /> Noam Brown and Tuomas Sandholm (July 11, 2019). Superhuman AI for multiplayer poker. Science 365.<br /> <br /> Osborne, Martin J.; Rubinstein, Ariel (July 12, 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br /> <br /> Justin Sermeno. (November 17, 2020). Vanilla Counterfactual Regret Minimization for Engineers. https://justinsermeno.com/posts/cfr/#:~:text=Counterfactual%20regret%20minimization%20%28CFR%29%20is%20an%20algorithm%20that,decision.%20It%20can%20be%20positive%2C%20negative%2C%20or%20zero<br /> <br /> Brown, N., Bakhtin, A., Lerer, A., &amp; Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Graph_Structure_of_Neural_Networks&diff=48104 Graph Structure of Neural Networks 2020-11-30T01:42:02Z <p>Z47shen: /* Critique */</p> <hr /> <div>= Presented By =<br /> <br /> Xiaolan Xu, Robin Wen, Yue Weng, Beizhen Chang<br /> <br /> = Introduction =<br /> <br /> A deep neural network is composed of neurons organized into layers and the connections between them. The architecture of a neural network can be captured by its &quot;computational graph&quot;, where neurons are represented as nodes, and directed edges link neurons in different layers. This graphical representation demonstrates how the network transmits and transforms information through its input neurons through the hidden layers and ultimately to the output neurons. <br /> <br /> However, few researchers have focused on the relationship between neural networks and their predictive performance, which is the main focus of this paper.<br /> <br /> In Neural Network research, it is often important to build a relation between a neural network’s accuracy and its underlying graph structure, because it would directly affect building more efficient and more accurate architectures. A natural choice is to use a computational graph representation, but this has many limitations including: <br /> <br /> (1) Lack of generality: Computational graphs have to follow allowed graph properties, which limits the use of the rich tools developed for general graphs. <br /> <br /> (2) Disconnection with biology/neuroscience: Biological neural networks have a much complicated and less standardized structure. For example, there might be information exchanges in the brain networks. It is difficult to represent these models with directed acyclic graphs. This disconnection between biology/neuroscience makes knowledge less transferable and interdisciplinary research more difficult.<br /> <br /> Thus, the authors developed a new way of representing a neural network as a graph, called a relational graph. The key insight in the new representation is to focus on message exchange, rather than just on directed data flow. For example, for a fixed-width fully-connected layer, an input channel and output channel pair can be represented as a single node, while an edge in the relational graph can represent the message exchange between the two nodes. Under this formulation, using the appropriate message exchange definition, it can be shown that the relational graph can represent many types of neural network layers.<br /> <br /> WS-flex is a graph generator that allows systematically exploring the design space of neural networks. Neural networks are characterized by the clustering coefficient and average path length of their relational graphs under the insights of neuroscience. Based on the insights from<br /> neuroscience, the authors characterize neural networks by the clustering coefficient and average path length of their relational graphs.<br /> <br /> = Neural Network as Relational Graph =<br /> <br /> The author proposes the concept of relational graphs to study the graphical structure of neural network. Each relational graph is based on an undirected graph &lt;math&gt;G =(V; E)&lt;/math&gt;, where &lt;math&gt;V =\{v_1,...,v_n\}&lt;/math&gt; is the set of all the nodes, and &lt;math&gt;E \subseteq \{(v_i,v_j)|v_i,v_j\in V\}&lt;/math&gt; is the set of all edges that connect nodes. Note that for the graph used here, all nodes have self edges, that is &lt;math&gt;(v_i,v_i)\in E&lt;/math&gt;. Graphically, a self edge connects an edge to itself, which forms a loop.<br /> <br /> To build a relational graph that captures the message exchange between neurons in the network, we associate various mathematical quantities to the graph &lt;math&gt;G&lt;/math&gt;. First, a feature quantity &lt;math&gt;x_v&lt;/math&gt; is associated with each node. The quantity &lt;math&gt;x_v&lt;/math&gt; might be a scalar, vector or tensor depending on what type of neural network it is (see the Table at the end of the section). Then a message function &lt;math&gt;f_{uv}(·)&lt;/math&gt; is associated with every edge in the graph. A message function specifically takes a node’s feature as the input and then outputs a message. An aggregation function &lt;math&gt;{\rm AGG}_v(·)&lt;/math&gt; then takes a set of messages (the outputs of the message function) and outputs the updated node feature. <br /> <br /> A relation graph is a graph &lt;math&gt;G&lt;/math&gt; associated with several message exchange rounds, which transform the feature quantity &lt;math&gt;x_v&lt;/math&gt; with the message function &lt;math&gt;f_{uv}(·)&lt;/math&gt; and the aggregation function &lt;math&gt;{\rm AGG}_v(·)&lt;/math&gt;. At each round of message exchange, each node sends messages to its neighbors and aggregates incoming messages from its neighbors. Each message is transformed at each edge through the message function, then they are aggregated at each node via the aggregation function. Suppose we have already conducted &lt;math&gt;r-1&lt;/math&gt; rounds of message exchange, then the &lt;math&gt;r^{th}&lt;/math&gt; round of message exchange for a node &lt;math&gt;v&lt;/math&gt; can be described as<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;\mathbf{x}_v^{(r+1)}= {\rm AGG}^{(r)}(\{f_v^{(r)}(\textbf{x}_u^{(r)}), \forall u\in N(v)\})&lt;/math&gt;&lt;/div&gt; <br /> <br /> where &lt;math&gt;\mathbf{x}^{(r+1)}&lt;/math&gt; is the feature of the &lt;math&gt;v&lt;/math&gt; node in the relational graph after the &lt;math&gt;r^{th}&lt;/math&gt; round of update. &lt;math&gt;u,v&lt;/math&gt; are nodes in Graph &lt;math&gt;G&lt;/math&gt;. &lt;math&gt;N(u)=\{u|(u,v)\in E\}&lt;/math&gt; is the set of all the neighbor nodes of &lt;math&gt;u&lt;/math&gt; in graph &lt;math&gt;G&lt;/math&gt;.<br /> <br /> To further illustrate the above, we use the basic Multilayer Perceptron (MLP) as an example. An MLP consists of layers of neurons, where each neuron performs a weighted sum over scalar inputs and outputs, followed by some non-linearity. Suppose the &lt;math&gt;r^{th}&lt;/math&gt; layer of an MLP takes &lt;math&gt;x^{(r)}&lt;/math&gt; as input and &lt;math&gt;x^{(r+1)}&lt;/math&gt; as output, then a neuron computes <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;x_i^{(r+1)}= \sigma(\Sigma_jw_{ij}^{(r)}x_j^{(r)})&lt;/math&gt;.&lt;/div&gt; <br /> <br /> where &lt;math&gt;w_{ij}^{(r)}&lt;/math&gt; is the trainable weight and &lt;math&gt;\sigma&lt;/math&gt; is the non-linearity function. Let's first consider the special case where the input and output of all the layers &lt;math&gt;x^{(r)}&lt;/math&gt;, &lt;math&gt;1 \leq r \leq R &lt;/math&gt; have the same feature dimensions &lt;math&gt;d&lt;/math&gt;. In this scenario, we can have &lt;math&gt;d&lt;/math&gt; nodes in the Graph &lt;math&gt;G&lt;/math&gt; with each node representing a neuron in MLP. Each layer of neural network will correspond with a round of message exchange, so there will be &lt;math&gt;R&lt;/math&gt; rounds of message exchange in total. The aggregation function here will be the summation with non-linearity transform &lt;math&gt;\sigma(\Sigma)&lt;/math&gt;, while the message function is simply the scalar multipication with weight. A fully-connected, fixed-width MLP layer can then be expressed with a complete relational graph, where each node &lt;math&gt;x_v&lt;/math&gt; connects to all the other nodes in &lt;math&gt;G&lt;/math&gt;, that is neighborhood set &lt;math&gt;N(v) = V&lt;/math&gt; for each node &lt;math&gt;v&lt;/math&gt;. The figure below shows the correspondence between the complete relation graph with a 5-layer 4-dimension fully-connected MLP.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:fully_connnected_MLP.png]]&lt;/div&gt;<br /> <br /> In fact, a fixed-width fully-connected MLP is only a special case under a much more general model family, where the message function, aggregation function, and most importantly, the relation graph structure can vary. The different relational graph will represent the different topological structure and information exchange pattern of the network, which is the property that the paper wants to examine. The plot below shows two examples of non-fully connected fixed-width MLP and their corresponding relational graphs. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:otherMLP.png]]&lt;/div&gt;<br /> <br /> We can generalize the above definitions for fixed-width MLP to Variable-width MLP, Convolutional Neural Network (CNN), and other modern network architecture like Resnet by allowing the node feature quantity &lt;math&gt;\textbf{x}_j^{(r)}&lt;/math&gt; to be a vector or tensor respectively. In this case, each node in the relational graph will represent multiple neurons in the network, and the number of neurons contained in each node at each round of message exchange does not need to be the same, which gives us a flexible representation of different neural network architecture. The message function will then change from the simple scalar multiplication to either matrix/tensor multiplication or convolution. And the weight matrix will change to the convolutional filter. The representation of these more complicated networks are described in details in the paper, and the correspondence between different networks and their relational graph properties is summarized in the table below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:relational_specification.png]]&lt;/div&gt;<br /> <br /> Overall, relational graphs provide a general representation for neural networks. With proper definitions of node features and message exchange, relational graphs can represent diverse neural architectures, thereby allowing us to study the performance of different graph structures.<br /> <br /> = Exploring and Generating Relational Graphs=<br /> <br /> We will deal with the design and how to explore the space of relational graphs in this section. There are three parts we need to consider:<br /> <br /> (1) '''Graph measures''' that characterize graph structural properties:<br /> <br /> We will use one global graph measure, average path length, and one local graph measure, clustering coefficient in this paper.<br /> To explain clearly, average path length measures the average shortest path distance between any pair of nodes; the clustering coefficient measures the proportion of edges between the nodes within a given node’s neighborhood, divided by the number of edges that could possibly exist between them, averaged over all the nodes.<br /> <br /> (2) '''Graph generators''' that can generate the diverse graph:<br /> <br /> With selected graph measures, we use a graph generator to generate diverse graphs to cover a large span of graph measures. To figure out the limitation of the graph generator and find out the best, we investigate some generators including ER, WS, BA, Harary, Ring, Complete graph and results are shown below:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:3.2 graph generator.png]]&lt;/div&gt;<br /> <br /> Thus, from the picture, we could obtain the WS-flex graph generator that can generate graphs with a wide coverage of graph measures; notably, WS-flex graphs almost encompass all the graphs generated by classic random generators mentioned above.<br /> <br /> (3) '''Computational Budget''' that we need to control so that the differences in performance of different neural networks are due to their diverse relational graph structures.<br /> <br /> It is important to ensure that all networks have approximately the same complexities so that the differences in performance are due to their relational graph structures when comparing neutral work by their diverse graph.<br /> <br /> We use FLOPS (# of multiply-adds) as the metric. We first compute the FLOPS of our baseline network instantiations (i.e., complete relational graph) and use them as the reference complexity in each experiment. From the description in section 2, a relational graph structure can be instantiated as a neural network with variable width. Therefore, we can adjust the width of a neural network to match the reference complexity without changing the relational graph structures.<br /> <br /> = Experimental Setup =<br /> The author studied the performance of 3942 sampled relational graphs (generated by WS-flex from the last section) of 64 nodes with two experiments: <br /> <br /> (1) CIFAR-10 dataset: 10 classes, 50K training images, and 10K validation images<br /> <br /> Relational Graph: all 3942 sampled relational graphs of 64 nodes<br /> <br /> Studied Network: 5-layer MLP with 512 hidden units<br /> <br /> The model was trained for 200 epochs with batch size 128, using cosine learning rate schedule with an initial learning rate of 0.1<br /> <br /> <br /> (2) ImageNet classification: 1K image classes, 1.28M training images and 50K validation images<br /> <br /> Relational Graph: Due to high computational cost, 52 graphs are uniformly sampled from the 3942 available graphs.<br /> <br /> Studied Network: <br /> *ResNet-34, which only consists of basic blocks of 3×3 convolutions (He et al., 2016)<br /> <br /> *ResNet-34-sep, a variant where we replace all 3×3 dense convolutions in ResNet-34 with 3×3 separable convolutions (Chollet, 2017)<br /> <br /> *ResNet-50, which consists of bottleneck blocks (He et al., 2016) of 1×1, 3×3, 1×1 convolutions<br /> <br /> *EfficientNet-B0 architecture (Tan &amp; Le, 2019)<br /> <br /> *8-layer CNN with 3×3 convolution<br /> <br /> = Results and Discussions =<br /> <br /> The paper summarizes the result of the experiment among multiple different relational graphs through sampling and analyzing and list six important observations during the experiments, These are:<br /> <br /> * There always exists a graph structure that has higher predictive accuracy under Top-1 error compared to the complete graph<br /> <br /> * There is a sweet spot such that the graph structure near the sweet spot usually outperforms the base graph<br /> <br /> * The predictive accuracy under top-1 error can be represented by a smooth function of Average Path Length &lt;math&gt; (L) &lt;/math&gt; and Clustering Coefficient &lt;math&gt; (C) &lt;/math&gt;<br /> <br /> * The Experiments are consistent across multiple datasets and multiple graph structures with similar Average Path Length and Clustering Coefficient.<br /> <br /> * The best graph structure can be identified easily.<br /> <br /> * There are similarities between the best artificial neurons and biological neurons.<br /> <br /> <br /> <br /> [[File:Result2_441_2020Group16.png |1000px]]<br /> <br /> $$\text{Figure - Results from Experiments}$$<br /> <br /> <br /> '''Neural networks performance depends on its structure'''<br /> <br /> During the experiment, Top-1 errors for all sampled relational graph among multiple tasks and graph structures are recorded. The parameters of the models are average path length and clustering coefficient. Heat maps were created to illustrate the difference in predictive performance among possible average path length and clustering coefficient. In '''Figure - Results from Experiments (a)(c)(f)''', The darker area represents a smaller top-1 error which indicates the model performs better than the light area.<br /> <br /> Compared to the complete graph which has parameter &lt;math&gt; L = 1 &lt;/math&gt; and &lt;math&gt; C = 1 &lt;/math&gt;, the best performing relational graph can outperform the complete graph baseline by 1.4% top-1 error for MLP on CIFAR-10, and 0.5% to 1.2% for models on ImageNet. Hence it is an indicator that the predictive performance of the neural networks highly depends on the graph structure, or equivalently that the completed graph does not always have the best performance.<br /> <br /> <br /> '''Sweet spot where performance is significantly improved'''<br /> <br /> It had been recognized that training noises often results in inconsistent predictive results. In the paper, the 3942 graphs in the sample had been grouped into 52 bins, each bin had been colored based on the average performance of graphs that fall into the bin. By taking the average, the training noises had been significantly reduced. Based on the heat map '''Figure - Results from Experiments (f)''', the well-performing graphs tend to cluster into a special spot that the paper called “sweet spot” shown in the red rectangle, the rectangle is approximately included clustering coefficient in the range &lt;math&gt;[0.1,0.7]&lt;/math&gt; and average path length within &lt;math&gt;[1.5,3]&lt;/math&gt;.<br /> <br /> <br /> '''Relationship between neural network’s performance and parameters'''<br /> <br /> When we visualize the heat map, we can see that there is no significant jump of performance that occurred as a small change of clustering coefficient and average path length ('''Figure - Results from Experiments (a)(c)(f)'''). In addition, if one of the variables is fixed in a small range, it is observed that a second-degree polynomial is a good visualization tool for the overall trend ('''Figure - Results from Experiments (b)(d)'''). Therefore, both the clustering coefficient and average path length are highly related to neural network performance by a U-shape. <br /> <br /> <br /> '''Consistency among many different tasks and datasets'''<br /> <br /> They observe that relational graphs with certain graph measures may consistently perform well regardless of how they are instantiated. The paper presents consistency uses two perspectives, one is qualitative consistency and another one is quantitative consistency.<br /> <br /> (1) '''Qualitative Consistency'''<br /> It is observed that the results are consistent from different points of view. Among multiple architecture dataset, it is observed that the clustering coefficient within &lt;math&gt;[0.1,0.7]&lt;/math&gt; and average path length within &lt;math&gt;[1.5,3]&lt;/math&gt; consistently outperform the baseline complete graph. <br /> <br /> (2) '''Quantitative Consistency'''<br /> Among different dataset with the network that has similar clustering coefficient and average path length, the results are correlated, The paper mentioned that ResNet-34 is much more complex than 5-layer MLP but a fixed set relational graph would perform similarly in both settings, with Pearson correlation of &lt;math&gt;0.658&lt;/math&gt;, the p-value for the Null hypothesis is less than &lt;math&gt;10^{-8}&lt;/math&gt;.<br /> <br /> <br /> '''Top architectures can be identified efficiently'''<br /> <br /> The computation cost of finding top architectures can be significantly reduced without training the entire data set for a large value of epoch or a relatively large sample. To achieve the top architectures, the number of graphs and training epochs need to be identified. For the number of graphs, a heatmap is a great tool to demonstrate the result. In the 5-layer MLP on CIFAR-10 example, taking a sample of the data around 52 graphs would have a correlation of 0.9, which indicates that fewer samples are needed for a similar analysis in practice. When determining the number of epochs, correlation can help to show the result. In ResNet34 on ImageNet example, the correlation between the variables is already high enough for future computation within 3 epochs. This means that good relational graphs perform well even at the<br /> initial training epochs.<br /> <br /> <br /> '''Well-performing neural networks have graph structure surprisingly similar to those of real biological neural networks'''<br /> <br /> The way we define relational graphs and average length in the graph is similar to the way information is exchanged in network science. The biological neural network also has a similar relational graph representation and graph measure with the best-performing relational graph.<br /> <br /> While there is some organizational similarity between a computational neural network and a biological neural network, we should refrain from saying that both these networks share many similarities or are essentially the same with just different substrates. The biological neurons are still quite poorly understood and it may take a while before their mechanisms are better understood.<br /> <br /> = Conclusions=<br /> Our works provided a new viewpoint about combining the fields of graph neural networks (GNNs) and general architecture design by establishing graph structures. It is to believe that the model helps to capture the diverse neural network architectures under a unified framework. In particular, GNNs are instances of general neural architectures where graph structures are seen as input rather than part of the architecture and message functions are shared across all edges of the graph. We found that the graph theories and techniques implemented in other disciplines have the capability to provide a good reference for understanding and designing the structures and functions of neural networks. This could provide effective help and inspiration for the study of neural networks.<br /> <br /> = Critique =<br /> <br /> 1. The experiment is only measuring on a single data set which might not be representative enough. As we can see in the whole paper, the &quot;sweet spot&quot; we talked about might be a special feature for the given data set only which is the CIFAR-10 data set. If we change the data set to another imaging data set like CK+, whether we are going to get a similar result is not shown by the paper. Hence, the result that is being concluded from the paper might not be representative enough. <br /> <br /> 2. When we are fitting the model in practice, we will fit the model with more than one epoch. The order of the model fitting should be randomized since we should create more random jumps to avoid staying inside a local minimum. With the same order within each epoch, the data might be grouped by different classes or levels, the model might result in a better performance with certain classes and worse performance with other classes. In this particular example, without randomization of the training data, the conclusion might not be precise enough.<br /> <br /> 3. This study shows empirical justification for choosing well-performing models from graphs differing only by average path length and clustering coefficient. An equally important question is whether there is a theoretical justification for why these graph properties may (or may not) contribute to the performance of a general classifier - for example, is there a combination of these properties that is sufficient to recover the universality theorem for MLP's?<br /> <br /> 4. It might be worth looking into how to identify the &quot;sweet spot&quot; for different datasets.<br /> <br /> 5. What would be considered a &quot;best graph structure &quot; in the discussion and conclusion part? It seems that the intermediate result of getting an accurate result was by binning graphs into smaller bins, what should we do if the graphs can not be binned into significantly smaller bins in order to proceed with the methodologies mentioned in the paper. Both CIFAR - 10 and ImageNet seem too trivial considering the amount of variation and categories in the dataset. What would the generalizability be to other presentations of images?<br /> <br /> 6. There is an interesting insight that the idea of the relational graph is similar to applying causal graphs in neuro networks, which is also closer to biology and neuroscience because human beings learning things based on causality. This new approach may lead to higher prediction accuracy but it needs more assumptions, such as correct relations and causalities.<br /> <br /> 7. This is an interesting topic that uses the knowledge in graph theory to introduce this new structure of Neural Networks. Using more data sets to discuss this approach might be more interesting, such as the MNIST dataset. We think it is interesting to discuss whether this structure will provide a better performance compare to the &quot;traditional&quot; structure of NN in any type of Neural Networks.<br /> <br /> 8. The key idea is to treat a neural network as a relational graph and investigate the messages exchange over the graphs. It will be interesting to discuss how much improvement a sweet spot can bring to the network.<br /> <br /> 9. It is interesting to see how figure &quot;b&quot; in the plots showing the experiment results has a U-shape. This shows a correlation between message exchange efficiency and capability of learning distributed representations, giving an idea about the tradeoff between them, as indicated in the paper.<br /> <br /> 10. From Results and Discussion part, we can find learning at a very abstract level of artificial neurons and biological neurons is similar. But the learning method is different. Artificial neural networks use gradient descent to minimize the loss function and reach the global minimum. Biological neural networks have another learning method.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=47860 Task Understanding from Confusing Multi-task Data 2020-11-29T22:32:52Z <p>Z47shen: /* Critique */</p> <hr /> <div>'''Presented By'''<br /> <br /> Qianlin Song, William Loh, Junyue Bai, Phoebe Choi<br /> <br /> = Introduction =<br /> <br /> Narrow AI is an artificial intelligence that outperforms humans in a narrowly defined task. The application of Narrow AI is becoming more and more common. For example, Narrow AI can be used for spam filtering, music recommendation services, and even self-driving cars. One of the most famous integrated forms of Narrow AI is Apple's Siri. Siri has no self-awareness or genuine intelligence, and hence often has challenges performing tasks outside its range of abilities. However, the widespread use of Narrow AI in important infrastructure functions raises some concerns. Some people think that the characteristics of Narrow AI make it fragile, and when neural networks can be used to control important systems (such as power grids, financial transactions), alternatives may be more inclined to avoid risks. While these machines help companies improve efficiency and cut costs, the limitations of Narrow AI encouraged researchers to look into General AI. <br /> <br /> General AI is a machine that can apply its learning to different contexts, which closely resembles human intelligence. This paper attempts to generalize the multi-task learning system that learns from data from multiple classification tasks. One application is image recognition. In figure 1, an image of an apple corresponds to 3 labels: “red”, “apple” and “sweet”. These labels correspond to 3 different classification tasks: color, fruit, and taste. <br /> <br /> [[File:CSLFigure1.PNG | 500px]]<br /> <br /> Currently, multi-task machines require researchers to construct a task definition. Otherwise, it will end up with different outputs with the same input value. Researchers manually assign tasks to each input in the sample to train the machine. See figure 1(a). This method incurs high annotation costs and restricts the machine’s ability to mirror the human recognition process. This paper is interested in developing an algorithm that understands task concepts and performs multi-task learning without manual task annotations. <br /> <br /> This paper proposed a new learning method called confusing supervised learning (CSL) which includes 2 functions: de-confusing function and mapping function. The first function allocates identifies an input to its respective task and the latter finds the relationship between the input and its label. See figure 1(b). To train a network of CSL, CSL-Net is constructed for representing CSL’s variables. However, this structure cannot be optimized by gradient back-propagation. This difficulty is solved by alternatively performing training for the de-confusing net and mapping net optimization. <br /> <br /> Experiments for function regression and image recognition problems were constructed and compared with multi-task learning with complete information to test CSL-Net’s performance. Experiment results show that CSL-Net can learn multiple mappings for every task simultaneously and achieve the same cognition result as the current multi-task machine sigh complete information.<br /> <br /> = Related Work =<br /> <br /> [[File:CSLFigure2.PNG | 700px]]<br /> <br /> ==Multi-task learning==<br /> Multi-task learning aims to learn multiple tasks simultaneously using a shared feature representation. In multi-task learning, the task to which every sample belongs is known. By exploiting similarities and differences between tasks, the learning from one task can improve the learning of another task. (Caruana, 1997) This results in improved learning efficiency. Multi-task learning is used in disciplines like computer vision, natural language processing, and reinforcement learning. In multi-task learning, the task to which every sample belongs is known. With this task definition, the input-output mapping of every task can be represented by a unified function. However, these task definitions are manually constructed, and machines need manual task annotations to learn. Without this annotation, our goal is to understand the task concept from confusing input-label pairs. Overall, It requires manual task annotation to learn and this paper is interested in machine learning without a clear task definition and manual task annotation.<br /> <br /> ==Latent variable learning==<br /> Latent variable learning aims to estimate the true function with mixed probability models. See '''figure 2a'''. In the multi-task learning problem without task annotations, samples are generated from multiple distributions instead of one distribution. While, in fact, all input-label pairs come from a unified distribution, and this distribution is estimated by a mixture of multiple probability models. Thus, Due to the lack of task information, latent variable learning is insufficient to solve the research problem, which is multi-task confusing samples.<br /> <br /> ==Multi-label learning==<br /> Multi-label learning aims to assign an input to a set of classes/labels. See '''figure 2b'''. It is a generalization of multi-class classification, which classifies an input into one class. In multi-label learning, an input can be classified into more than one class. Unlike multi-task learning, multi-label does not consider the relationship between different label judgments and it is assumed that each judgment is independent. An example where multi-label learning is applicable is the scenario where a website wants to automatically assign applicable tags/categories to an article. Since an article can be related to multiple categories (eg. an article can be tagged under the politics and business categories) multi-label learning is of primary concern here.<br /> <br /> = Confusing Supervised Learning =<br /> <br /> == Description of the Problem ==<br /> <br /> Confusing supervised learning (CSL) offers a solution to the issue at hand. A major area of improvement can be seen in the choice of risk measure. In traditional supervised learning, let &lt;math&gt; (x,y)&lt;/math&gt; be the training samples from &lt;math&gt;y=f(x)&lt;/math&gt;, which is an identical but unknown mapping relationship. Assuming the risk measure is mean squared error (MSE), the expected risk function is<br /> <br /> $$R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x$$<br /> <br /> where &lt;math&gt;p(x)&lt;/math&gt; is the data distribution of the input variable &lt;math&gt;x&lt;/math&gt;. In practice, the methods select the optimal function by minimizing the empirical risk:<br /> <br /> $$R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2$$<br /> <br /> The theoretically optimal solution is &lt;math&gt; f(x) &lt;/math&gt;.<br /> <br /> When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let &lt;math&gt;f_j(x)&lt;/math&gt; be the true ground-truth function for each task &lt;math&gt; j &lt;/math&gt;. Therefore, for some input variable &lt;math&gt; x_i &lt;/math&gt;, an ideal model &lt;math&gt;g&lt;/math&gt; would predict &lt;math&gt; g(x_i) = f_j(x_i) &lt;/math&gt;. With this, the risk function can be modified to fit this new task for traditional supervised learning methods.<br /> <br /> $$R(g) = \int_x \sum_{j=1}^n (f_j(x) - g(x))^2 p(f_j) p(x) \; \mathrm{d}x$$<br /> <br /> We call &lt;math&gt; (f_j(x) - g(x))^2 p(f_j) &lt;/math&gt; the '''confusing multiple mappings'''. Then the optimal solution &lt;math&gt;g^*(x)&lt;/math&gt; is &lt;math&gt;\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)&lt;/math&gt;. However, the optimal solution is not conditional on the specific task at hand but rather on the entire ground-truth functions. Therefore, for every non-trivial set of tasks where &lt;math&gt;f_u(x) \neq f_v(x)&lt;/math&gt; for some input &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;u \neq v&lt;/math&gt;, &lt;math&gt;R(g^*) &gt; 0&lt;/math&gt; which implies that there is an unavoidable confusion risk.<br /> <br /> == Learning Functions of CSL ==<br /> <br /> To overcome this issue, the authors introduce two types of learning functions:<br /> * '''Deconfusing function''' &amp;mdash; allocation of which samples come from the same task<br /> * '''Mapping function''' &amp;mdash; mapping relation from input to the output of every learned task<br /> <br /> Suppose there are &lt;math&gt;n&lt;/math&gt; ground-truth mappings &lt;math&gt;\{f_j : 1 \leq j \leq n\}&lt;/math&gt; that we wish to approximate with a set of mapping functions &lt;math&gt;\{g_k : 1 \leq k \leq l\}&lt;/math&gt;. The authors define the deconfusing function as an indicator function &lt;math&gt;h(x, y, g_k) &lt;/math&gt; which takes some sample &lt;math&gt;(x,y)&lt;/math&gt; and determines whether the sample is assigned to task &lt;math&gt;g_k&lt;/math&gt;. Under the CSL framework, the risk functional (using MSE loss) is <br /> <br /> $$R(g,h) = \int_x \sum_{j,k} (f_j(x) - g_k(x))^2 \; h(x, f_j(x), g_k) \;p(f_j) \; p(x) \;\mathrm{d}x$$<br /> <br /> which can be estimated empirically with<br /> <br /> $$R_e(g,h) = \sum_{i=1}^m \sum_{k=1}^n |y_i - g_k(x_i)|^2 \cdot h(x_i, y_i, g_k)$$<br /> <br /> The risk metric of every sample affects only its assigned task.<br /> <br /> == Theoretical Results ==<br /> <br /> This novel framework yields some theoretical results to show the viability of its construction.<br /> <br /> '''Theorem 1 (Existence of Solution)'''<br /> ''With the confusing supervised learning framework, there is an optimal solution''<br /> $$h^*(x, f_j(x), g_k) = \mathbb{I}[j=k]$$<br /> <br /> $$g_k^*(x) = f_k(x)$$<br /> <br /> ''for each &lt;math&gt;k=1,..., n&lt;/math&gt; that makes the expected risk function of the CSL problem zero.''<br /> <br /> However, necessity constraints are needed to avoid the meaningless trivial solutions in all optimal risk solutions.<br /> <br /> '''Theorem 2 (Error Bound of CSL)'''<br /> ''With probability at least &lt;math&gt;1 - \eta&lt;/math&gt; simultaneously with finite VC dimension &lt;math&gt;\tau&lt;/math&gt; of CSL learning framework, the risk measure is bounded by<br /> <br /> $$R(\alpha) \leq R_e(\alpha) + \frac{B\epsilon(m)}{2} \left(1 + \sqrt{1 + \frac{4R_e(\alpha)}{B\epsilon(m)}}\right)$$<br /> <br /> ''where &lt;math&gt;\alpha&lt;/math&gt; is the total parameters of learning functions &lt;math&gt;g, h&lt;/math&gt;, &lt;math&gt;B&lt;/math&gt; is the upper bound of one sample's risk, &lt;math&gt;m&lt;/math&gt; is the size of training data and''<br /> $$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<br /> <br /> This theorem shows the method of empirical risk minimization is valid in the CSL framework. Moreover, the assumed number of tasks affects the VC dimension of the learning functions, which is positively related with the generalization error. Therefore, to make the training risk small, we need to choose the ''minimum number'' of tasks when determining the task.<br /> <br /> = CSL-Net =<br /> In this section, the authors describe how to implement and train a network for CSL.<br /> <br /> == The Structure of CSL-Net ==<br /> Two neural networks, deconfusing-net and mapping-net are trained to implement two learning function variables in empirical risk. The optimization target of the training algorithm is:<br /> $$\min_{g, h} R_e = \sum_{i=1}^{m}\sum_{k=1}^{n} (y_i - g_k(x_i))^2 \cdot h(x_i, y_i; g_k)$$<br /> <br /> The mapping-net is corresponding to functions set &lt;math&gt;g_k&lt;/math&gt;, where &lt;math&gt;y_k = g_k(x)&lt;/math&gt; represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample &lt;math&gt;(x,y)&lt;/math&gt; and output is an n-dimensional one-hot vector. This output vector determines which task the sample &lt;math&gt;(x,y)&lt;/math&gt; should be assigned to. The core difficulty of this algorithm is that the risk function cannot be optimized by gradient back-propagation due to the constraint of one-hot output from deconfusing-net. Approximation of softmax will lead the deconfusing-net output into a non-one-hot form, which results in meaningless trivial solutions.<br /> <br /> == Iterative Deconfusing Algorithm ==<br /> To overcome the training difficulty, the authors divide the empirical risk minimization into two local optimization problems. In each single-network optimization step, the parameters of one network are updated while the parameters of another remain fixed. With one network's parameters unchanged, the problem can be solved by a gradient descent method of neural networks. <br /> <br /> '''Training of Mapping-Net''': With function h from deconfusing-net being determined, the goal is to train every mapping function &lt;math&gt;g_k&lt;/math&gt; with its corresponding sample &lt;math&gt;(x_i^k, y_i^k)&lt;/math&gt;. The optimization problem becomes: &lt;math&gt;\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2&lt;/math&gt;. Back-propagation algorithm can be applied to solve this optimization problem.<br /> <br /> '''Training of Deconfusing-Net''': The task allocation is re-evaluated during the training phase while the parameters of the mapping-net remain fixed. To minimize the original risk, every sample &lt;math&gt;(x, y)&lt;/math&gt; will be assigned to &lt;math&gt;g_k&lt;/math&gt; that is closest to label y among all different &lt;math&gt;k&lt;/math&gt;s. Mapping-net thus provides a temporary solution for deconfusing-net: &lt;math&gt;\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2&lt;/math&gt;. The optimization becomes: &lt;math&gt;\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2&lt;/math&gt;. Similarly, the optimization problem can be solved by updating the deconfusing-net with a back-propagation algorithm.<br /> <br /> The two optimization stages are carried out alternately until the solution converges.<br /> <br /> =Experiment=<br /> ==Setup==<br /> <br /> 3 data sets are used to compare CSL to existing methods, 1 function regression task, and 2 image classification tasks. <br /> <br /> '''Function Regression''': The function regression data comes in the form of &lt;math&gt;(x_i,y_i),i=1,...,m&lt;/math&gt; pairs. However, unlike typical regression problems, there are multiple &lt;math&gt;f_j(x),j=1,...,n&lt;/math&gt; mapping functions, so the goal is to recover both the mapping functions &lt;math&gt;f_j&lt;/math&gt; as well as determine which mapping function corresponds to each of the &lt;math&gt;m&lt;/math&gt; observations. 3 scalar-valued, scalar-input functions that intersect at several points with each other have been chosen as the different tasks. <br /> <br /> '''Colorful-MNIST''': The first image classification data set consists of the MNIST digit data that has been colored. Each observation in this modified set consists of a colored image (&lt;math&gt;x_i&lt;/math&gt;) and either the color, or the digit it represents (&lt;math&gt;y_i&lt;/math&gt;). The goal is to recover the classification task (&quot;color&quot; or &quot;digit&quot;) for each observation and construct the 2 classifiers for both tasks. <br /> <br /> '''Kaggle Fashion Product''': This data set has more observations than the &quot;colored-MNIST&quot; data and consists of pictures labeled with either the “Gender”, “Category”, and “Color” of the clothing item.<br /> <br /> ==Use of Pre-Trained CNN Feature Layers==<br /> <br /> In the Kaggle Fashion Product experiment, CSL trains fully-connected layers that have been attached to feature-identifying layers from pre-trained Convolutional Neural Networks.<br /> <br /> ==Metrics of Confusing Supervised Learning==<br /> <br /> There are two measures of accuracy used to evaluate and compare CSL to other methods, corresponding respectively to the accuracy of the task labeling and the accuracy of the learned mapping function. <br /> <br /> '''Task Prediction Accuracy''': &lt;math&gt;\alpha_T(j)&lt;/math&gt; is the average number of times the learned deconfusing function &lt;math&gt;h&lt;/math&gt; agrees with the task-assignment ability of humans &lt;math&gt;\tilde h&lt;/math&gt; on whether each observation in the data &quot;is&quot; or &quot;is not&quot; in task &lt;math&gt;j&lt;/math&gt;.<br /> <br /> $$\alpha_T(j) = \operatorname{max}_k\frac{1}{m}\sum_{i=1}^m I[h(x_i,y_i;f_k),\tilde h(x_i,y_i;f_j)]$$<br /> <br /> The max over &lt;math&gt;k&lt;/math&gt; is taken because we need to determine which learned task corresponds to which ground-truth task.<br /> <br /> '''Label Prediction Accuracy''': &lt;math&gt;\alpha_L(j)&lt;/math&gt; again chooses &lt;math&gt;f_k&lt;/math&gt;, the learned mapping function that is closest to the ground-truth of task &lt;math&gt;j&lt;/math&gt;, and measures its average absolute accuracy compared to the ground-truth of task &lt;math&gt;j&lt;/math&gt;, &lt;math&gt;f_j&lt;/math&gt;, across all &lt;math&gt;m&lt;/math&gt; observations.<br /> <br /> $$\alpha_L(j) = \operatorname{max}_k\frac{1}{m}\sum_{i=1}^m 1-\dfrac{|g_k(x_i)-f_j(x_i)|}{|f_j(x_i)|}$$<br /> <br /> The purpose of this measure arises from the fact that, in addition to learning mapping allocations like humans, machines should be able to approximate all mapping functions accurately in order to provide corresponding labels. The Label Prediction Accuracy measure captures the exchange equivalence of the following task: each mapping contains its ground-truth output, and machines should be predicting the correct output that is close to the ground-truth. <br /> <br /> ==Results==<br /> <br /> Given confusing data, CSL performs better than traditional supervised learning methods, Pseudo-Label(Lee, 2013), and SMiLE(Tan et al., 2017). This is demonstrated by CSL's &lt;math&gt;\alpha_L&lt;/math&gt; scores of around 95%, compared to &lt;math&gt;\alpha_L&lt;/math&gt; scores of under 50% for the other methods. This supports the assertion that traditional methods only learn the means of all the ground-truth mapping functions when presented with confusing data.<br /> <br /> '''Function Regression''': To &quot;correctly&quot; partition the observations into the correct tasks, a 5-shot warm-up was used. In this situation, the CSL methods work well in learning the ground-truth. That means the initialization of the neural network is set up properly.<br /> <br /> '''Image Classification''': Visualizations created through Spectral embedding confirm the task labelling proficiency of the deconfusing neural network &lt;math&gt;h&lt;/math&gt;.<br /> <br /> The classification and function prediction accuracy of CSL are comparable to supervised learning programs that have been given access to the ground-truth labels.<br /> <br /> ==Application of Multi-label Learning==<br /> <br /> CSL also had better accuracy than traditional supervised learning methods, Pseudo-Label(Lee, 2013), and SMiLE(Tan et al., 2017) when presented with partially labelled multi-label data &lt;math&gt;(x_i,y_i)&lt;/math&gt;, where &lt;math&gt;y_i&lt;/math&gt; is a &lt;math&gt;n&lt;/math&gt;-long indicator vector for whether the image &lt;math&gt;(x_i,y_i)&lt;/math&gt; corresponds to each of the &lt;math&gt;n&lt;/math&gt; labels.<br /> <br /> Applications of multi-label classification include building a recommendation system, social media targeting, as well as detecting adverse drug reaction from text.<br /> <br /> Multi-label can be used to improve the syndrome diagnosis of a patient by focusing on multiple syndromes instead of a single syndrome.<br /> <br /> ==Limitations==<br /> <br /> '''Number of Tasks''': The number of tasks is determined by increasing the task numbers progressively and testing the performance. Ideally, a better way of deciding the number of tasks is expected rather than increasing it one by one and seeing which is the minimum number of tasks that gives the smallest risk. Adding low-quality constraints to deconfusing-net is a reasonable solution to this problem.<br /> <br /> '''Learning of Basic Features''': The CSL framework is not good at learning features. So far, a pre-trained CNN backbone is needed for complicated image classification problems. Even though the effectiveness of the proposed algorithm in learning confusing data based on pre-trained features hasn't been affected, the full-connect network can only be trained based on learned CNN features. It is still a challenge for the current algorithm to learn basic features directly through a CNN structure and understand tasks simultaneously.<br /> <br /> = Conclusion =<br /> <br /> This paper proposes the CSL method for tackling the multi-task learning problem with manual task annotations in the input data. The model obtains a basic task concept by differentiating multiple mappings. The paper also demonstrates that the CSL method is an important step to moving from Narrow AI towards General AI for multi-task learning.<br /> <br /> However, there are some limitations that can be improved for future work:<br /> The repeated training process of determining the lowest best task number that has the closest to zero causes inefficiency in the learning process; The current algorithm is difficult to learn basic features directly through the CNN structure, and it is necessary to learn and train a fully connected network based on CNN features in the experiment.<br /> <br /> = Critique =<br /> <br /> The classification accuracy of CSL was made with algorithms not designed to deal with confusing data and which do not first classify the task of each observation.<br /> <br /> Human task annotation is also imperfect, so one additional application of CSL may be to attempt to flag task annotation errors made by humans, such as in sorting comments for items sold by online retailers; concerned customers, in particular, may not correctly label their comments as &quot;refund&quot;, &quot;order didn't arrive&quot;, &quot;order damaged&quot;, &quot;how good the item is&quot; etc.<br /> <br /> This algorithm will also have a huge issue in scaling, as the proposed method requires repeated training processes, so it might be too expensive for researchers to implement and improve on this algorithm.<br /> <br /> This research paper should have included a plot on loss (of both functions) against epochs in the paper. A common issue with fixing the parameters of one network and updating the other is the variability during training. This is prevalent in other algorithms with similar training methods such as generative adversarial networks (GAN). For instance, ''mode collapse'' is the issue of one network stuck in local minima and other networks that rely on this network may receive incorrect signals during backpropagation. In the case of CSL-Net, since the Deconfusing-Net directly relies on Mapping-Net for training labels, if the Mapping-Net is unable to sufficiently converge, the Deconfusing-Net may incorrectly learn the mapping from inputs to the task. For data with high noise, oscillations may severely prolong the time needed to converge because of the strong correlation in prediction between the two networks.<br /> <br /> - It would be interesting to see this implemented in more examples, to test the robustness of different types of data.<br /> <br /> Even though this paper has already included some examples when testing the CSL in experiments, it will be better to include more detailed examples for partial-label in the &quot;Application of Multi-label Learning&quot; section.<br /> <br /> When using this framework for classification, the order of the one-hot classification labels for each task will likely influence the relationships learned between each task, since the same output header is used for all tasks. This may be why this method fails to learn low-level representations, and requires pretraining. I would like to see more explanation in the paper about why this isn't a problem, if it was investigated.<br /> <br /> It would be a good idea to include comparison details in the summary to make the results and the conclusion more convincing. For instance, though the paper introduced the result generated using confusion data, and provide some applications for multi-label learning, these two sections still fell short and could use some technical details as supporting evidence.<br /> <br /> It is interesting to investigate if the order of adding tasks will influence the model performance.<br /> <br /> It would be interesting to see the effectiveness of applying CSL in face recognition, such that not only does the algorithm map the face to an identity, it also categorizes the face based on other features like beard/no beard and glasses/no glasses simultaneously.<br /> <br /> For pattern recognition,pre-trained features were used in the algorithm. It would be interesting to see how the effectiveness of the model changes if we train it with data directly from the CNN structure in the future.<br /> <br /> So basically given a confused dataset CSL finds the important tasks or labels from the dataset as can be seen from the fruit example. In the example, fruits are grouped under their names, their tastes, and their color, when CSL is given a mixed dataset. Hence given an unstructured data, unlabeled , confused dataset CSL helps in finding the labels, which in turn can help in cleaning the dataset and further in preparing high quality training data set which are very important in different ML algorithms. Since at present preparing these dataset requires manual data annotations, CSL can save time in that process.<br /> <br /> For the Colorful-Mnist data set, the goal is to understand the concept of multiple classification tasks from these examples. All inputs have multiple classification tasks. Each observed sample only represents the classification result of one task, and the task from which the sample comes is unknown.<br /> <br /> = References =<br /> <br />  Su, Xin, et al. &quot;Task Understanding from Confusing Multi-task Data.&quot;<br /> <br />  Caruana, R. (1997) &quot;Multi-task learning&quot;<br /> <br />  Lee, D.-H. Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. Workshop on challenges in representation learning, ICML, vol. 3, 2013, pp. 2–8. <br /> <br />  Tan, Q., Yu, Y., Yu, G., and Wang, J. Semi-supervised multi-label classification using incomplete label information. Neurocomputing, vol. 260, 2017, pp. 192–202.<br /> <br />  Chavdarova, Tatjana, and François Fleuret. &quot;Sgan: An alternative training of generative adversarial networks.&quot; In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.<br /> <br />  Guo-Ping Liu, Jian-Jun Yan, Yi-Qin Wang, Jing-Jing Fu, Zhao-Xia Xu, Rui Guo, Peng Qian, &quot;Application of Multilabel Learning Using the Relevant Feature for Each Label in Chronic Gastritis Syndrome Diagnosis&quot;, Evidence-Based Complementary and Alternative Medicine, vol. 2012, Article ID 135387, 9 pages, 2012. https://doi.org/10.1155/2012/135387</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=47855 User:Cvmustat 2020-11-29T22:24:07Z <p>Z47shen: /* 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 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 in relation to the rest of the sentence. A neural tensor layer is introduced on top of the RNN to obtain the fusion of bi-directional contextual information surrounding a particular word. This method combines these two matrix representations and classifies the text, 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.<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 manages to be the best performing in 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:<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 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 /> == 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 it 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 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 /> 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.<br /> <br /> 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 /> 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 /> 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 /> - Could this be applied to hieroglyphs to decipher/better understand them?<br /> <br /> 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 /> -This is an interesting topic. 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 /> 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 /> -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 /> -From experiments, LSTM outperforms CRNN in some cases. It would be interesting to compare CNN+LSTM and CRNN's performance. Another application for CRNN might be classifying spoken language.<br /> <br /> - 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 /> == 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 />  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> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=47849 User:J46hou 2020-11-29T22:12:42Z <p>Z47shen: /* Critiques/Insights */</p> <hr /> <div>DROCC: Deep Robust One-Class Classification<br /> == Presented by == <br /> Jinjiang Lian, Yisheng Zhu, Jiawen Hou, Mingzhe Huang<br /> == Introduction ==<br /> In this paper, the “one-class” classification, whose goal is to obtain accurate discriminators for a special class, has been studied. Popular uses of this technique include anomaly detection which is widely used in detecting outliers. Anomaly detection is a well-studied area of research, which aims to learn a model that accurately describes &quot;normality&quot;. Its application ranges from fraud detection to medical diagnosis; however, the conventional approach of modeling with typical data using a simple function falls short when it comes to complex domains such as vision or speech. Another case where this would be useful is when recognizing “wake-word” while waking up AI systems such as Alexa. <br /> <br /> Deep learning based on anomaly detection methods attempts to learn features automatically but has some limitations. One approach is based on extending the classical data modeling techniques over the learned representations, but in this case, all the points may be mapped to a single point which makes the layer look &quot;perfect&quot;. The second approach is based on learning the salient geometric structure of data and training the discriminator to predict applied transformation. The result could be considered anomalous if the discriminator fails to predict the transformation accurately.<br /> <br /> Thus, in this paper, a new approach called Deep Robust One-Class Classification (DROCC) was presented to solve the above concerns. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. More specifically, we are presenting DROCC-LF which is an outlier-exposure style extension of DROCC. This extension combines the DROCC's anomaly detection loss with standard classification loss over the negative data and exploits the negative examples to learn a Mahalanobis distance.<br /> <br /> == Previous Work ==<br /> Traditional approaches for one-class problems include one-class SVM (Scholkopf et al., 1999) and Isolation Forest (Liu et al., 2008). One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of the art methodologies to tackle these kinds of problems are: <br /> <br /> 1. Approach based on prediction transformations (Golan &amp; El-Yaniv, 2018; Hendrycks et al.,2019a)  This work is based on learning the salient geometric structure of typical data by applying specific transformations to the input data and training the discriminator to preduct applied transformation. This approach has some shortcomings in the sense that it depends heavily on an appropriate domain-specific set of transformations that are in general hard to obtain. <br /> <br /> 2. Approach of minimizing a classical one-class loss on the learned final layer representations such as DeepSVDD. (Ruff et al.,2018) This such work has proposed some heuristics to mitigate issues like setting the bias to zero but it is often insufficient in practice. This method suffers from the fundamental drawback of representation collapse, where the learned transformation might map all the points to a single point (like origin), leading to a degenerate solution and poor discrimination between normal points and the anomalous points.<br /> <br /> 3. Approach based on balancing unbalanced training data sets using methods such as SMOTE to synthetically create outlier data to train models on.<br /> <br /> == Motivation ==<br /> Anomaly detection is a well-studied problem with a large body of research (Aggarwal, 2016; Chandola et al., 2009) . The goal is to identify the outliers - the points not following a typical distribution. <br /> [[File:abnormal.jpeg | thumb | center | 1000px | Abnormal Data (Data Driven Investor, 2020)]]<br /> Classical approaches for anomaly detection are based on modeling the typical data using simple functions over the low-dimensional subspace or a tree-structured partition of the input space to detect anomalies (Sch¨olkopf et al., 1999; Liu et al., 2008; Lakhina et al., 2004) , such as constructing a minimum-enclosing ball around the typical data points (Tax &amp; Duin, 2004) . They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods, and Side-information based AD. While these techniques are well-suited when the input is featured appropriately, they struggle on complex domains like vision and speech, where hand-designing features are difficult.<br /> <br /> '''AD via Generative Modeling:''' involves deep autoencoders and GAN based methods and have been deeply studied. But, this method solves a much harder problem than required and reconstructs the entire input during the decoding step<br /> <br /> '''Deep One-Class SVM:''' Deep SVDD attempts to learn a neural network which maps data into a hypersphere. Mappings which fall within the hypersphere are considered &quot;normal&quot;. It was the first method to introduce deep one-class classification for the purpose of anomaly detection, but is impeded by representation collapse.<br /> <br /> '''Transformations based methods:''' Are more recent methods that are based on self-supervised training. The training process of these methods applies transformations to the regular points and training then trains the classifier to identify the transformations used. The model relies on the assumption that a point is normal iff the transformations applied to the point can be identified. Some proposed transformations are as simple as rotations and flips, or can be handcrafted and much more complicated. The various transformations that have been proposed are heavily domain dependent and are hard to design.<br /> <br /> '''Side-information based AD:''' incorporate labelled anomalous data or out-of-distribution samples. DROCC makes no assumptions regarding access to side-information.<br /> <br /> Another related problem is the one-class classification under limited negatives (OCLN). In this case, only a few negative samples are available. The goal is to find a classifier that would not misfire close negatives so that the false positive rate will be low. <br /> <br /> DROCC is robust to representation collapse by involving a discriminative component that is general and empirically accurate on most standard domains like tabular, time-series and vision without requiring any additional side information. DROCC is motivated by the key observation that generally, the typical data lies on a low-dimensional manifold, which is well-sampled in the training data. This is believed to be true even in complex domains such as vision, speech, and natural language (Pless &amp; Souvenir, 2009). <br /> <br /> == Model Explanation ==<br /> [[File:drocc_f1.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 1'''&lt;/div&gt;<br /> <br /> (a): A normal data manifold with red dots representing generated anomalous points in Ni(r). <br /> <br /> (b): Decision boundary learned by DROCC when applied to the data from (a). Blue represents points classified as normal and red points are classified as abnormal. We observe from here that DROCC is able to capture the manifold accurately; whereas the classical methods OC-SVM and DeepSVDD perform poorly as they both try to learn a minimum enclosing ball for the whole set of positive data points. <br /> <br /> (c), (d): First two dimensions of the decision boundary of DROCC and DROCC–LF, when applied to noisy data (Section 5.2). DROCC–LF is nearly optimal while DROCC’s decision boundary is inaccurate. Yellow color sine wave depicts the train data.<br /> <br /> == DROCC ==<br /> The model is based on the assumption that the true data lies on a manifold. As manifolds resemble Euclidean space locally, our discriminative component is based on classifying a point as anomalous if it is outside the union of small L2 norm balls around the training typical points (See Figure 1a, 1b for an illustration). Importantly, the above definition allows us to synthetically generate anomalous points, and we adaptively generate the most effective anomalous points while training via a gradient ascent phase reminiscent of adversarial training. In other words, DROCC has a gradient ascent phase to adaptively add anomalous points to our training set and a gradient descent phase to minimize the classification loss by learning a representation and a classifier on top of the representations to separate typical points from the generated anomalous points. In this way, DROCC automatically learns an appropriate representation (like DeepSVDD) but is robust to a representation collapse as mapping all points to the same value would lead to poor discrimination between normal points and the generated anomalous points.<br /> <br /> The algorithm that was used to train the model is laid out below in pseudocode.<br /> &lt;center&gt;<br /> [[File:DROCCtrain.png]]<br /> &lt;/center&gt;<br /> <br /> For a DNN &lt;math&gt;f_\theta: \mathbb{R}^d \to \mathbb{R}&lt;/math&gt; that is parameterized by a set of parameters &lt;math&gt;\theta&lt;/math&gt;, DROCC estimates &lt;math&gt;\theta^{dr} = \min_\theta\ell^{dr}(\theta)&lt;/math&gt; where <br /> $$\ell^{dr}(\theta) = \lambda\|\theta\|^2 + \sum_{i=1}^n[\ell(f_\theta(x_i),1)+\mu\max_{\tilde{x}_i \in N_i(r)}\ell(f_\theta(\tilde{x}_i),-1)]$$<br /> Here, &lt;math&gt;N_i(r) = \{\|\tilde{x}_i-x_i\|_2\leq\gamma\cdot r; r \leq \|\tilde{x}_i - x_j\|, \forall j=1,2,...n\}&lt;/math&gt; contains all the points that are at least distance &lt;math&gt;r&lt;/math&gt; from the training points. The &lt;math&gt;\gamma \geq 1&lt;/math&gt; is a regularization term, and &lt;math&gt;\ell:\mathbb{R} \times \mathbb{R} \to \mathbb{R}&lt;/math&gt; is a loss function. The &lt;math&gt;x_i&lt;/math&gt; are normal points that should be classified as positive and the &lt;math&gt;\tilde{x}_i&lt;/math&gt; are anomalous points that should be classified as negative. This formulation is a saddle point problem.<br /> <br /> == DROCC-LF ==<br /> To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) , DROCC–LF, an outlier-exposure style extension of DROCC was proposed. Intuitively, DROCC–LF combines DROCC’s anomaly detection loss (that is over only the positive data points) with standard classification loss over the negative data. In addition, DROCC–LF exploits the negative examples to learn a Mahalanobis distance to compare points over the manifold instead of using the standard Euclidean distance, which can be inaccurate for high-dimensional data with relatively fewer samples. (See Figure 1c, 1d for illustration)<br /> <br /> == Popular Dataset Benchmark Result ==<br /> <br /> [[File:drocc_auc.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 2: AUC result'''&lt;/div&gt;<br /> <br /> The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. The average AUC (with standard deviation) for one-vs-all anomaly detection on CIFAR-10 is shown in table 1. DROCC outperforms baselines on most classes, with gains as high as 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br /> <br /> [[File:drocc_f1score.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 3: F1-Score'''&lt;/div&gt;<br /> <br /> Figure 3 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from the UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about an 11.5% performance increase.<br /> Results on One-class Classification with Limited Negatives (OCLN): <br /> [[File:ocln.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''&lt;/div&gt;<br /> MNIST 0 vs. 1 Classification: <br /> We consider an experimental setup on the MNIST dataset, where the training data consists of Digit 0, the normal class, and Digit 1 as the anomaly. During the evaluation, in addition to samples from training distribution, we also have half zeros, which act as challenging OOD points (close negatives). These half zeros are generated by randomly masking 50% of the pixels (Figure 2). BCE performs poorly, with a recall of 54% only at a fixed FPR of 3%. DROCC–OE gives a recall value of 98:16% outperforming DeepSAD by a margin of 7%, which gives a recall value of 90:91%. DROCC–LF provides further improvement with a recall of 99:4% at 3% FPR. <br /> <br /> [[File:ocln_2.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 5: OCLN on Audio Commands.'''&lt;/div&gt;<br /> Wake word Detection: <br /> Finally, we evaluate DROCC–LF on the practical problem of wake word detection with low FPR against arbitrary OOD negatives. To this end, we identify a keyword, say “Marvin” from the audio commands dataset (Warden, 2018)  as the positive class, and the remaining 34 keywords are labeled as the negative class. For training, we sample points uniformly at random from the above-mentioned dataset. However, for evaluation, we sample positives from the train distribution, but negatives contain a few challenging OOD points as well. Sampling challenging negatives itself is a hard task and is the key motivating reason for studying the problem. So, we manually list close-by keywords to Marvin such as Mar, Vin, Marvelous, etc. We then generate audio snippets for these keywords via a speech synthesis tool 2 with a variety of accents.<br /> Figure 5 shows that for 3% and 5% FPR settings, DROCC–LF is significantly more accurate than the baselines. For example, with FPR=3%, DROCC–LF is 10% more accurate than the baselines. We repeated the same experiment with the keyword: Seven, and observed a similar trend. In summary, DROCC–LF is able to generalize well against negatives that are “close” to the true positives even when such negatives were not supplied with the training data.<br /> <br /> == Conclusion and Future Work ==<br /> We introduced DROCC method for deep anomaly detection. It models normal data points using a low-dimensional sub-manifold inside the feature space, and the anomalous points are characterized via their Euclidean distance from the sub-manifold. Based on this intuition, DROCC’s optimization is formulated as a saddle point problem which is solved via a standard gradient descent-ascent algorithm. We then extended DROCC to OCLN problem where the goal is to generalize well against arbitrary negatives, assuming the positive class is well sampled and a small number of negative points are also available. Both the methods perform significantly better than strong baselines, in their respective problem settings. <br /> <br /> For computational efficiency, we simplified the projection set of both methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with the stricter set is an exciting research direction. Further, we would also like to rigorously analyze DROCC, assuming enough samples from a low-curvature manifold. Finally, as OCLN is an exciting problem that routinely comes up in a variety of real-world applications, we would like to apply DROCC–LF to a few high impact scenarios.<br /> <br /> The results of this study showed that DROCC is comparatively better for anomaly detection across many different areas, such as tabular data, images, audio, and time series, when compared to existing state-of-the-art techniques.<br /> <br /> <br /> == References ==<br /> : Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br /> <br /> : Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M¨uller, E., and Kloft, M. Deep one-class classification. In International Conference on Machine Learning (ICML), 2018.<br /> <br /> : Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br /> <br /> : Sch¨olkopf, B., Williamson, R., Smola, A., Shawe-Taylor, J., and Platt, J. Support vector method for novelty detection. In Proceedings of the 12th International Conference on Neural Information Processing Systems, 1999.<br /> <br /> : Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br /> <br /> : Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br /> <br /> : Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br /> <br /> : Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br /> <br /> : Liu, F. T., Ting, K. M., and Zhou, Z.-H. Isolation forest. In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 2008.<br /> <br /> == Critiques/Insights ==<br /> <br /> 1. It would be interesting to see this implemented in self-driving cars, for instance, to detect unusual road conditions.<br /> <br /> 2. Figure 1 shows a good representation on how this model works. However, how can we know that this model is not prone to overfitting? There are many situations where there are valid points that lie outside of the line, especially new data that the model has never see before. An explanation on how this is avoided would be good.<br /> <br /> 3.In the introduction part, it should first explain what is &quot;one class&quot;, and then make a detailed application. Moreover, special definition words are used in many places in the text. No detailed explanation was given. In the end, the future application fields of DROCC and the research direction of the group can be explained.<br /> <br /> 4. It will also be interesting to see if one change from using &lt;math&gt;\ell_{2}&lt;/math&gt; Euclidean distance to other distances. When the low-dimensional manifold is highly non-linear, using the local linear distance to characterize anomalous points might fail.<br /> <br /> 5. This is a nice summary and the authors introduce clearly on the performance of DROCC. It is nice to use Alexa as an example to catch readers' attention. I think it will be nice to include the algorithm of the DROCC or the architecture of DROCC in this summary to help us know the whole view of this method. Maybe it will be interesting to apply DROCC in biomedical studies? since one-class classification is often used in biomedical studies.<br /> <br /> 6. The training method resembles adversarial learning with gradient ascent, however, there is no evaluation of this method on adversarial examples. This is quite unusual considering the paper proposed a method for robust one-class classification, and can be a security threat in real life in critical applications.<br /> <br /> 7. The underlying idea behind OCLN is very similar to how neural networks are implemented in recommender systems and trained over positive/negative triplet models. In that case as well, due to the nature of implicit and explicit feedback, positive data tends to dominate the system. It would be interesting to see if insights from that area could be used to further boost the model presented in this paper.<br /> <br /> 8. The paper shows the performance of DROCC being evaluated for time series data. It is interesting to see high AUC scores for DROCC against baselines like nearest neighbours and REBMs.Because detecting abnormal data in time series datasets is not common to practise.<br /> <br /> 9. Figure1 presented results on a simple 2-D sine wave dataset to visualize the kind of classifiers learnt by DROCC. And the 1a is the positive data lies on a 1-D manifold. We can see from 1b that DROCC is able to capture the manifold accurately.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=47848 User:J46hou 2020-11-29T22:12:31Z <p>Z47shen: /* Critiques/Insights */</p> <hr /> <div>DROCC: Deep Robust One-Class Classification<br /> == Presented by == <br /> Jinjiang Lian, Yisheng Zhu, Jiawen Hou, Mingzhe Huang<br /> == Introduction ==<br /> In this paper, the “one-class” classification, whose goal is to obtain accurate discriminators for a special class, has been studied. Popular uses of this technique include anomaly detection which is widely used in detecting outliers. Anomaly detection is a well-studied area of research, which aims to learn a model that accurately describes &quot;normality&quot;. Its application ranges from fraud detection to medical diagnosis; however, the conventional approach of modeling with typical data using a simple function falls short when it comes to complex domains such as vision or speech. Another case where this would be useful is when recognizing “wake-word” while waking up AI systems such as Alexa. <br /> <br /> Deep learning based on anomaly detection methods attempts to learn features automatically but has some limitations. One approach is based on extending the classical data modeling techniques over the learned representations, but in this case, all the points may be mapped to a single point which makes the layer look &quot;perfect&quot;. The second approach is based on learning the salient geometric structure of data and training the discriminator to predict applied transformation. The result could be considered anomalous if the discriminator fails to predict the transformation accurately.<br /> <br /> Thus, in this paper, a new approach called Deep Robust One-Class Classification (DROCC) was presented to solve the above concerns. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. More specifically, we are presenting DROCC-LF which is an outlier-exposure style extension of DROCC. This extension combines the DROCC's anomaly detection loss with standard classification loss over the negative data and exploits the negative examples to learn a Mahalanobis distance.<br /> <br /> == Previous Work ==<br /> Traditional approaches for one-class problems include one-class SVM (Scholkopf et al., 1999) and Isolation Forest (Liu et al., 2008). One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of the art methodologies to tackle these kinds of problems are: <br /> <br /> 1. Approach based on prediction transformations (Golan &amp; El-Yaniv, 2018; Hendrycks et al.,2019a)  This work is based on learning the salient geometric structure of typical data by applying specific transformations to the input data and training the discriminator to preduct applied transformation. This approach has some shortcomings in the sense that it depends heavily on an appropriate domain-specific set of transformations that are in general hard to obtain. <br /> <br /> 2. Approach of minimizing a classical one-class loss on the learned final layer representations such as DeepSVDD. (Ruff et al.,2018) This such work has proposed some heuristics to mitigate issues like setting the bias to zero but it is often insufficient in practice. This method suffers from the fundamental drawback of representation collapse, where the learned transformation might map all the points to a single point (like origin), leading to a degenerate solution and poor discrimination between normal points and the anomalous points.<br /> <br /> 3. Approach based on balancing unbalanced training data sets using methods such as SMOTE to synthetically create outlier data to train models on.<br /> <br /> == Motivation ==<br /> Anomaly detection is a well-studied problem with a large body of research (Aggarwal, 2016; Chandola et al., 2009) . The goal is to identify the outliers - the points not following a typical distribution. <br /> [[File:abnormal.jpeg | thumb | center | 1000px | Abnormal Data (Data Driven Investor, 2020)]]<br /> Classical approaches for anomaly detection are based on modeling the typical data using simple functions over the low-dimensional subspace or a tree-structured partition of the input space to detect anomalies (Sch¨olkopf et al., 1999; Liu et al., 2008; Lakhina et al., 2004) , such as constructing a minimum-enclosing ball around the typical data points (Tax &amp; Duin, 2004) . They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods, and Side-information based AD. While these techniques are well-suited when the input is featured appropriately, they struggle on complex domains like vision and speech, where hand-designing features are difficult.<br /> <br /> '''AD via Generative Modeling:''' involves deep autoencoders and GAN based methods and have been deeply studied. But, this method solves a much harder problem than required and reconstructs the entire input during the decoding step<br /> <br /> '''Deep One-Class SVM:''' Deep SVDD attempts to learn a neural network which maps data into a hypersphere. Mappings which fall within the hypersphere are considered &quot;normal&quot;. It was the first method to introduce deep one-class classification for the purpose of anomaly detection, but is impeded by representation collapse.<br /> <br /> '''Transformations based methods:''' Are more recent methods that are based on self-supervised training. The training process of these methods applies transformations to the regular points and training then trains the classifier to identify the transformations used. The model relies on the assumption that a point is normal iff the transformations applied to the point can be identified. Some proposed transformations are as simple as rotations and flips, or can be handcrafted and much more complicated. The various transformations that have been proposed are heavily domain dependent and are hard to design.<br /> <br /> '''Side-information based AD:''' incorporate labelled anomalous data or out-of-distribution samples. DROCC makes no assumptions regarding access to side-information.<br /> <br /> Another related problem is the one-class classification under limited negatives (OCLN). In this case, only a few negative samples are available. The goal is to find a classifier that would not misfire close negatives so that the false positive rate will be low. <br /> <br /> DROCC is robust to representation collapse by involving a discriminative component that is general and empirically accurate on most standard domains like tabular, time-series and vision without requiring any additional side information. DROCC is motivated by the key observation that generally, the typical data lies on a low-dimensional manifold, which is well-sampled in the training data. This is believed to be true even in complex domains such as vision, speech, and natural language (Pless &amp; Souvenir, 2009). <br /> <br /> == Model Explanation ==<br /> [[File:drocc_f1.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 1'''&lt;/div&gt;<br /> <br /> (a): A normal data manifold with red dots representing generated anomalous points in Ni(r). <br /> <br /> (b): Decision boundary learned by DROCC when applied to the data from (a). Blue represents points classified as normal and red points are classified as abnormal. We observe from here that DROCC is able to capture the manifold accurately; whereas the classical methods OC-SVM and DeepSVDD perform poorly as they both try to learn a minimum enclosing ball for the whole set of positive data points. <br /> <br /> (c), (d): First two dimensions of the decision boundary of DROCC and DROCC–LF, when applied to noisy data (Section 5.2). DROCC–LF is nearly optimal while DROCC’s decision boundary is inaccurate. Yellow color sine wave depicts the train data.<br /> <br /> == DROCC ==<br /> The model is based on the assumption that the true data lies on a manifold. As manifolds resemble Euclidean space locally, our discriminative component is based on classifying a point as anomalous if it is outside the union of small L2 norm balls around the training typical points (See Figure 1a, 1b for an illustration). Importantly, the above definition allows us to synthetically generate anomalous points, and we adaptively generate the most effective anomalous points while training via a gradient ascent phase reminiscent of adversarial training. In other words, DROCC has a gradient ascent phase to adaptively add anomalous points to our training set and a gradient descent phase to minimize the classification loss by learning a representation and a classifier on top of the representations to separate typical points from the generated anomalous points. In this way, DROCC automatically learns an appropriate representation (like DeepSVDD) but is robust to a representation collapse as mapping all points to the same value would lead to poor discrimination between normal points and the generated anomalous points.<br /> <br /> The algorithm that was used to train the model is laid out below in pseudocode.<br /> &lt;center&gt;<br /> [[File:DROCCtrain.png]]<br /> &lt;/center&gt;<br /> <br /> For a DNN &lt;math&gt;f_\theta: \mathbb{R}^d \to \mathbb{R}&lt;/math&gt; that is parameterized by a set of parameters &lt;math&gt;\theta&lt;/math&gt;, DROCC estimates &lt;math&gt;\theta^{dr} = \min_\theta\ell^{dr}(\theta)&lt;/math&gt; where <br /> $$\ell^{dr}(\theta) = \lambda\|\theta\|^2 + \sum_{i=1}^n[\ell(f_\theta(x_i),1)+\mu\max_{\tilde{x}_i \in N_i(r)}\ell(f_\theta(\tilde{x}_i),-1)]$$<br /> Here, &lt;math&gt;N_i(r) = \{\|\tilde{x}_i-x_i\|_2\leq\gamma\cdot r; r \leq \|\tilde{x}_i - x_j\|, \forall j=1,2,...n\}&lt;/math&gt; contains all the points that are at least distance &lt;math&gt;r&lt;/math&gt; from the training points. The &lt;math&gt;\gamma \geq 1&lt;/math&gt; is a regularization term, and &lt;math&gt;\ell:\mathbb{R} \times \mathbb{R} \to \mathbb{R}&lt;/math&gt; is a loss function. The &lt;math&gt;x_i&lt;/math&gt; are normal points that should be classified as positive and the &lt;math&gt;\tilde{x}_i&lt;/math&gt; are anomalous points that should be classified as negative. This formulation is a saddle point problem.<br /> <br /> == DROCC-LF ==<br /> To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) , DROCC–LF, an outlier-exposure style extension of DROCC was proposed. Intuitively, DROCC–LF combines DROCC’s anomaly detection loss (that is over only the positive data points) with standard classification loss over the negative data. In addition, DROCC–LF exploits the negative examples to learn a Mahalanobis distance to compare points over the manifold instead of using the standard Euclidean distance, which can be inaccurate for high-dimensional data with relatively fewer samples. (See Figure 1c, 1d for illustration)<br /> <br /> == Popular Dataset Benchmark Result ==<br /> <br /> [[File:drocc_auc.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 2: AUC result'''&lt;/div&gt;<br /> <br /> The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. The average AUC (with standard deviation) for one-vs-all anomaly detection on CIFAR-10 is shown in table 1. DROCC outperforms baselines on most classes, with gains as high as 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br /> <br /> [[File:drocc_f1score.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 3: F1-Score'''&lt;/div&gt;<br /> <br /> Figure 3 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from the UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about an 11.5% performance increase.<br /> Results on One-class Classification with Limited Negatives (OCLN): <br /> [[File:ocln.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''&lt;/div&gt;<br /> MNIST 0 vs. 1 Classification: <br /> We consider an experimental setup on the MNIST dataset, where the training data consists of Digit 0, the normal class, and Digit 1 as the anomaly. During the evaluation, in addition to samples from training distribution, we also have half zeros, which act as challenging OOD points (close negatives). These half zeros are generated by randomly masking 50% of the pixels (Figure 2). BCE performs poorly, with a recall of 54% only at a fixed FPR of 3%. DROCC–OE gives a recall value of 98:16% outperforming DeepSAD by a margin of 7%, which gives a recall value of 90:91%. DROCC–LF provides further improvement with a recall of 99:4% at 3% FPR. <br /> <br /> [[File:ocln_2.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 5: OCLN on Audio Commands.'''&lt;/div&gt;<br /> Wake word Detection: <br /> Finally, we evaluate DROCC–LF on the practical problem of wake word detection with low FPR against arbitrary OOD negatives. To this end, we identify a keyword, say “Marvin” from the audio commands dataset (Warden, 2018)  as the positive class, and the remaining 34 keywords are labeled as the negative class. For training, we sample points uniformly at random from the above-mentioned dataset. However, for evaluation, we sample positives from the train distribution, but negatives contain a few challenging OOD points as well. Sampling challenging negatives itself is a hard task and is the key motivating reason for studying the problem. So, we manually list close-by keywords to Marvin such as Mar, Vin, Marvelous, etc. We then generate audio snippets for these keywords via a speech synthesis tool 2 with a variety of accents.<br /> Figure 5 shows that for 3% and 5% FPR settings, DROCC–LF is significantly more accurate than the baselines. For example, with FPR=3%, DROCC–LF is 10% more accurate than the baselines. We repeated the same experiment with the keyword: Seven, and observed a similar trend. In summary, DROCC–LF is able to generalize well against negatives that are “close” to the true positives even when such negatives were not supplied with the training data.<br /> <br /> == Conclusion and Future Work ==<br /> We introduced DROCC method for deep anomaly detection. It models normal data points using a low-dimensional sub-manifold inside the feature space, and the anomalous points are characterized via their Euclidean distance from the sub-manifold. Based on this intuition, DROCC’s optimization is formulated as a saddle point problem which is solved via a standard gradient descent-ascent algorithm. We then extended DROCC to OCLN problem where the goal is to generalize well against arbitrary negatives, assuming the positive class is well sampled and a small number of negative points are also available. Both the methods perform significantly better than strong baselines, in their respective problem settings. <br /> <br /> For computational efficiency, we simplified the projection set of both methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with the stricter set is an exciting research direction. Further, we would also like to rigorously analyze DROCC, assuming enough samples from a low-curvature manifold. Finally, as OCLN is an exciting problem that routinely comes up in a variety of real-world applications, we would like to apply DROCC–LF to a few high impact scenarios.<br /> <br /> The results of this study showed that DROCC is comparatively better for anomaly detection across many different areas, such as tabular data, images, audio, and time series, when compared to existing state-of-the-art techniques.<br /> <br /> <br /> == References ==<br /> : Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br /> <br /> : Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M¨uller, E., and Kloft, M. Deep one-class classification. In International Conference on Machine Learning (ICML), 2018.<br /> <br /> : Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br /> <br /> : Sch¨olkopf, B., Williamson, R., Smola, A., Shawe-Taylor, J., and Platt, J. Support vector method for novelty detection. In Proceedings of the 12th International Conference on Neural Information Processing Systems, 1999.<br /> <br /> : Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br /> <br /> : Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br /> <br /> : Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br /> <br /> : Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br /> <br /> : Liu, F. T., Ting, K. M., and Zhou, Z.-H. Isolation forest. In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 2008.<br /> <br /> == Critiques/Insights ==<br /> <br /> 1. It would be interesting to see this implemented in self-driving cars, for instance, to detect unusual road conditions.<br /> <br /> 2. Figure 1 shows a good representation on how this model works. However, how can we know that this model is not prone to overfitting? There are many situations where there are valid points that lie outside of the line, especially new data that the model has never see before. An explanation on how this is avoided would be good.<br /> <br /> 3.In the introduction part, it should first explain what is &quot;one class&quot;, and then make a detailed application. Moreover, special definition words are used in many places in the text. No detailed explanation was given. In the end, the future application fields of DROCC and the research direction of the group can be explained.<br /> <br /> 4. It will also be interesting to see if one change from using &lt;math&gt;\ell_{2}&lt;/math&gt; Euclidean distance to other distances. When the low-dimensional manifold is highly non-linear, using the local linear distance to characterize anomalous points might fail.<br /> <br /> 5. This is a nice summary and the authors introduce clearly on the performance of DROCC. It is nice to use Alexa as an example to catch readers' attention. I think it will be nice to include the algorithm of the DROCC or the architecture of DROCC in this summary to help us know the whole view of this method. Maybe it will be interesting to apply DROCC in biomedical studies? since one-class classification is often used in biomedical studies.<br /> <br /> 6. The training method resembles adversarial learning with gradient ascent, however, there is no evaluation of this method on adversarial examples. This is quite unusual considering the paper proposed a method for robust one-class classification, and can be a security threat in real life in critical applications.<br /> <br /> 7. The underlying idea behind OCLN is very similar to how neural networks are implemented in recommender systems and trained over positive/negative triplet models. In that case as well, due to the nature of implicit and explicit feedback, positive data tends to dominate the system. It would be interesting to see if insights from that area could be used to further boost the model presented in this paper.<br /> <br /> 8. The paper shows the performance of DROCC being evaluated for time series data. It is interesting to see high AUC scores for DROCC against baselines like nearest neighbours and REBMs.Because detecting abnormal data in time series datasets is not common to practise.<br /> <br /> 9.Figure1 presented results on a simple 2-D sine wave dataset to visualize the kind of classifiers learnt by DROCC. And the 1a is the positive data lies on a 1-D manifold. We can see from 1b that DROCC is able to capture the manifold accurately.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems&diff=47822 Adversarial Attacks on Copyright Detection Systems 2020-11-29T21:38:02Z <p>Z47shen: /* Audio Fingerprinting Model */</p> <hr /> <div>== Presented by == <br /> Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun<br /> <br /> ==Introduction ==<br /> The copyright detection system is one of the most commonly used machine learning systems. Important real-world applications include tools such as Google Jigsaw which can identify and remove videos promoting terrorism, or companies like YouTube who use machine learning systems it to flag content that infringes copyrights. Failure to do so will result in legal consequences. However, the adversarial attacks on these systems have not been widely addressed by the public and remain largely unexplored. Adversarial attacks are instances where inputs are intentionally designed by people to cause misclassification in the model. <br /> <br /> Copyright detection systems are vulnerable to attacks for three reasons:<br /> <br /> 1. Unlike physical-world attacks where adversarial samples need to survive under different conditions like resolutions and viewing angles, any digital files can be uploaded directly to the web without going through a camera or microphone.<br /> <br /> 2. The detection system is an open-set problem, which means that the uploaded files may not correspond to an existing class. In this case, it will prevent people from uploading unprotected audio/video whereas most of the uploaded files nowadays are not protected.<br /> <br /> 3. The detection system needs to handle a vast majority of content which have different labels but similar features. For example, in the ImageNet classification task, the system is easily attacked when there are two cats/dogs/birds with high similarities but from different classes.<br /> <br /> The goal of this paper is to raise awareness of the security threats faced by copyright detection systems. In this paper, different types of copyright detection systems will be introduced. A widely used detection model from Shazam, a popular app used for recognizing music, will be discussed. As a proof-of-concept, the paper generates audio fingerprints using convolutional neural networks and formulates the adversarial loss function using standard gradient methods. An example of remixing music is given to show how adversarial examples can be created. Then, the adversarial attacks are applied to the industrial systems like AudioTag and YouTube Content ID to evaluate the effectiveness of the systems.<br /> <br /> == Types of copyright detection systems ==<br /> Fingerprinting algorithms work by extracting the features of a source file as a hash and then utilizes a matching algorithm to compare that to the materials protected by copyright in the database. If enough matches are found between the source and existing data, the two samples are considered identical and the copyright detection system is able to reject the copyright declaration of the source. Most audio, image and video fingerprinting algorithms work by training a neural network to output features or extracting hand-crafted features.<br /> <br /> In terms of video fingerprinting, a useful algorithm is to detect the entering/leaving time of the objects in the video (Saviaga &amp; Toxtli, 2018). The final hash consists of the entering/leaving of different objects and a unique relationship of the objects. However, most of these video fingerprinting algorithms only train their neural networks by using simple distortions such as adding noise or flipping the video rather than adversarial perturbations. This leads to algorithms that are strong against pre-defined distortions, but not adversarial attacks.<br /> <br /> Moreover, some plagiarism detection systems also depend on neural networks to generate a fingerprint of the input document. Though using deep feature representations as a fingerprint is efficient in detecting plagiarism, it still might be weak to adversarial attacks.<br /> <br /> Audio fingerprinting may perform better than the algorithms above since most of the time the hash is generated by extracting hand-crafted features rather than training a neural network. That being said, it still is easy to attack.<br /> <br /> == Case study: evading audio fingerprinting ==<br /> <br /> === Audio Fingerprinting Model===<br /> The audio fingerprinting model plays an important role in copyright detection. It is useful for quickly locating or finding similar samples inside an audio database. Shazam is a popular music recognition application, which uses one of the most well-known fingerprinting models. Because of the three properties: temporal locality, translation invariance, and robustness, Shazam's algorithm is treated as a good fingerprinting algorithm. It shows strong robustness even in presence of noise by using local maximum in spectrogram to form hashes. Spectrograms are two-dimensional representations of audio frequency spectra over time. An example is shown below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:Spectrogram-19thC.png|Spectrogram-19thC|390px]]&lt;/div&gt;<br /> &lt;div align=&quot;center&quot;&gt;&lt;span style=&quot;font-size:80%&quot;&gt;Source:https://commons.wikimedia.org/wiki/File:Spectrogram-19thC.png&lt;/span&gt;&lt;/div&gt;<br /> <br /> === Interpreting the fingerprint extractor as a CNN ===<br /> The intention of this section is to build a differentiable neural network whose function resembles that of an audio fingerprinting algorithm, which is well-known for its ability to identify the meta-data, i.e. song names, artists and albums, while independent of an audio format (Group et al., 2005). The generic neural network model will then be used as an example of black-box attacks on many popular real-world systems, in this case, YouTube and AudioTag. <br /> <br /> The generic neural network model consists of two convolutional layers and a max-pooling layer, which is used for dimension reduction. This is depicted in the figure below. As mentioned above, the convolutional neural network is well-known for its properties of temporal locality and transformational invariance. The purpose of this network is to generate audio fingerprinting signals that extract features that uniquely identify a signal, regardless of the starting and ending times of the inputs.<br /> <br /> [[File:cov network.png | thumb | center | 500px ]]<br /> <br /> While an audio sample enters the neural network, it is first transformed by the initial network layer, which can be described as a normalized Hann function. The form of the function is shown below, with N being the width of the Kernel. <br /> <br /> $$f_{1}(n)=\frac {\sin^2(\frac{\pi n} {N})} {\sum_{i=0}^N \sin^2(\frac{\pi i}{N})}$$ <br /> <br /> The intention of the normalized Hann function is to smooth the adversarial perturbation of the input audio signal, which removes the discontinuity as well as the bad spectral properties. This transformation enhances the efficiency of black-box attacks that is later implemented.<br /> <br /> The next convolutional layer applies a Short Term Fourier Transformation to the input signal by computing the spectrogram of the waveform and converts the input into a feature representation. Once the input signal enters this network layer, it is being transformed by the convolutional function below. <br /> <br /> $$f_{2}(k,n)=e^{-i 2 \pi k n / N}$$<br /> where k &lt;math&gt;{\in}&lt;/math&gt; 0,1,...,N-1 (output channel index) and n &lt;math&gt;{\in}&lt;/math&gt; 0,1,...,N-1 (index of filter coefficient)<br /> <br /> The output of this layer is described as φ(x) (x being the input signal), a feature representation of the audio signal sample. <br /> However, this representation is flawed due to its vulnerability to noise and perturbation, as well as its difficulty to store and inspect. Therefore, a maximum pooling layer is being implemented to φ(x), in which the network computes a local maximum using a max-pooling function to become robust to changes in the position of the feature. This network layer outputs a binary fingerprint ψ (x) (x being the input signal) that will be used later to search for a signal against a database of previously processed signals.<br /> <br /> === Formulating the adversarial loss function ===<br /> <br /> In the previous section, local maxima of the spectrogram are used to generate fingerprints by CNN, but a loss has not been quantified to compare how similar two fingerprints are. After the loss is found, standard gradient methods can be used to find a perturbation &lt;math&gt;{\delta}&lt;/math&gt;, which can be added to a signal so that the copyright detection system will be tricked. Also, a bound is set to make sure the generated fingerprints are close enough to the original audio signal. <br /> $$\text{bound:}\ ||\delta||_p\le\epsilon$$<br /> <br /> where &lt;math&gt;{||\delta||_p\le\epsilon}&lt;/math&gt; is the &lt;math&gt;{l_p}&lt;/math&gt;-norm of the perturbation and &lt;math&gt;{\epsilon}&lt;/math&gt; is the bound of the difference between the original file and the adversarial example. <br /> <br /> <br /> To compare how similar two binary fingerprints are, Hamming distance is employed. Hamming distance between two strings is the number of digits that are different (Hamming distance, 2020). For example, the Hamming distance between 101100 and 100110 is 2. <br /> <br /> Let &lt;math&gt;{\psi(x)}&lt;/math&gt; and &lt;math&gt;{\psi(y)}&lt;/math&gt; be two binary fingerprints outputted from the model, the number of peaks shared by &lt;math&gt;{x}&lt;/math&gt; and &lt;math&gt;{y}&lt;/math&gt; can be found through &lt;math&gt;{|\psi(x)\cdot\psi(y)|}&lt;/math&gt;. Now, to get a differentiable loss function, the equation is found to be <br /> <br /> $$J(x,y)=|\phi(x)\cdot\psi(x)\cdot\psi(y)|$$<br /> <br /> <br /> This is effective for white-box attacks by knowing the fingerprinting system. However, the loss can be easily minimized by modifying the location of the peaks by one pixel, which would not be reliable to transfer to black-box industrial systems. To make it more transferable, a new loss function that involves more movements of the local maxima of the spectrogram is proposed. The idea is to move the locations of peaks in &lt;math&gt;{\psi(x)}&lt;/math&gt; outside of neighborhood of the peaks of &lt;math&gt;{\psi(y)}&lt;/math&gt;. In order to implement the model more efficiently, two max-pooling layers are used. One of the layers has a bigger width &lt;math&gt;{w_1}&lt;/math&gt; while the other one has a smaller width &lt;math&gt;{w_2}&lt;/math&gt;. For any location, if the output of &lt;math&gt;{w_1}&lt;/math&gt; pooling is strictly greater than the output of &lt;math&gt;{w_2}&lt;/math&gt; pooling, then it can be concluded that no peak is in that location with radius &lt;math&gt;{w_2}&lt;/math&gt;. <br /> <br /> The loss function is as the following:<br /> <br /> $$J(x,y) = \sum_i\bigg(\text{ReLU}\bigg(c-\bigg(\underset{|j| \leq w_1}{\max}\phi(i+j;x)-\underset{|j| \leq w_2}{\max}\phi(i+j;x)\bigg)\bigg)\cdot\psi(i;y)\bigg)$$<br /> The equation above penalizes the peaks of &lt;math&gt;{x}&lt;/math&gt; which are in neighborhood of peaks of &lt;math&gt;{y}&lt;/math&gt; with radius of &lt;math&gt;{w_2}&lt;/math&gt;. The activation function uses &lt;math&gt;{ReLU}&lt;/math&gt;. &lt;math&gt;{c}&lt;/math&gt; is the difference between the outputs of two max-pooling layers. <br /> <br /> <br /> Lastly, instead of the maximum operator, smoothed max function is used here:<br /> $$S_\alpha(x_1,x_2,...,x_n) = \frac{\sum_{i=1}^{n}x_ie^{\alpha x_i}}{\sum_{i=1}^{n}e^{\alpha x_i}}$$<br /> where &lt;math&gt;{\alpha}&lt;/math&gt; is a smoothing hyper parameter. When &lt;math&gt;{\alpha}&lt;/math&gt; approaches positive infinity, &lt;math&gt;{S_\alpha}&lt;/math&gt; is closer to the actual max function. <br /> <br /> To summarize, the optimization problem can be formulated as the following:<br /> <br /> $$<br /> \underset{\delta}{\min}J(x+\delta,x)\\<br /> s.t.||\delta||_{\infty}\le\epsilon<br />$$<br /> where &lt;math&gt;{x}&lt;/math&gt; is the input signal, &lt;math&gt;{J}&lt;/math&gt; is the loss function with the smoothed max function. Note that &lt;math&gt;||\delta||_\infty = \max_k |\delta_k|&lt;/math&gt; (the largest component of &lt;math&gt;\delta&lt;/math&gt;) which makes it relatively easy to satisfy the above constraint by clipping the values of each iteration of &lt;math&gt;\delta&lt;/math&gt; to be less than &lt;math&gt;\epsilon&lt;/math&gt;. However, since &lt;math&gt;||\delta||_\infty \leq \dots \leq ||\delta||_2 \leq ||\delta||_1&lt;/math&gt; this choice of norm results in the loosest bound, and therefore admits a larger selection of perturbations &lt;math&gt;\delta&lt;/math&gt; than might be permitted by other choices of norms.<br /> <br /> === Remix adversarial examples===<br /> While solving the optimization problem, the resulted example would be able to fool the copyright detection system. But it could sound unnatural with the perturbations.<br /> <br /> Instead, the fingerprinting could be made in a more natural way (i.e., a different audio signal). <br /> <br /> By modifying the loss function, which switches the order of the max-pooling layers in the smooth maximum components in the loss function, this remix loss function is to make two signals x and y look as similar as possible.<br /> <br /> $$J_{remix}(x,y) = \sum_i\bigg(ReLU\bigg(c-\bigg(\underset{|j| \leq w_2}{\max}\phi(i+j;x)-\underset{|j| \leq w_1}{\max}\phi(i+j;x)\bigg)\bigg)\cdot\psi(i;y)\bigg)$$<br /> <br /> By adding this new loss function, a new optimization problem could be defined. <br /> <br /> $$<br /> \underset{\delta}{\min}J(x+\delta,x) + \lambda J_{remix}(x+\delta,y)\\<br /> s.t.||\delta||_{p}\le\epsilon<br />$$<br /> <br /> where &lt;math&gt;{\lambda}&lt;/math&gt; is a scalar parameter that controls the similarity of &lt;math&gt;{x+\delta}&lt;/math&gt; and &lt;math&gt;{y}&lt;/math&gt;.<br /> <br /> This optimization problem is able to generate an adversarial example from the selected source, and also enforce the adversarial example to be similar to another signal. The resulting adversarial example is called Remix adversarial example because it gets the references to its source signal and another signal.<br /> <br /> == Evaluating transfer attacks on industrial systems==<br /> The effectiveness of default and remix adversarial examples is tested through white-box attacks on the proposed model and black-box attacks on two real-world audio copyright detection systems - AudioTag and YouTube “Content ID” system. &lt;math&gt;{l_{\infty}}&lt;/math&gt; norm and &lt;math&gt;{l_{2}}&lt;/math&gt; norm of perturbations are two measures of modification. Both of them are calculated after normalizing the signals so that the samples could lie between 0 and 1.<br /> <br /> Before evaluating black-box attacks against real-world systems, white-box attacks against our own proposed model is used to provide the baseline of adversarial examples’ effectiveness. Loss function &lt;math&gt;{J(x,y)=|\phi(x)\cdot\psi(x)\cdot\psi(y)|}&lt;/math&gt; is used to generate white-box attacks. The unnoticeable fingerprints of the audio with the noise can be changed or removed by optimizing the loss function.<br /> <br /> [[File:Table_1_White-box.jpg |center ]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Table 1: Norms of the perturbations for white-box attacks&lt;/div&gt;<br /> <br /> In black-box attacks, by applying random perturbations to the audio recordings, AudioTag’s claim of being robust to input<br /> distortions was verified. However, the AudioTag system is found to be relatively sensitive to the attacks since it can detect the songs with a benign signal while it failed to detect both default and remix adversarial examples. The architecture of the AudioTag fingerprint model and surrogate CNN model is guessed to be similar based on the experimental observations. <br /> <br /> Similar to AudioTag, the YouTube “Content ID” system also got the result with successful identification of benign songs but failure to detect adversarial examples. However, to fool the YouTube Content ID system, a larger value of the parameter &lt;math&gt;{\epsilon}&lt;/math&gt; is required, which makes perturbations obvious although songs can still be recognized by humans. YouTube Content ID system has a more robust fingerprint model.<br /> <br /> <br /> [[File:Table_2_Black-box.jpg |center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Table 2: Norms of the perturbations for black-box attacks&lt;/div&gt;<br /> <br /> [[File:YouTube_Figure.jpg |center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 2: YouTube’s copyright detection recall against the magnitude of noise&lt;/div&gt;<br /> <br /> == Conclusion ==<br /> In this paper, we obtain that many industrial copyright detection systems used in popular video and music websites, such as YouTube and AudioTag, are significantly vulnerable to adversarial attacks established in the existing literature. By building a simple music identification system resembling that of Shazam using a neural network and attack it by the well-known gradient method, this paper firmly proved the lack of robustness of the current online detector. <br /> <br /> Although the method used in the paper isn't optimal, the attacks can be strengthened using sharper technical. Also, we could transfer attacks using rudimentary surrogate models that rely on hand-crafted features, while commercial systems likely rely on trainable neural nets.<br /> <br /> Our goal here is not to facilitate but the intention of this paper is to raise the awareness of the vulnerability of the current online system to adversarial attacks and to emphasize the significance of copyright detection system. A number of mitigating approaches already exist, such as adversarial training, but they need to be further developed and examined in order to robustly protect against the threat of adversarial copyright attacks.<br /> <br /> == Appendix ==<br /> === Feature Extraction Process in Audio-Fingerprinting System ===<br /> <br /> 1. Preprocessing. In this step, the audio signal is digitalized and quantized at first.<br /> Then, it is converted to a mono signal by averaging two channels if necessary.<br /> Finally, it is resampled if the sampling rate is different from the target rate.<br /> <br /> 2. Framing. Framing means dividing the audio signal into frames of equal length<br /> by a window function.<br /> <br /> 3. Transformation. This step is designed to transform the set of frames into a new set<br /> of features, in order to reduce the redundancy. <br /> <br /> 4. Feature Extraction. After transformation, final acoustic features are extracted<br /> from the time-frequency representation. The main purpose is to reduce the<br /> dimensionality and increase the robustness to distortions.<br /> <br /> 5. Post-processing. To capture the temporal variations of the audio signal, higher<br /> order time derivatives are required sometimes.<br /> <br /> == Critiques ==<br /> - The experiments in this paper appear to be a proof-of-concept rather than a serious evaluation of a model. One problem is that the norm is used to evaluate the perturbation. Unlike the norm in image domains which can be visualized and easily understood, the perturbations in the audio domain are more difficult to comprehend. A cognitive study or something like a user study might need to be conducted in order to understand this. Another question related to this is that if the random noise is 2x bigger or 3x bigger in terms of the norm, does this make a huge difference when listening to it? Are these two perturbations both very obvious or unnoticeable? In addition, it seems that a dataset is built but the stats are missing. Third, no baseline methods are being compared to in this paper, not even an ablation study. The proposed two methods (default and remix) seem to perform similarly.<br /> <br /> - There could be an improvement in term of how to find the threshold in general, it mentioned how to measure the similarity of two pieces of content but have not discussed what threshold should we set for this model. In fact, it is always a challenge to determine the boundary of &quot;Copyright Issue&quot; or &quot;Not Copyright Issue&quot; and this is some important information that may be discussed in the paper.<br /> <br /> - The fingerprinting technique used in this paper seems rather elementary, which is a downfall in this context because the focus of this paper is adversarial attacks on these methods. A recent 2019 work (https://arxiv.org/pdf/1907.12956.pdf) proposed a deep fingerprinting algorithm along with some novel framing of the problem. There are several other older works in this area that also give useful insights that would have improved the algorithm in this paper.<br /> <br /> - In the experiment section, authors could provide more background information on the dataset used. For example, the number of songs in the dataset and a brief introduction of different features.<br /> <br /> - Since the paper didn't go into details of how features are extracted in an audio-fingerprinting system, the details are listed out above in &quot;Feature Extraction Process in Audio-Fingerprinting System&quot;<br /> <br /> - In addition to Audio files, can this system detect copyright attacks on mixed data such as say, embedded audio files in the text? It will be interesting to see if it can do it. Nowadays, a lot of data is coming in mixed form, e.g. text+video, audio+text etc and therefore having a system to detect adversarial attacks on copyright detection systems for mixed data will be a useful development.<br /> <br /> - When introducing the types of copyright detection systems, there is a lack of clearness in explaining fingerprinting algorithms for audios and images. Besides a brief, one-line explanation, justifications regarding why audio fingerprinting algorithms are better compared to video fingerprinting algorithms were not provided. Moreover, discussions regarding image fingerprinting algorithms were missing. Hence, it would be beneficial to add these two sections to enhance the readers' understanding of this summary.<br /> <br /> == References ==<br /> <br /> Group, P., Cano, P., Group, M., Group, E., Batlle, E., Ton Kalker Philips Research Laboratories Eindhoven, . . . Authors: Pedro Cano Music Technology Group. (2005, November 01). A Review of Audio Fingerprinting. Retrieved November 13, 2020, from https://dl.acm.org/doi/10.1007/s11265-005-4151-3<br /> <br /> Hamming distance. (2020, November 1). In ''Wikipedia''. https://en.wikipedia.org/wiki/Hamming_distance<br /> <br /> Jovanovic. (2015, February 2). ''How does Shazam work? Music Recognition Algorithms, Fingerprinting, and Processing''. Toptal Engineering Blog. https://www.toptal.com/algorithms/shazam-it-music-processing-fingerprinting-and-recognition<br /> <br /> Saadatpanah, P., Shafahi, A., &amp;amp; Goldstein, T. (2019, June 17). ''Adversarial attacks on copyright detection systems''. Retrieved November 13, 2020, from https://arxiv.org/abs/1906.07153.<br /> <br /> Saviaga, C. and Toxtli, C. ''Deepiracy: Video piracy detection system by using longest common subsequence and deep learning'', 2018. https://medium.com/hciwvu/piracy-detection-using-longestcommon-subsequence-and-neuralnetworks-a6f689a541a6<br /> <br /> Wang, A. et al. ''An industrial strength audio search algorithm''. In Ismir, volume 2003, pp. 7–13. Washington, DC, 2003.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs&diff=47820 Neural ODEs 2020-11-29T21:33:53Z <p>Z47shen: /* Scope and Limitations */</p> <hr /> <div>== Introduction ==<br /> Chen et al. propose a new class of neural networks called neural ordinary differential equations (ODEs) in their 2018 paper under the same title. Neural network models, such as residual or recurrent networks, can be generalized as a set of transformations through hidden states (a.k.a layers) &lt;math&gt;\mathbf{h}&lt;/math&gt;, given by the equation <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \mathbf{h}_{t+1} = \mathbf{h}_t + f(\mathbf{h}_t,\theta_t) &lt;/math&gt; (1) &lt;/div&gt;<br /> <br /> where &lt;math&gt;t \in \{0,...,T\}&lt;/math&gt; and &lt;math&gt;\theta_t&lt;/math&gt; corresponds to the set of parameters or weights in state &lt;math&gt;t&lt;/math&gt;. It is important to note that it has been shown (Lu et al., 2017)(Haber<br /> and Ruthotto, 2017)(Ruthotto and Haber, 2018) that Equation 1 can be viewed as an Euler discretization. Given this Euler description, if the number of layers and step size between layers are taken to their limits, then Equation 1 can instead be described continuously in the form of the ODE, <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \frac{d\mathbf{h}(t)}{dt} = f(\mathbf{h}(t),t,\theta) &lt;/math&gt; (2). &lt;/div&gt;<br /> <br /> Equation 2 now describes a network where the output layer &lt;math&gt;\mathbf{h}(T)&lt;/math&gt; is generated by solving for the ODE at time &lt;math&gt;T&lt;/math&gt;, given the initial value at &lt;math&gt;t=0&lt;/math&gt;, where &lt;math&gt;\mathbf{h}(0)&lt;/math&gt; is the input layer of the network. <br /> <br /> With a vast amount of theory and research in the field of solving ODEs numerically, there are a number of benefits to formulating the hidden state dynamics this way. One major advantage is that a continuous description of the network allows for the calculation of &lt;math&gt;f&lt;/math&gt; at arbitrary intervals and locations. The authors provide an example in section five of how the neural ODE network outperforms the discretized version i.e. residual networks, by taking advantage of the continuity of &lt;math&gt;f&lt;/math&gt;. A depiction of this distinction is shown in the figure below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; [[File:NeuralODEs_Fig1.png|350px]] &lt;/div&gt;<br /> <br /> In section four the authors show that the single-unit bottleneck of normalizing flows can be overcome by constructing a new class of density models that incorporates the neural ODE network formulation.<br /> The next section on automatic differentiation will describe how utilizing ODE solvers allows for the calculation of gradients of the loss function without storing any of the hidden state information. This results in a very low memory requirement for neural ODE networks in comparison to traditional networks that rely on intermediate hidden state quantities for backpropagation.<br /> <br /> == Reverse-mode Automatic Differentiation of ODE Solutions ==<br /> Like most neural networks, optimizing the weight parameters &lt;math&gt;\theta&lt;/math&gt; for a neural ODE network involves finding the gradient of a loss function with respect to those parameters. Differentiating in the forward direction is a simple task, however, this method is very computationally expensive and unstable, as it introduces additional numerical error. Instead, the authors suggest that the gradients can be calculated in the reverse-mode with the adjoint sensitivity method (Pontryagin et al., 1962). This &quot;backpropagation&quot; method solves an augmented version of the forward ODE problem but in reverse, which is something that all ODE solvers are capable of. Section 3 provides results showing that this method gives very desirable memory costs and numerical stability. <br /> <br /> The authors provide an example of the adjoint method by considering the minimization of the scalar-valued loss function &lt;math&gt;L&lt;/math&gt;, which takes the solution of the ODE solver as its argument.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs_Eq1.png|700px]],&lt;/div&gt; <br /> This minimization problem requires the calculation of &lt;math&gt;\frac{\partial L}{\partial \mathbf{z}(t_0)}&lt;/math&gt; and &lt;math&gt;\frac{\partial L}{\partial \theta}&lt;/math&gt;.<br /> <br /> The adjoint itself is defined as &lt;math&gt;\mathbf{a}(t) = \frac{\partial L}{\partial \mathbf{z}(t)}&lt;/math&gt;, which describes the gradient of the loss with respect to the hidden state &lt;math&gt;\mathbf{z}(t)&lt;/math&gt;. By taking the first derivative of the adjoint, another ODE arises in the form of,<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;\frac{d \mathbf{a}(t)}{dt} = -\mathbf{a}(t)^T \frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \mathbf{z}}&lt;/math&gt; (3).&lt;/div&gt; <br /> <br /> Since the value &lt;math&gt;\mathbf{a}(t_0)&lt;/math&gt; is required to minimize the loss, the ODE in equation 3 must be solved backwards in time from &lt;math&gt;\mathbf{a}(t_1)&lt;/math&gt;. Solving this problem is dependent on the knowledge of the hidden state &lt;math&gt;\mathbf{z}(t)&lt;/math&gt; for all &lt;math&gt;t&lt;/math&gt;, which an neural ODE does not save on the forward pass. Luckily, both &lt;math&gt;\mathbf{a}(t)&lt;/math&gt; and &lt;math&gt;\mathbf{z}(t)&lt;/math&gt; can be calculated in reverse, at the same time, by setting up an augmented version of the dynamics and is shown in the final algorithm. Finally, the derivative &lt;math&gt;dL/d\theta&lt;/math&gt; can be expressed in terms of the adjoint and the hidden state as, <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \frac{dL}{d\theta} -\int_{t_1}^{t_0} \mathbf{a}(t)^T\frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \theta}dt&lt;/math&gt; (4).&lt;/div&gt;<br /> <br /> To obtain very inexpensive calculations of &lt;math&gt;\frac{\partial f}{\partial z}&lt;/math&gt; and &lt;math&gt;\frac{\partial f}{\partial \theta}&lt;/math&gt; in equation 3 and 4, automatic differentiation can be utilized. The authors present an algorithm to calculate the gradients of &lt;math&gt;L&lt;/math&gt; and their dependent quantities with only one call to an ODE solver and is shown below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Algorithm1.png|850px]]&lt;/div&gt;<br /> <br /> If the loss function has a stronger dependence on the hidden states for &lt;math&gt;t \neq t_0,t_1&lt;/math&gt;, then Algorithm 1 can be modified to handle multiple calls to the ODESolve step since most ODE solvers have the capability to provide &lt;math&gt;z(t)&lt;/math&gt; at arbitrary times. A visual depiction of this scenario is shown below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODES Fig2.png|350px]]&lt;/div&gt;<br /> <br /> Please see the [https://arxiv.org/pdf/1806.07366.pdf#page=13 appendix] for extended versions of Algorithm 1 and detailed derivations of each equation in this section.<br /> <br /> == Replacing Residual Networks with ODEs for Supervised Learning ==<br /> Section three of the paper investigates an application of the reverse-mode differentiation described in section two, for the training of neural ODE networks on the MNIST digit data set. To solve for the forward pass in the neural ODE network, the following experiment used Adams-Moulton (AM) method, which is an implicit ODE solver. Although it has a marked improvement over explicit ODE solvers in numerical accuracy, integrating backward through the network for backpropagation is still not preferred and the adjoint sensitivity method is used to perform efficient weight optimization. The network with this &quot;backpropagation&quot; technique is referred to as ODE-Net in this section. <br /> <br /> === Implementation ===<br /> A residual network (ResNet), studied by He et al. (2016), with six standard residual blocks was used as a comparative model for this experiment. The competing model, ODE-net, replaces the residual blocks of the ResNet with the AM solver. As a hybrid of the two models ResNet and ODE-net, a third network was created called RK-Net, which solves the weight optimization of the neural ODE network explicitly through backward Runge-Kutta integration. The following table shows the training and performance results of each network. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Table1.png|400px]]&lt;/div&gt;<br /> <br /> Note that &lt;math&gt;L&lt;/math&gt; and &lt;math&gt;\tilde{L}&lt;/math&gt; are the number of layers in ResNet and the number of function calls that the AM method makes for the two ODE networks and are effectively analogous quantities. As shown in Table 1, both of the ODE networks achieve comparable performance to that of the ResNet with a notable decrease in memory cost for ODE-net.<br /> <br /> <br /> Another interesting component of ODE networks is the ability to control the tolerance in the ODE solver used and subsequently the numerical error in the solution. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Fig3.png|700px]]&lt;/div&gt;<br /> <br /> The tolerance of the ODE solver is represented by the colour bar in Figure 3 above and notice that a variety of effects arise from adjusting this parameter. Primarily, if one was to treat the tolerance as a hyperparameter of sorts, you could tune it such that you find a balance between accuracy (Figure 3a) and computational complexity (Figure 3b). Figure 3c also provides further evidence for the benefits of the adjoint method for the backward pass in ODE-nets since there is a nearly 1:0.5 ratio of forward to backward function calls. In the ResNet and RK-Net examples, this ratio is 1:1.<br /> <br /> Additionally, the authors loosely define the concept of depth in a neural ODE network by referring to Figure 3d. Here it's evident that as you continue to train an ODE network, the number of function evaluations the ODE solver performs increases. As previously mentioned, this quantity is comparable to the network depth of a discretized network. However, as the authors note, this result should be seen as the progression of the network's complexity over training epochs, which is something we expect to increase over time.<br /> <br /> == Continuous Normalizing Flows ==<br /> <br /> Section four tackles the implementation of continuous-depth Neural Networks, but to do so, in the first part of section four the authors discuss theoretically how to establish this kind of network through the use of normalizing flows. The authors use a change of variables method presented in other works (Rezende and Mohamed, 2015), (Dinh et al., 2014), to compute the change of a probability distribution if sample points are transformed through a bijective function, &lt;math&gt;f&lt;/math&gt;.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;z_1=f(z_0) \Rightarrow \log⁡(p(z_1))=\log⁡(p(z_0))-\log⁡|\det⁡\frac{\partial f}{\partial z_0}|&lt;/math&gt;&lt;/div&gt;<br /> <br /> Where p(z) is the probability distribution of the samples and &lt;math&gt;det⁡\frac{\partial f}{\partial z_0}&lt;/math&gt; is the determinant of the Jacobian which has a cubic cost in the dimension of '''z''' or the number of hidden units in the network. The authors discovered however that transforming the discrete set of hidden layers in the normalizing flow network to continuous transformations simplifies the computations significantly, due primarily to the following theorem:<br /> <br /> '''''Theorem 1:''' (Instantaneous Change of Variables). Let z(t) be a finite continuous random variable with probability p(z(t)) dependent on time. Let dz/dt=f(z(t),t) be a differential equation describing a continuous-in-time transformation of z(t). Assuming that f is uniformly Lipschitz continuous in z and continuous in t, then the change in log probability also follows a differential equation:''<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;\frac{\partial \log(p(z(t)))}{\partial t}=-tr\left(\frac{df}{dz(t)}\right)&lt;/math&gt;&lt;/div&gt;<br /> <br /> The biggest advantage to using this theorem is that the trace function is a linear function, so if the dynamics of the problem, f, is represented by a sum of functions, then so is the log density. This essentially means that you can now compute flow models with only a linear cost with respect to the number of hidden units, &lt;math&gt;M&lt;/math&gt;. In standard normalizing flow models, the cost is &lt;math&gt;O(M^3)&lt;/math&gt;, so they will generally fit many layers with a single hidden unit in each layer.<br /> <br /> Finally the authors use these realizations to construct Continuous Normalizing Flow networks (CNFs) by specifying the parameters of the flow as a function of ''t'', ie, &lt;math&gt;f(z(t),t)&lt;/math&gt;. They also use a gating mechanism for each hidden unit, &lt;math&gt;\frac{dz}{dt}=\sum_n \sigma_n(t)f_n(z)&lt;/math&gt; where &lt;math&gt;\sigma_n(t)\in (0,1)&lt;/math&gt; is a separate neural network which learns when to apply each dynamic &lt;math&gt;f_n&lt;/math&gt;.<br /> <br /> ===Implementation===<br /> <br /> The authors construct two separate types of neural networks to compare against each other, the first is the standard planar Normalizing Flow network (NF) using 64 layers of single hidden units, and the second is their new CNF with 64 hidden units. The NF model is trained over 500,000 iterations using RMSprop, and the CNF network is trained over 10,000 iterations using Adam(algorithm for first-order gradient-based optimization of stochastic objective functions). The loss function is &lt;math&gt;KL(q(x)||p(x))&lt;/math&gt; where &lt;math&gt;q(x)&lt;/math&gt; is the flow model and &lt;math&gt;p(x)&lt;/math&gt; is the target probability density.<br /> <br /> One of the biggest advantages when implementing CNF is that you can train the flow parameters just by performing maximum likelihood estimation on &lt;math&gt;\log(q(x))&lt;/math&gt; given &lt;math&gt;p(x)&lt;/math&gt;, where &lt;math&gt;q(x)&lt;/math&gt; is found via the theorem above, and then reversing the CNF to generate random samples from &lt;math&gt;q(x)&lt;/math&gt;. This reversal of the CNF is done with about the same cost of the forward pass which is not able to be done in an NF network. The following two figures demonstrate the ability of CNF to generate more expressive and accurate output data as compared to standard NF networks.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:CNFcomparisons.png]]<br /> <br /> [[Image:CNFtransitions.png]]<br /> &lt;/div&gt;<br /> <br /> Figure 4 shows clearly that the CNF structure exhibits significantly lower loss functions than NF. In figure 5 both networks were tasked with transforming a standard Gaussian distribution into a target distribution, not only was the CNF network more accurate on the two moons target, but also the steps it took along the way are much more intuitive than the output from NF.<br /> <br /> == A Generative Latent Function Time-Series Model ==<br /> <br /> One of the largest issues at play in terms of Neural ODE networks is the fact that in many instances, data points are either very sparsely distributed, or irregularly-sampled. The latent dynamics are discretized and the observations are in the bins of fixed duration. This creates issues with missing data and ill-defined latent variables. An example of this is medical records which are only updated when a patient visits a doctor or the hospital. To solve this issue the authors had to create a generative time-series model which would be able to fill in the gaps of missing data. The authors consider each time series as a latent trajectory stemming from the initial local state &lt;math&gt;z_{t_0 }&lt;/math&gt; and determined from a global set of latent parameters. Given a set of observation times and initial state, the generative model constructs points via the following sample procedure:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> &lt;math&gt;<br /> z_{t_0}∼p(z_{t_0}) <br /> &lt;/math&gt;<br /> &lt;/div&gt; <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> &lt;math&gt;<br /> z_{t_1},z_{t_2},\dots,z_{t_N}={\rm ODESolve}(z_{t_0},f,θ_f,t_0,...,t_N)<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> each <br /> &lt;math&gt;<br /> x_{t_i}∼p(x│z_{t_i},θ_x)<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;math&gt;f&lt;/math&gt; is a function which outputs the gradient &lt;math&gt;\frac{\partial z(t)}{\partial t}=f(z(t),θ_f)&lt;/math&gt; which is parameterized via a neural net. In order to train this latent variable model, the authors had to first encode their given data and observation times using an RNN encoder, construct the new points using the trained parameters, then decode the points back into the original space. The following figure describes this process:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:EncodingFigure.png]]<br /> &lt;/div&gt;<br /> <br /> Another variable which could affect the latent state of a time-series model is how often an event actually occurs. The authors solved this by parameterizing the rate of events in terms of a Poisson process. They described the set of independent observation times in an interval &lt;math&gt;\left[t_{start},t_{end}\right]&lt;/math&gt; as:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; <br /> &lt;math&gt;<br /> {\rm log}⁡(p(t_1,t_2,\dots,t_N ))=\sum_{i=1}^N{\rm log}⁡(\lambda(z(t_i)))-\int_{t_{start}}^{t_{end}}λ(z(t))dt<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> where &lt;math&gt;\lambda(*)&lt;/math&gt; is parameterized via another neural network.<br /> <br /> ===Implementation===<br /> <br /> To test the effectiveness of the Latent time-series ODE model (LODE), they fit the encoder with 25 hidden units, parametrize function f with a one-layer 20 hidden unit network, and the decoder as another neural network with 20 hidden units. They compare this against a standard recurrent neural net (RNN) with 25 hidden units trained to minimize Gaussian log-likelihood. The authors tested both of these network systems on a dataset of 2-dimensional spirals which either rotated clockwise or counter-clockwise and sampled the positions of each spiral at 100 equally spaced time steps. They can then simulate irregularly timed data by taking random amounts of points without replacement from each spiral. The next two figures show the outcome of these experiments:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:LODEtestresults.png]] [[Image:SpiralFigure.png|The blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model]]<br /> &lt;/div&gt;<br /> <br /> In the figure on the right the blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model. It is noted that the LODE performs significantly better than the standard RNN model, especially on smaller sets of data points.<br /> <br /> == Scope and Limitations ==<br /> <br /> This part mainly discusses the scope and limitations of the paper. Firstly, while “batching” the training data is a useful step in standard neural nets, and can still be applied here by combining the ODEs associated with each batch, the authors found that controlling the error, in this case, may increase the number of calculations required. In practice, however, the number of calculations did not increase significantly.<br /> <br /> So long as the model proposed in this paper uses finite weights and Lipschitz nonlinearities, Picard’s existence theorem (Coddington and Levinson, 1955) applies, which guarantees that the solution to the IVP exists and is unique. This theorem holds for the model presented above when the network has finite weights and uses nonlinearities in the Lipshitz class. <br /> <br /> In controlling the amount of error in the model, the authors were only able to reduce tolerances to approximately &lt;math&gt;10^{-3}&lt;/math&gt; and &lt;math&gt;10^{-5}&lt;/math&gt; in classification and density estimation respectively without also degrading the computational performance.<br /> <br /> The authors believe that reconstructing state trajectories by running the dynamics backwards can introduce extra numerical error. They address a possible solution to this problem by checkpointing certain time steps and storing intermediate values of z on the forward pass. Then while reconstructing, you do each part individually between checkpoints. The authors acknowledged that they informally checked the validity of this method since they don’t consider it a practical problem.<br /> <br /> There remain, however, areas where standard neural networks may perform better than Neural ODEs. Firstly, conventional nets can fit non-homeomorphic functions, for example, functions whose output has a smaller dimension that their input, or that change the topology of the input space. However, this could be handled by composing ODE nets with standard network layers. Another point is that conventional nets can be evaluated exactly with a fixed amount of computation, and are typically faster to train, and do not require an error tolerance for a solver.<br /> <br /> == Conclusions and Critiques ==<br /> <br /> We covered the use of black-box ODE solvers as a model component and their application to initial value problems constructed from real applications​. Neural ODE Networks show promising gains in computational cost without large sacrifices in accuracy when applied to certain problems​. A drawback of some of these implementations is that the ODE Neural Networks are limited by the underlying distributions of the problems they are trying to solve (requirement of Lipschitz continuity, etc.)​. There are plenty of further advances to be made in this field as hundreds of years of ODE theory and literature is available, so this is currently an important area of research.<br /> <br /> ODEs indeed represent an important area of applied mathematics where neural networks can be used to solve them numerically. Perhaps, a parallel area of investigation can be PDEs (Partial Differential Equations). PDEs are also widely encountered in many areas of applied mathematics, physics, social sciences, and many other fields. It will be interesting to see how neural networks can be used to solve PDEs.<br /> <br /> == More Critiques ==<br /> <br /> This paper covers the memory efficiency of Neural ODE Networks, but does not address runtime. In practice, most systems are bound by latency requirements more-so than memory requirements (except in edge device cases). Though it may be unreasonable to expect the authors to produce a performance-optimized implementation, it would be insightful to understand the computational bottlenecks so existing frameworks can take steps to address them. This model looks promising and practical performance is the key to enabling future research in this.<br /> <br /> The above critique also questions the need for a neural network for such a problem. This problem was studied by Brunel et al. and they presented their solution in their paper ''Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions''. While this solution also requires iteratively solving a complex optimization problem, they did not require the massive memory and runtime overhead of a neural network. For the neural network solution to demonstrate its potential, it should be including experimental comparisons with specialized ordinary differential equation algorithms instead of simply comparing with a general recurrent neural network.<br /> <br /> Table 2 shows that potential ODEs have lower predicted RMSE, and more relevant information should be provided. For example, the reason of setting the n to 30/50/100 can be simply described. And it is good to talk more about the performance of Latent ODE since the change of n does not have much impact on its RMSE.<br /> <br /> == References ==<br /> Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong. Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations. ''arXiv preprint arXiv'':1710.10121, 2017.<br /> <br /> Eldad Haber and Lars Ruthotto. Stable architectures for deep neural networks. ''Inverse Problems'', 34 (1):014004, 2017.<br /> <br /> Lars Ruthotto and Eldad Haber. Deep neural networks motivated by partial differential equations. ''arXiv preprint arXiv'':1804.04272, 2018.<br /> <br /> Lev Semenovich Pontryagin, EF Mishchenko, VG Boltyanskii, and RV Gamkrelidze. ''The mathematical theory of optimal processes''. 1962.<br /> <br /> Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In ''European conference on computer vision'', pages 630–645. Springer, 2016b.<br /> <br /> Earl A Coddington and Norman Levinson. ''Theory of ordinary differential equations''. Tata McGrawHill Education, 1955.<br /> <br /> Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. ''arXiv preprint arXiv:1505.05770'', 2015.<br /> <br /> Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear independent components estimation. ''arXiv preprint arXiv:1410.8516'', 2014.<br /> <br /> Brunel, N. J., Clairon, Q., &amp; d’Alché-Buc, F. (2014). Parametric estimation of ordinary differential equations with orthogonality conditions. ''Journal of the American Statistical Association'', 109(505), 173-185.<br /> <br /> A. Iserles. A first course in the numerical analysis of differential equations. Cambridge Texts in Applied Mathematics, second edition, 2009</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs&diff=47819 Neural ODEs 2020-11-29T21:29:59Z <p>Z47shen: /* More Critiques */</p> <hr /> <div>== Introduction ==<br /> Chen et al. propose a new class of neural networks called neural ordinary differential equations (ODEs) in their 2018 paper under the same title. Neural network models, such as residual or recurrent networks, can be generalized as a set of transformations through hidden states (a.k.a layers) &lt;math&gt;\mathbf{h}&lt;/math&gt;, given by the equation <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \mathbf{h}_{t+1} = \mathbf{h}_t + f(\mathbf{h}_t,\theta_t) &lt;/math&gt; (1) &lt;/div&gt;<br /> <br /> where &lt;math&gt;t \in \{0,...,T\}&lt;/math&gt; and &lt;math&gt;\theta_t&lt;/math&gt; corresponds to the set of parameters or weights in state &lt;math&gt;t&lt;/math&gt;. It is important to note that it has been shown (Lu et al., 2017)(Haber<br /> and Ruthotto, 2017)(Ruthotto and Haber, 2018) that Equation 1 can be viewed as an Euler discretization. Given this Euler description, if the number of layers and step size between layers are taken to their limits, then Equation 1 can instead be described continuously in the form of the ODE, <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \frac{d\mathbf{h}(t)}{dt} = f(\mathbf{h}(t),t,\theta) &lt;/math&gt; (2). &lt;/div&gt;<br /> <br /> Equation 2 now describes a network where the output layer &lt;math&gt;\mathbf{h}(T)&lt;/math&gt; is generated by solving for the ODE at time &lt;math&gt;T&lt;/math&gt;, given the initial value at &lt;math&gt;t=0&lt;/math&gt;, where &lt;math&gt;\mathbf{h}(0)&lt;/math&gt; is the input layer of the network. <br /> <br /> With a vast amount of theory and research in the field of solving ODEs numerically, there are a number of benefits to formulating the hidden state dynamics this way. One major advantage is that a continuous description of the network allows for the calculation of &lt;math&gt;f&lt;/math&gt; at arbitrary intervals and locations. The authors provide an example in section five of how the neural ODE network outperforms the discretized version i.e. residual networks, by taking advantage of the continuity of &lt;math&gt;f&lt;/math&gt;. A depiction of this distinction is shown in the figure below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; [[File:NeuralODEs_Fig1.png|350px]] &lt;/div&gt;<br /> <br /> In section four the authors show that the single-unit bottleneck of normalizing flows can be overcome by constructing a new class of density models that incorporates the neural ODE network formulation.<br /> The next section on automatic differentiation will describe how utilizing ODE solvers allows for the calculation of gradients of the loss function without storing any of the hidden state information. This results in a very low memory requirement for neural ODE networks in comparison to traditional networks that rely on intermediate hidden state quantities for backpropagation.<br /> <br /> == Reverse-mode Automatic Differentiation of ODE Solutions ==<br /> Like most neural networks, optimizing the weight parameters &lt;math&gt;\theta&lt;/math&gt; for a neural ODE network involves finding the gradient of a loss function with respect to those parameters. Differentiating in the forward direction is a simple task, however, this method is very computationally expensive and unstable, as it introduces additional numerical error. Instead, the authors suggest that the gradients can be calculated in the reverse-mode with the adjoint sensitivity method (Pontryagin et al., 1962). This &quot;backpropagation&quot; method solves an augmented version of the forward ODE problem but in reverse, which is something that all ODE solvers are capable of. Section 3 provides results showing that this method gives very desirable memory costs and numerical stability. <br /> <br /> The authors provide an example of the adjoint method by considering the minimization of the scalar-valued loss function &lt;math&gt;L&lt;/math&gt;, which takes the solution of the ODE solver as its argument.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs_Eq1.png|700px]],&lt;/div&gt; <br /> This minimization problem requires the calculation of &lt;math&gt;\frac{\partial L}{\partial \mathbf{z}(t_0)}&lt;/math&gt; and &lt;math&gt;\frac{\partial L}{\partial \theta}&lt;/math&gt;.<br /> <br /> The adjoint itself is defined as &lt;math&gt;\mathbf{a}(t) = \frac{\partial L}{\partial \mathbf{z}(t)}&lt;/math&gt;, which describes the gradient of the loss with respect to the hidden state &lt;math&gt;\mathbf{z}(t)&lt;/math&gt;. By taking the first derivative of the adjoint, another ODE arises in the form of,<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;\frac{d \mathbf{a}(t)}{dt} = -\mathbf{a}(t)^T \frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \mathbf{z}}&lt;/math&gt; (3).&lt;/div&gt; <br /> <br /> Since the value &lt;math&gt;\mathbf{a}(t_0)&lt;/math&gt; is required to minimize the loss, the ODE in equation 3 must be solved backwards in time from &lt;math&gt;\mathbf{a}(t_1)&lt;/math&gt;. Solving this problem is dependent on the knowledge of the hidden state &lt;math&gt;\mathbf{z}(t)&lt;/math&gt; for all &lt;math&gt;t&lt;/math&gt;, which an neural ODE does not save on the forward pass. Luckily, both &lt;math&gt;\mathbf{a}(t)&lt;/math&gt; and &lt;math&gt;\mathbf{z}(t)&lt;/math&gt; can be calculated in reverse, at the same time, by setting up an augmented version of the dynamics and is shown in the final algorithm. Finally, the derivative &lt;math&gt;dL/d\theta&lt;/math&gt; can be expressed in terms of the adjoint and the hidden state as, <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt; \frac{dL}{d\theta} -\int_{t_1}^{t_0} \mathbf{a}(t)^T\frac{\partial f(\mathbf{z}(t),t,\theta)}{\partial \theta}dt&lt;/math&gt; (4).&lt;/div&gt;<br /> <br /> To obtain very inexpensive calculations of &lt;math&gt;\frac{\partial f}{\partial z}&lt;/math&gt; and &lt;math&gt;\frac{\partial f}{\partial \theta}&lt;/math&gt; in equation 3 and 4, automatic differentiation can be utilized. The authors present an algorithm to calculate the gradients of &lt;math&gt;L&lt;/math&gt; and their dependent quantities with only one call to an ODE solver and is shown below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Algorithm1.png|850px]]&lt;/div&gt;<br /> <br /> If the loss function has a stronger dependence on the hidden states for &lt;math&gt;t \neq t_0,t_1&lt;/math&gt;, then Algorithm 1 can be modified to handle multiple calls to the ODESolve step since most ODE solvers have the capability to provide &lt;math&gt;z(t)&lt;/math&gt; at arbitrary times. A visual depiction of this scenario is shown below. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODES Fig2.png|350px]]&lt;/div&gt;<br /> <br /> Please see the [https://arxiv.org/pdf/1806.07366.pdf#page=13 appendix] for extended versions of Algorithm 1 and detailed derivations of each equation in this section.<br /> <br /> == Replacing Residual Networks with ODEs for Supervised Learning ==<br /> Section three of the paper investigates an application of the reverse-mode differentiation described in section two, for the training of neural ODE networks on the MNIST digit data set. To solve for the forward pass in the neural ODE network, the following experiment used Adams-Moulton (AM) method, which is an implicit ODE solver. Although it has a marked improvement over explicit ODE solvers in numerical accuracy, integrating backward through the network for backpropagation is still not preferred and the adjoint sensitivity method is used to perform efficient weight optimization. The network with this &quot;backpropagation&quot; technique is referred to as ODE-Net in this section. <br /> <br /> === Implementation ===<br /> A residual network (ResNet), studied by He et al. (2016), with six standard residual blocks was used as a comparative model for this experiment. The competing model, ODE-net, replaces the residual blocks of the ResNet with the AM solver. As a hybrid of the two models ResNet and ODE-net, a third network was created called RK-Net, which solves the weight optimization of the neural ODE network explicitly through backward Runge-Kutta integration. The following table shows the training and performance results of each network. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Table1.png|400px]]&lt;/div&gt;<br /> <br /> Note that &lt;math&gt;L&lt;/math&gt; and &lt;math&gt;\tilde{L}&lt;/math&gt; are the number of layers in ResNet and the number of function calls that the AM method makes for the two ODE networks and are effectively analogous quantities. As shown in Table 1, both of the ODE networks achieve comparable performance to that of the ResNet with a notable decrease in memory cost for ODE-net.<br /> <br /> <br /> Another interesting component of ODE networks is the ability to control the tolerance in the ODE solver used and subsequently the numerical error in the solution. <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;[[File:NeuralODEs Fig3.png|700px]]&lt;/div&gt;<br /> <br /> The tolerance of the ODE solver is represented by the colour bar in Figure 3 above and notice that a variety of effects arise from adjusting this parameter. Primarily, if one was to treat the tolerance as a hyperparameter of sorts, you could tune it such that you find a balance between accuracy (Figure 3a) and computational complexity (Figure 3b). Figure 3c also provides further evidence for the benefits of the adjoint method for the backward pass in ODE-nets since there is a nearly 1:0.5 ratio of forward to backward function calls. In the ResNet and RK-Net examples, this ratio is 1:1.<br /> <br /> Additionally, the authors loosely define the concept of depth in a neural ODE network by referring to Figure 3d. Here it's evident that as you continue to train an ODE network, the number of function evaluations the ODE solver performs increases. As previously mentioned, this quantity is comparable to the network depth of a discretized network. However, as the authors note, this result should be seen as the progression of the network's complexity over training epochs, which is something we expect to increase over time.<br /> <br /> == Continuous Normalizing Flows ==<br /> <br /> Section four tackles the implementation of continuous-depth Neural Networks, but to do so, in the first part of section four the authors discuss theoretically how to establish this kind of network through the use of normalizing flows. The authors use a change of variables method presented in other works (Rezende and Mohamed, 2015), (Dinh et al., 2014), to compute the change of a probability distribution if sample points are transformed through a bijective function, &lt;math&gt;f&lt;/math&gt;.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;z_1=f(z_0) \Rightarrow \log⁡(p(z_1))=\log⁡(p(z_0))-\log⁡|\det⁡\frac{\partial f}{\partial z_0}|&lt;/math&gt;&lt;/div&gt;<br /> <br /> Where p(z) is the probability distribution of the samples and &lt;math&gt;det⁡\frac{\partial f}{\partial z_0}&lt;/math&gt; is the determinant of the Jacobian which has a cubic cost in the dimension of '''z''' or the number of hidden units in the network. The authors discovered however that transforming the discrete set of hidden layers in the normalizing flow network to continuous transformations simplifies the computations significantly, due primarily to the following theorem:<br /> <br /> '''''Theorem 1:''' (Instantaneous Change of Variables). Let z(t) be a finite continuous random variable with probability p(z(t)) dependent on time. Let dz/dt=f(z(t),t) be a differential equation describing a continuous-in-time transformation of z(t). Assuming that f is uniformly Lipschitz continuous in z and continuous in t, then the change in log probability also follows a differential equation:''<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;&lt;math&gt;\frac{\partial \log(p(z(t)))}{\partial t}=-tr\left(\frac{df}{dz(t)}\right)&lt;/math&gt;&lt;/div&gt;<br /> <br /> The biggest advantage to using this theorem is that the trace function is a linear function, so if the dynamics of the problem, f, is represented by a sum of functions, then so is the log density. This essentially means that you can now compute flow models with only a linear cost with respect to the number of hidden units, &lt;math&gt;M&lt;/math&gt;. In standard normalizing flow models, the cost is &lt;math&gt;O(M^3)&lt;/math&gt;, so they will generally fit many layers with a single hidden unit in each layer.<br /> <br /> Finally the authors use these realizations to construct Continuous Normalizing Flow networks (CNFs) by specifying the parameters of the flow as a function of ''t'', ie, &lt;math&gt;f(z(t),t)&lt;/math&gt;. They also use a gating mechanism for each hidden unit, &lt;math&gt;\frac{dz}{dt}=\sum_n \sigma_n(t)f_n(z)&lt;/math&gt; where &lt;math&gt;\sigma_n(t)\in (0,1)&lt;/math&gt; is a separate neural network which learns when to apply each dynamic &lt;math&gt;f_n&lt;/math&gt;.<br /> <br /> ===Implementation===<br /> <br /> The authors construct two separate types of neural networks to compare against each other, the first is the standard planar Normalizing Flow network (NF) using 64 layers of single hidden units, and the second is their new CNF with 64 hidden units. The NF model is trained over 500,000 iterations using RMSprop, and the CNF network is trained over 10,000 iterations using Adam(algorithm for first-order gradient-based optimization of stochastic objective functions). The loss function is &lt;math&gt;KL(q(x)||p(x))&lt;/math&gt; where &lt;math&gt;q(x)&lt;/math&gt; is the flow model and &lt;math&gt;p(x)&lt;/math&gt; is the target probability density.<br /> <br /> One of the biggest advantages when implementing CNF is that you can train the flow parameters just by performing maximum likelihood estimation on &lt;math&gt;\log(q(x))&lt;/math&gt; given &lt;math&gt;p(x)&lt;/math&gt;, where &lt;math&gt;q(x)&lt;/math&gt; is found via the theorem above, and then reversing the CNF to generate random samples from &lt;math&gt;q(x)&lt;/math&gt;. This reversal of the CNF is done with about the same cost of the forward pass which is not able to be done in an NF network. The following two figures demonstrate the ability of CNF to generate more expressive and accurate output data as compared to standard NF networks.<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:CNFcomparisons.png]]<br /> <br /> [[Image:CNFtransitions.png]]<br /> &lt;/div&gt;<br /> <br /> Figure 4 shows clearly that the CNF structure exhibits significantly lower loss functions than NF. In figure 5 both networks were tasked with transforming a standard Gaussian distribution into a target distribution, not only was the CNF network more accurate on the two moons target, but also the steps it took along the way are much more intuitive than the output from NF.<br /> <br /> == A Generative Latent Function Time-Series Model ==<br /> <br /> One of the largest issues at play in terms of Neural ODE networks is the fact that in many instances, data points are either very sparsely distributed, or irregularly-sampled. The latent dynamics are discretized and the observations are in the bins of fixed duration. This creates issues with missing data and ill-defined latent variables. An example of this is medical records which are only updated when a patient visits a doctor or the hospital. To solve this issue the authors had to create a generative time-series model which would be able to fill in the gaps of missing data. The authors consider each time series as a latent trajectory stemming from the initial local state &lt;math&gt;z_{t_0 }&lt;/math&gt; and determined from a global set of latent parameters. Given a set of observation times and initial state, the generative model constructs points via the following sample procedure:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> &lt;math&gt;<br /> z_{t_0}∼p(z_{t_0}) <br /> &lt;/math&gt;<br /> &lt;/div&gt; <br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> &lt;math&gt;<br /> z_{t_1},z_{t_2},\dots,z_{t_N}={\rm ODESolve}(z_{t_0},f,θ_f,t_0,...,t_N)<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> each <br /> &lt;math&gt;<br /> x_{t_i}∼p(x│z_{t_i},θ_x)<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;math&gt;f&lt;/math&gt; is a function which outputs the gradient &lt;math&gt;\frac{\partial z(t)}{\partial t}=f(z(t),θ_f)&lt;/math&gt; which is parameterized via a neural net. In order to train this latent variable model, the authors had to first encode their given data and observation times using an RNN encoder, construct the new points using the trained parameters, then decode the points back into the original space. The following figure describes this process:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:EncodingFigure.png]]<br /> &lt;/div&gt;<br /> <br /> Another variable which could affect the latent state of a time-series model is how often an event actually occurs. The authors solved this by parameterizing the rate of events in terms of a Poisson process. They described the set of independent observation times in an interval &lt;math&gt;\left[t_{start},t_{end}\right]&lt;/math&gt; as:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt; <br /> &lt;math&gt;<br /> {\rm log}⁡(p(t_1,t_2,\dots,t_N ))=\sum_{i=1}^N{\rm log}⁡(\lambda(z(t_i)))-\int_{t_{start}}^{t_{end}}λ(z(t))dt<br /> &lt;/math&gt;<br /> &lt;/div&gt;<br /> <br /> where &lt;math&gt;\lambda(*)&lt;/math&gt; is parameterized via another neural network.<br /> <br /> ===Implementation===<br /> <br /> To test the effectiveness of the Latent time-series ODE model (LODE), they fit the encoder with 25 hidden units, parametrize function f with a one-layer 20 hidden unit network, and the decoder as another neural network with 20 hidden units. They compare this against a standard recurrent neural net (RNN) with 25 hidden units trained to minimize Gaussian log-likelihood. The authors tested both of these network systems on a dataset of 2-dimensional spirals which either rotated clockwise or counter-clockwise and sampled the positions of each spiral at 100 equally spaced time steps. They can then simulate irregularly timed data by taking random amounts of points without replacement from each spiral. The next two figures show the outcome of these experiments:<br /> <br /> &lt;div style=&quot;text-align:center;&quot;&gt;<br /> [[Image:LODEtestresults.png]] [[Image:SpiralFigure.png|The blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model]]<br /> &lt;/div&gt;<br /> <br /> In the figure on the right the blue lines represent the test data learned curves and the red lines represent the extrapolated curves predicted by each model. It is noted that the LODE performs significantly better than the standard RNN model, especially on smaller sets of data points.<br /> <br /> == Scope and Limitations ==<br /> <br /> Section 6 mainly discusses the scope and limitations of the paper. Firstly, while “batching” the training data is a useful step in standard neural nets, and can still be applied here by combining the ODEs associated with each batch, the authors found that controlling the error, in this case, may increase the number of calculations required. In practice, however, the number of calculations did not increase significantly.<br /> <br /> So long as the model proposed in this paper uses finite weights and Lipschitz nonlinearities, Picard’s existence theorem (Coddington and Levinson, 1955) applies, which guarantees that the solution to the IVP exists and is unique. This theorem holds for the model presented above when the network has finite weights and uses nonlinearities in the Lipshitz class. <br /> <br /> In controlling the amount of error in the model, the authors were only able to reduce tolerances to approximately &lt;math&gt;10^{-3}&lt;/math&gt; and &lt;math&gt;10^{-5}&lt;/math&gt; in classification and density estimation respectively without also degrading the computational performance.<br /> <br /> The authors believe that reconstructing state trajectories by running the dynamics backwards can introduce extra numerical error. They address a possible solution to this problem by checkpointing certain time steps and storing intermediate values of z on the forward pass. Then while reconstructing, you do each part individually between checkpoints. The authors acknowledged that they informally checked the validity of this method since they don’t consider it a practical problem.<br /> <br /> There remain, however, areas where standard neural networks may perform better than Neural ODEs. Firstly, conventional nets can fit non-homeomorphic functions, for example, functions whose output has a smaller dimension that their input, or that change the topology of the input space. However, this could be handled by composing ODE nets with standard network layers. Another point is that conventional nets can be evaluated exactly with a fixed amount of computation, and are typically faster to train, and do not require an error tolerance for a solver.<br /> <br /> == Conclusions and Critiques ==<br /> <br /> We covered the use of black-box ODE solvers as a model component and their application to initial value problems constructed from real applications​. Neural ODE Networks show promising gains in computational cost without large sacrifices in accuracy when applied to certain problems​. A drawback of some of these implementations is that the ODE Neural Networks are limited by the underlying distributions of the problems they are trying to solve (requirement of Lipschitz continuity, etc.)​. There are plenty of further advances to be made in this field as hundreds of years of ODE theory and literature is available, so this is currently an important area of research.<br /> <br /> ODEs indeed represent an important area of applied mathematics where neural networks can be used to solve them numerically. Perhaps, a parallel area of investigation can be PDEs (Partial Differential Equations). PDEs are also widely encountered in many areas of applied mathematics, physics, social sciences, and many other fields. It will be interesting to see how neural networks can be used to solve PDEs.<br /> <br /> == More Critiques ==<br /> <br /> This paper covers the memory efficiency of Neural ODE Networks, but does not address runtime. In practice, most systems are bound by latency requirements more-so than memory requirements (except in edge device cases). Though it may be unreasonable to expect the authors to produce a performance-optimized implementation, it would be insightful to understand the computational bottlenecks so existing frameworks can take steps to address them. This model looks promising and practical performance is the key to enabling future research in this.<br /> <br /> The above critique also questions the need for a neural network for such a problem. This problem was studied by Brunel et al. and they presented their solution in their paper ''Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions''. While this solution also requires iteratively solving a complex optimization problem, they did not require the massive memory and runtime overhead of a neural network. For the neural network solution to demonstrate its potential, it should be including experimental comparisons with specialized ordinary differential equation algorithms instead of simply comparing with a general recurrent neural network.<br /> <br /> Table 2 shows that potential ODEs have lower predicted RMSE, and more relevant information should be provided. For example, the reason of setting the n to 30/50/100 can be simply described. And it is good to talk more about the performance of Latent ODE since the change of n does not have much impact on its RMSE.<br /> <br /> == References ==<br /> Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong. Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations. ''arXiv preprint arXiv'':1710.10121, 2017.<br /> <br /> Eldad Haber and Lars Ruthotto. Stable architectures for deep neural networks. ''Inverse Problems'', 34 (1):014004, 2017.<br /> <br /> Lars Ruthotto and Eldad Haber. Deep neural networks motivated by partial differential equations. ''arXiv preprint arXiv'':1804.04272, 2018.<br /> <br /> Lev Semenovich Pontryagin, EF Mishchenko, VG Boltyanskii, and RV Gamkrelidze. ''The mathematical theory of optimal processes''. 1962.<br /> <br /> Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In ''European conference on computer vision'', pages 630–645. Springer, 2016b.<br /> <br /> Earl A Coddington and Norman Levinson. ''Theory of ordinary differential equations''. Tata McGrawHill Education, 1955.<br /> <br /> Danilo Jimenez Rezende and Shakir Mohamed. Variational inference with normalizing flows. ''arXiv preprint arXiv:1505.05770'', 2015.<br /> <br /> Laurent Dinh, David Krueger, and Yoshua Bengio. NICE: Non-linear independent components estimation. ''arXiv preprint arXiv:1410.8516'', 2014.<br /> <br /> Brunel, N. J., Clairon, Q., &amp; d’Alché-Buc, F. (2014). Parametric estimation of ordinary differential equations with orthogonality conditions. ''Journal of the American Statistical Association'', 109(505), 173-185.<br /> <br /> A. Iserles. A first course in the numerical analysis of differential equations. Cambridge Texts in Applied Mathematics, second edition, 2009</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=47816 User:J46hou 2020-11-29T21:14:52Z <p>Z47shen: /* Popular Dataset Benchmark Result */</p> <hr /> <div>DROCC: Deep Robust One-Class Classification<br /> == Presented by == <br /> Jinjiang Lian, Yisheng Zhu, Jiawen Hou, Mingzhe Huang<br /> == Introduction ==<br /> In this paper, the “one-class” classification, whose goal is to obtain accurate discriminators for a special class, has been studied. Popular uses of this technique include anomaly detection which is widely used in detecting outliers. Anomaly detection is a well-studied area of research, which aims to learn a model that accurately describes &quot;normality&quot;. Its application ranges from fraud detection to medical diagnosis; however, the conventional approach of modeling with typical data using a simple function falls short when it comes to complex domains such as vision or speech. Another case where this would be useful is when recognizing “wake-word” while waking up AI systems such as Alexa. <br /> <br /> Deep learning based on anomaly detection methods attempts to learn features automatically but has some limitations. One approach is based on extending the classical data modeling techniques over the learned representations, but in this case, all the points may be mapped to a single point which makes the layer look &quot;perfect&quot;. The second approach is based on learning the salient geometric structure of data and training the discriminator to predict applied transformation. The result could be considered anomalous if the discriminator fails to predict the transformation accurately.<br /> <br /> Thus, in this paper, a new approach called Deep Robust One-Class Classification (DROCC) was presented to solve the above concerns. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. More specifically, we are presenting DROCC-LF which is an outlier-exposure style extension of DROCC. This extension combines the DROCC's anomaly detection loss with standard classification loss over the negative data and exploits the negative examples to learn a Mahalanobis distance.<br /> <br /> == Previous Work ==<br /> Traditional approaches for one-class problems include one-class SVM (Scholkopf et al., 1999) and Isolation Forest (Liu et al., 2008). One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of the art methodologies to tackle these kinds of problems are: <br /> <br /> 1. Approach based on prediction transformations (Golan &amp; El-Yaniv, 2018; Hendrycks et al.,2019a)  This work is based on learning the salient geometric structure of typical data by applying specific transformations to the input data and training the discriminator to preduct applied transformation. This approach has some shortcomings in the sense that it depends heavily on an appropriate domain-specific set of transformations that are in general hard to obtain. <br /> <br /> 2. Approach of minimizing a classical one-class loss on the learned final layer representations such as DeepSVDD. (Ruff et al.,2018) This such work has proposed some heuristics to mitigate issues like setting the bias to zero but it is often insufficient in practice. This method suffers from the fundamental drawback of representation collapse where the model is no longer being able to accurately recognize the feature representations.<br /> <br /> 3. Approach based on balancing unbalanced training data sets using methods such as SMOTE to synthetically create outlier data to train models on.<br /> <br /> == Motivation ==<br /> Anomaly detection is a well-studied problem with a large body of research (Aggarwal, 2016; Chandola et al., 2009) . The goal is to identify the outliers - the points not following a typical distribution. <br /> [[File:abnormal.jpeg | thumb | center | 1000px | Abnormal Data (Data Driven Investor, 2020)]]<br /> Classical approaches for anomaly detection are based on modeling the typical data using simple functions over the low-dimensional subspace or a tree-structured partition of the input space to detect anomalies (Sch¨olkopf et al., 1999; Liu et al., 2008; Lakhina et al., 2004) , such as constructing a minimum-enclosing ball around the typical data points (Tax &amp; Duin, 2004) . They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods, and Side-information based AD. While these techniques are well-suited when the input is featured appropriately, they struggle on complex domains like vision and speech, where hand-designing features are difficult.<br /> <br /> '''AD via Generative Modeling:''' involves deep autoencoders and GAN based methods and have been deeply studied. But, this method solves a much harder problem than required and reconstructs the entire input during the decoding step<br /> <br /> '''Deep One-Class SVM:''' Deep SVDD attempts to learn a neural network which maps data into a hypersphere. Mappings which fall within the hypersphere are considered &quot;normal&quot;. It was the first method to introduce deep one-class classification for the purpose of anomaly detection, but is impeded by representation collapse.<br /> <br /> '''Transformations based methods:''' Are more recent methods that are based on self-supervised training. The training process of these methods applies transformations to the regular points and training then trains the classifier to identify the transformations used. The model relies on the assumption that a point is normal iff the transformations applied to the point can be identified. Some proposed transformations are as simple as rotations and flips, or can be handcrafted and much more complicated. The various transformations that have been proposed are heavily domain dependent and are hard to design.<br /> <br /> '''Side-information based AD:''' incorporate labelled anomalous data or out-of-distribution samples. DROCC makes no assumptions regarding access to side-information.<br /> <br /> Another related problem is the one-class classification under limited negatives (OCLN). In this case, only a few negative samples are available. The goal is to find a classifier that would not misfire close negatives so that the false positive rate will be low. <br /> <br /> DROCC is robust to representation collapse by involving a discriminative component that is general and empirically accurate on most standard domains like tabular, time-series and vision without requiring any additional side information. DROCC is motivated by the key observation that generally, the typical data lies on a low-dimensional manifold, which is well-sampled in the training data. This is believed to be true even in complex domains such as vision, speech, and natural language (Pless &amp; Souvenir, 2009). <br /> <br /> == Model Explanation ==<br /> [[File:drocc_f1.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 1'''&lt;/div&gt;<br /> <br /> (a): A normal data manifold with red dots representing generated anomalous points in Ni(r). <br /> <br /> (b): Decision boundary learned by DROCC when applied to the data from (a). Blue represents points classified as normal and red points are classified as abnormal. We observe from here that DROCC is able to capture the manifold accurately; whereas the classical methods OC-SVM and DeepSVDD perform poorly as they both try to learn a minimum enclosing ball for the whole set of positive data points. <br /> <br /> (c), (d): First two dimensions of the decision boundary of DROCC and DROCC–LF, when applied to noisy data (Section 5.2). DROCC–LF is nearly optimal while DROCC’s decision boundary is inaccurate. Yellow color sine wave depicts the train data.<br /> <br /> == DROCC ==<br /> The model is based on the assumption that the true data lies on a manifold. As manifolds resemble Euclidean space locally, our discriminative component is based on classifying a point as anomalous if it is outside the union of small L2 norm balls around the training typical points (See Figure 1a, 1b for an illustration). Importantly, the above definition allows us to synthetically generate anomalous points, and we adaptively generate the most effective anomalous points while training via a gradient ascent phase reminiscent of adversarial training. In other words, DROCC has a gradient ascent phase to adaptively add anomalous points to our training set and a gradient descent phase to minimize the classification loss by learning a representation and a classifier on top of the representations to separate typical points from the generated anomalous points. In this way, DROCC automatically learns an appropriate representation (like DeepSVDD) but is robust to a representation collapse as mapping all points to the same value would lead to poor discrimination between normal points and the generated anomalous points.<br /> <br /> The algorithm that was used to train the model is laid out below in pseudocode.<br /> &lt;center&gt;<br /> [[File:DROCCtrain.png]]<br /> &lt;/center&gt;<br /> <br /> For a DNN &lt;math&gt;f_\theta: \mathbb{R}^d \to \mathbb{R}&lt;/math&gt; that is parameterized by a set of parameters &lt;math&gt;\theta&lt;/math&gt;, DROCC estimates &lt;math&gt;\theta^{dr} = \min_\theta\ell^{dr}(\theta)&lt;/math&gt; where <br /> $$\ell^{dr}(\theta) = \lambda\|\theta\|^2 + \sum_{i=1}^n[\ell(f_\theta(x_i),1)+\mu\max_{\tilde{x}_i \in N_i(r)}\ell(f_\theta(\tilde{x}_i),-1)]$$<br /> Here, &lt;math&gt;N_i(r) = \{\|\tilde{x}_i-x_i\|_2\leq\gamma\cdot r; r \leq \|\tilde{x}_i - x_j\|, \forall j=1,2,...n\}&lt;/math&gt; contains all the points that are at least distance &lt;math&gt;r&lt;/math&gt; from the training points. The &lt;math&gt;\gamma \geq 1&lt;/math&gt; is a regularization term, and &lt;math&gt;\ell:\mathbb{R} \times \mathbb{R} \to \mathbb{R}&lt;/math&gt; is a loss function. The &lt;math&gt;x_i&lt;/math&gt; are normal points that should be classified as positive and the &lt;math&gt;\tilde{x}_i&lt;/math&gt; are anomalous points that should be classified as negative. This formulation is a saddle point problem.<br /> <br /> == DROCC-LF ==<br /> To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) , DROCC–LF, an outlier-exposure style extension of DROCC was proposed. Intuitively, DROCC–LF combines DROCC’s anomaly detection loss (that is over only the positive data points) with standard classification loss over the negative data. In addition, DROCC–LF exploits the negative examples to learn a Mahalanobis distance to compare points over the manifold instead of using the standard Euclidean distance, which can be inaccurate for high-dimensional data with relatively fewer samples. (See Figure 1c, 1d for illustration)<br /> <br /> == Popular Dataset Benchmark Result ==<br /> <br /> [[File:drocc_auc.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 2: AUC result'''&lt;/div&gt;<br /> <br /> The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. The average AUC (with standard deviation) for one-vs-all anomaly detection on CIFAR-10 is shown in table 1. DROCC outperforms baselines on most classes, with gains as high as 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br /> <br /> [[File:drocc_f1score.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 3: F1-Score'''&lt;/div&gt;<br /> <br /> Figure 3 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from the UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about an 11.5% performance increase.<br /> Results on One-class Classification with Limited Negatives (OCLN): <br /> [[File:ocln.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''&lt;/div&gt;<br /> MNIST 0 vs. 1 Classification: <br /> We consider an experimental setup on the MNIST dataset, where the training data consists of Digit 0, the normal class, and Digit 1 as the anomaly. During the evaluation, in addition to samples from training distribution, we also have half zeros, which act as challenging OOD points (close negatives). These half zeros are generated by randomly masking 50% of the pixels (Figure 2). BCE performs poorly, with a recall of 54% only at a fixed FPR of 3%. DROCC–OE gives a recall value of 98:16% outperforming DeepSAD by a margin of 7%, which gives a recall value of 90:91%. DROCC–LF provides further improvement with a recall of 99:4% at 3% FPR. <br /> <br /> [[File:ocln_2.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 5: OCLN on Audio Commands.'''&lt;/div&gt;<br /> Wake word Detection: <br /> Finally, we evaluate DROCC–LF on the practical problem of wake word detection with low FPR against arbitrary OOD negatives. To this end, we identify a keyword, say “Marvin” from the audio commands dataset (Warden, 2018)  as the positive class, and the remaining 34 keywords are labeled as the negative class. For training, we sample points uniformly at random from the above-mentioned dataset. However, for evaluation, we sample positives from the train distribution, but negatives contain a few challenging OOD points as well. Sampling challenging negatives itself is a hard task and is the key motivating reason for studying the problem. So, we manually list close-by keywords to Marvin such as Mar, Vin, Marvelous, etc. We then generate audio snippets for these keywords via a speech synthesis tool 2 with a variety of accents.<br /> Figure 5 shows that for 3% and 5% FPR settings, DROCC–LF is significantly more accurate than the baselines. For example, with FPR=3%, DROCC–LF is 10% more accurate than the baselines. We repeated the same experiment with the keyword: Seven, and observed a similar trend. In summary, DROCC–LF is able to generalize well against negatives that are “close” to the true positives even when such negatives were not supplied with the training data.<br /> <br /> == Conclusion and Future Work ==<br /> We introduced DROCC method for deep anomaly detection. It models normal data points using a low-dimensional manifold, so these close points can be compared via Euclidean distance. Based on this intuition, DROCC’s optimization is formulated as a saddle point problem which is solved via a standard gradient descent-ascent algorithm. We then extended DROCC to OCLN problem where the goal is to generalize well against arbitrary negatives, assuming the positive class is well sampled and a small number of negative points are also available. Both the methods perform significantly better than strong baselines, in their respective problem settings. <br /> <br /> For computational efficiency, we simplified the projection set of both methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with the stricter set is an exciting research direction. Further, we would also like to rigorously analyze DROCC, assuming enough samples from a low-curvature manifold. Finally, as OCLN is an exciting problem that routinely comes up in a variety of real-world applications, we would like to apply DROCC–LF to a few high impact scenarios.<br /> <br /> The results of this study showed that DROCC is comparatively better for anomaly detection across many different areas, such as tabular data, images, audio, and time series, when compared to existing state-of-the-art techniques.<br /> <br /> It would be interesting to see how the DROCC method performs in situations where the anomaly is very rare, say detecting signals of volcanic explosion from seismic activity data. Such challenging anomalous situations will be a test of endurance for this method and can even help advance work in this area.<br /> <br /> == References ==<br /> : Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br /> <br /> : Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M¨uller, E., and Kloft, M. Deep one-class classification. In International Conference on Machine Learning (ICML), 2018.<br /> <br /> : Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br /> <br /> : Sch¨olkopf, B., Williamson, R., Smola, A., Shawe-Taylor, J., and Platt, J. Support vector method for novelty detection. In Proceedings of the 12th International Conference on Neural Information Processing Systems, 1999.<br /> <br /> : Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br /> <br /> : Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br /> <br /> : Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br /> <br /> : Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br /> <br /> : Liu, F. T., Ting, K. M., and Zhou, Z.-H. Isolation forest. In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 2008.<br /> <br /> == Critiques/Insights ==<br /> <br /> 1. It would be interesting to see this implemented in self-driving cars, for instance, to detect unusual road conditions.<br /> <br /> 2. Figure 1 shows a good representation on how this model works. However, how can we know that this model is not prone to overfitting? There are many situations where there are valid points that lie outside of the line, especially new data that the model has never see before. An explanation on how this is avoided would be good.<br /> <br /> 3.In the introduction part, it should first explain what is &quot;one class&quot;, and then make a detailed application. Moreover, special definition words are used in many places in the text. No detailed explanation was given. In the end, the future application fields of DROCC and the research direction of the group can be explained.<br /> <br /> 4. The geometry of this technique (classification based on incidence outside of a ball centred at a known point &lt;math&gt;x&lt;/math&gt;) sounds quite similar to K-nearest neighbors. While the authors compared DROCC to single-nearest neighbor classification, choosing a higher K would result in a stronger, more regularized model. It would be interesting to see how DROCC compares to the general KNN classifier<br /> <br /> 5. This is a nice summary and the authors introduce clearly on the performance of DROCC. It is nice to use Alexa as an example to catch readers' attention. I think it will be nice to include the algorithm of the DROCC or the architecture of DROCC in this summary to help us know the whole view of this method. Maybe it will be interesting to apply DROCC in biomedical studies? since one-class classification is often used in biomedical studies.<br /> <br /> 6. The training method resembles adversarial learning with gradient ascent, however, there is no evaluation of this method on adversarial examples. This is quite unusual considering the paper proposed a method for robust one-class classification, and can be a security threat in real life in critical applications.<br /> <br /> 7. The underlying idea behind OCLN is very similar to how neural networks are implemented in recommender systems and trained over positive/negative triplet models. In that case as well, due to the nature of implicit and explicit feedback, positive data tends to dominate the system. It would be interesting to see if insights from that area could be used to further boost the model presented in this paper.<br /> <br /> 8. The paper shows the performance of DROCC being evaluated for time series data. It is interesting to see high AUC scores for DROCC against baselines like nearest neighbours and REBMs.Because detecting abnormal data in time series datasets is not common to practise.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=47812 User:J46hou 2020-11-29T21:11:43Z <p>Z47shen: /* Conclusion and Future Work */</p> <hr /> <div>DROCC: Deep Robust One-Class Classification<br /> == Presented by == <br /> Jinjiang Lian, Yisheng Zhu, Jiawen Hou, Mingzhe Huang<br /> == Introduction ==<br /> In this paper, the “one-class” classification, whose goal is to obtain accurate discriminators for a special class, has been studied. Popular uses of this technique include anomaly detection which is widely used in detecting outliers. Anomaly detection is a well-studied area of research, which aims to learn a model that accurately describes &quot;normality&quot;. Its application ranges from fraud detection to medical diagnosis; however, the conventional approach of modeling with typical data using a simple function falls short when it comes to complex domains such as vision or speech. Another case where this would be useful is when recognizing “wake-word” while waking up AI systems such as Alexa. <br /> <br /> Deep learning based on anomaly detection methods attempts to learn features automatically but has some limitations. One approach is based on extending the classical data modeling techniques over the learned representations, but in this case, all the points may be mapped to a single point which makes the layer look &quot;perfect&quot;. The second approach is based on learning the salient geometric structure of data and training the discriminator to predict applied transformation. The result could be considered anomalous if the discriminator fails to predict the transformation accurately.<br /> <br /> Thus, in this paper, a new approach called Deep Robust One-Class Classification (DROCC) was presented to solve the above concerns. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. More specifically, we are presenting DROCC-LF which is an outlier-exposure style extension of DROCC. This extension combines the DROCC's anomaly detection loss with standard classification loss over the negative data and exploits the negative examples to learn a Mahalanobis distance.<br /> <br /> == Previous Work ==<br /> Traditional approaches for one-class problems include one-class SVM (Scholkopf et al., 1999) and Isolation Forest (Liu et al., 2008). One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of the art methodologies to tackle these kinds of problems are: <br /> <br /> 1. Approach based on prediction transformations (Golan &amp; El-Yaniv, 2018; Hendrycks et al.,2019a)  This work is based on learning the salient geometric structure of typical data by applying specific transformations to the input data and training the discriminator to preduct applied transformation. This approach has some shortcomings in the sense that it depends heavily on an appropriate domain-specific set of transformations that are in general hard to obtain. <br /> <br /> 2. Approach of minimizing a classical one-class loss on the learned final layer representations such as DeepSVDD. (Ruff et al.,2018) This such work has proposed some heuristics to mitigate issues like setting the bias to zero but it is often insufficient in practice. This method suffers from the fundamental drawback of representation collapse where the model is no longer being able to accurately recognize the feature representations.<br /> <br /> 3. Approach based on balancing unbalanced training data sets using methods such as SMOTE to synthetically create outlier data to train models on.<br /> <br /> == Motivation ==<br /> Anomaly detection is a well-studied problem with a large body of research (Aggarwal, 2016; Chandola et al., 2009) . The goal is to identify the outliers - the points not following a typical distribution. <br /> [[File:abnormal.jpeg | thumb | center | 1000px | Abnormal Data (Data Driven Investor, 2020)]]<br /> Classical approaches for anomaly detection are based on modeling the typical data using simple functions over the low-dimensional subspace or a tree-structured partition of the input space to detect anomalies (Sch¨olkopf et al., 1999; Liu et al., 2008; Lakhina et al., 2004) , such as constructing a minimum-enclosing ball around the typical data points (Tax &amp; Duin, 2004) . They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods, and Side-information based AD. While these techniques are well-suited when the input is featured appropriately, they struggle on complex domains like vision and speech, where hand-designing features are difficult.<br /> <br /> '''AD via Generative Modeling:''' involves deep autoencoders and GAN based methods and have been deeply studied. But, this method solves a much harder problem than required and reconstructs the entire input during the decoding step<br /> <br /> '''Deep One-Class SVM:''' Deep SVDD attempts to learn a neural network which maps data into a hypersphere. Mappings which fall within the hypersphere are considered &quot;normal&quot;. It was the first method to introduce deep one-class classification for the purpose of anomaly detection, but is impeded by representation collapse.<br /> <br /> '''Transformations based methods:''' Are more recent methods that are based on self-supervised training. The training process of these methods applies transformations to the regular points and training then trains the classifier to identify the transformations used. The model relies on the assumption that a point is normal iff the transformations applied to the point can be identified. Some proposed transformations are as simple as rotations and flips, or can be handcrafted and much more complicated. The various transformations that have been proposed are heavily domain dependent and are hard to design.<br /> <br /> '''Side-information based AD:''' incorporate labelled anomalous data or out-of-distribution samples. DROCC makes no assumptions regarding access to side-information.<br /> <br /> Another related problem is the one-class classification under limited negatives (OCLN). In this case, only a few negative samples are available. The goal is to find a classifier that would not misfire close negatives so that the false positive rate will be low. <br /> <br /> DROCC is robust to representation collapse by involving a discriminative component that is general and empirically accurate on most standard domains like tabular, time-series and vision without requiring any additional side information. DROCC is motivated by the key observation that generally, the typical data lies on a low-dimensional manifold, which is well-sampled in the training data. This is believed to be true even in complex domains such as vision, speech, and natural language (Pless &amp; Souvenir, 2009). <br /> <br /> == Model Explanation ==<br /> [[File:drocc_f1.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 1'''&lt;/div&gt;<br /> <br /> (a): A normal data manifold with red dots representing generated anomalous points in Ni(r). <br /> <br /> (b): Decision boundary learned by DROCC when applied to the data from (a). Blue represents points classified as normal and red points are classified as abnormal. We observe from here that DROCC is able to capture the manifold accurately; whereas the classical methods OC-SVM and DeepSVDD perform poorly as they both try to learn a minimum enclosing ball for the whole set of positive data points. <br /> <br /> (c), (d): First two dimensions of the decision boundary of DROCC and DROCC–LF, when applied to noisy data (Section 5.2). DROCC–LF is nearly optimal while DROCC’s decision boundary is inaccurate. Yellow color sine wave depicts the train data.<br /> <br /> == DROCC ==<br /> The model is based on the assumption that the true data lies on a manifold. As manifolds resemble Euclidean space locally, our discriminative component is based on classifying a point as anomalous if it is outside the union of small L2 norm balls around the training typical points (See Figure 1a, 1b for an illustration). Importantly, the above definition allows us to synthetically generate anomalous points, and we adaptively generate the most effective anomalous points while training via a gradient ascent phase reminiscent of adversarial training. In other words, DROCC has a gradient ascent phase to adaptively add anomalous points to our training set and a gradient descent phase to minimize the classification loss by learning a representation and a classifier on top of the representations to separate typical points from the generated anomalous points. In this way, DROCC automatically learns an appropriate representation (like DeepSVDD) but is robust to a representation collapse as mapping all points to the same value would lead to poor discrimination between normal points and the generated anomalous points.<br /> <br /> The algorithm that was used to train the model is laid out below in pseudocode.<br /> &lt;center&gt;<br /> [[File:DROCCtrain.png]]<br /> &lt;/center&gt;<br /> <br /> For a DNN &lt;math&gt;f_\theta: \mathbb{R}^d \to \mathbb{R}&lt;/math&gt; that is parameterized by a set of parameters &lt;math&gt;\theta&lt;/math&gt;, DROCC estimates &lt;math&gt;\theta^{dr} = \min_\theta\ell^{dr}(\theta)&lt;/math&gt; where <br /> $$\ell^{dr}(\theta) = \lambda\|\theta\|^2 + \sum_{i=1}^n[\ell(f_\theta(x_i),1)+\mu\max_{\tilde{x}_i \in N_i(r)}\ell(f_\theta(\tilde{x}_i),-1)]$$<br /> Here, &lt;math&gt;N_i(r) = \{\|\tilde{x}_i-x_i\|_2\leq\gamma\cdot r; r \leq \|\tilde{x}_i - x_j\|, \forall j=1,2,...n\}&lt;/math&gt; contains all the points that are at least distance &lt;math&gt;r&lt;/math&gt; from the training points. The &lt;math&gt;\gamma \geq 1&lt;/math&gt; is a regularization term, and &lt;math&gt;\ell:\mathbb{R} \times \mathbb{R} \to \mathbb{R}&lt;/math&gt; is a loss function. The &lt;math&gt;x_i&lt;/math&gt; are normal points that should be classified as positive and the &lt;math&gt;\tilde{x}_i&lt;/math&gt; are anomalous points that should be classified as negative. This formulation is a saddle point problem.<br /> <br /> == DROCC-LF ==<br /> To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) , DROCC–LF, an outlier-exposure style extension of DROCC was proposed. Intuitively, DROCC–LF combines DROCC’s anomaly detection loss (that is over only the positive data points) with standard classification loss over the negative data. In addition, DROCC–LF exploits the negative examples to learn a Mahalanobis distance to compare points over the manifold instead of using the standard Euclidean distance, which can be inaccurate for high-dimensional data with relatively fewer samples. (See Figure 1c, 1d for illustration)<br /> <br /> == Popular Dataset Benchmark Result ==<br /> <br /> [[File:drocc_auc.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 2: AUC result'''&lt;/div&gt;<br /> <br /> The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. The average AUC (with standard deviation) for one-vs-all anomaly detection on CIFAR-10 is shown in table 1. DROCC outperforms baselines on most classes, with gains as high as 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br /> <br /> [[File:drocc_f1score.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 3: F1-Score'''&lt;/div&gt;<br /> <br /> Figure 3 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from the UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about an 11.5% performance increase.<br /> Results on One-class Classification with Limited Negatives (OCLN): <br /> [[File:ocln.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''&lt;/div&gt;<br /> MNIST 0 vs. 1 Classification: <br /> We consider an experimental setup on the MNIST dataset, where the training data consists of Digit 0, the normal class, and Digit 1 as the anomaly. During the evaluation, in addition to samples from training distribution, we also have half zeros, which act as challenging OOD points (close negatives). These half zeros are generated by randomly masking 50% of the pixels (Figure 2). BCE performs poorly, with a recall of 54% only at a fixed FPR of 3%. DROCC–OE gives a recall value of 98:16% outperforming DeepSAD by a margin of 7%, which gives a recall value of 90:91%. DROCC–LF provides further improvement with a recall of 99:4% at 3% FPR. <br /> <br /> [[File:ocln_2.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 5: OCLN on Audio Commands.'''&lt;/div&gt;<br /> Wake word Detection: <br /> Finally, we evaluate DROCC–LF on the practical problem of wake word detection with low FPR against arbitrary OOD negatives. To this end, we identify a keyword, say “Marvin” from the audio commands dataset (Warden, 2018)  as the positive class, and the remaining 34 keywords are labeled as the negative class. For training, we sample points uniformly at random from the above-mentioned dataset. However, for evaluation, we sample positives from the train distribution, but negatives contain a few challenging OOD points as well. Sampling challenging negatives itself is a hard task and is the key motivating reason for studying the problem. So, we manually list close-by keywords to Marvin such as Mar, Vin, Marvelous, etc. We then generate audio snippets for these keywords via a speech synthesis tool 2 with a variety of accents.<br /> Figure 3 shows that for 3% and 5% FPR settings, DROCC–LF is significantly more accurate than the baselines. For example, with FPR=3%, DROCC–LF is 10% more accurate than the baselines. We repeated the same experiment with the keyword: Seven, and observed a similar trend. In summary, DROCC–LF is able to generalize well against negatives that are “close” to the true positives even when such negatives were not supplied with the training data.<br /> <br /> == Conclusion and Future Work ==<br /> We introduced DROCC method for deep anomaly detection. It models normal data points using a low-dimensional manifold, so these close points can be compared via Euclidean distance. Based on this intuition, DROCC’s optimization is formulated as a saddle point problem which is solved via a standard gradient descent-ascent algorithm. We then extended DROCC to OCLN problem where the goal is to generalize well against arbitrary negatives, assuming the positive class is well sampled and a small number of negative points are also available. Both the methods perform significantly better than strong baselines, in their respective problem settings. <br /> <br /> For computational efficiency, we simplified the projection set of both methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with the stricter set is an exciting research direction. Further, we would also like to rigorously analyze DROCC, assuming enough samples from a low-curvature manifold. Finally, as OCLN is an exciting problem that routinely comes up in a variety of real-world applications, we would like to apply DROCC–LF to a few high impact scenarios.<br /> <br /> The results of this study showed that DROCC is comparatively better for anomaly detection across many different areas, such as tabular data, images, audio, and time series, when compared to existing state-of-the-art techniques.<br /> <br /> It would be interesting to see how the DROCC method performs in situations where the anomaly is very rare, say detecting signals of volcanic explosion from seismic activity data. Such challenging anomalous situations will be a test of endurance for this method and can even help advance work in this area.<br /> <br /> == References ==<br /> : Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br /> <br /> : Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M¨uller, E., and Kloft, M. Deep one-class classification. In International Conference on Machine Learning (ICML), 2018.<br /> <br /> : Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br /> <br /> : Sch¨olkopf, B., Williamson, R., Smola, A., Shawe-Taylor, J., and Platt, J. Support vector method for novelty detection. In Proceedings of the 12th International Conference on Neural Information Processing Systems, 1999.<br /> <br /> : Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br /> <br /> : Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br /> <br /> : Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br /> <br /> : Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br /> <br /> : Liu, F. T., Ting, K. M., and Zhou, Z.-H. Isolation forest. In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 2008.<br /> <br /> == Critiques/Insights ==<br /> <br /> 1. It would be interesting to see this implemented in self-driving cars, for instance, to detect unusual road conditions.<br /> <br /> 2. Figure 1 shows a good representation on how this model works. However, how can we know that this model is not prone to overfitting? There are many situations where there are valid points that lie outside of the line, especially new data that the model has never see before. An explanation on how this is avoided would be good.<br /> <br /> 3.In the introduction part, it should first explain what is &quot;one class&quot;, and then make a detailed application. Moreover, special definition words are used in many places in the text. No detailed explanation was given. In the end, the future application fields of DROCC and the research direction of the group can be explained.<br /> <br /> 4. The geometry of this technique (classification based on incidence outside of a ball centred at a known point &lt;math&gt;x&lt;/math&gt;) sounds quite similar to K-nearest neighbors. While the authors compared DROCC to single-nearest neighbor classification, choosing a higher K would result in a stronger, more regularized model. It would be interesting to see how DROCC compares to the general KNN classifier<br /> <br /> 5. This is a nice summary and the authors introduce clearly on the performance of DROCC. It is nice to use Alexa as an example to catch readers' attention. I think it will be nice to include the algorithm of the DROCC or the architecture of DROCC in this summary to help us know the whole view of this method. Maybe it will be interesting to apply DROCC in biomedical studies? since one-class classification is often used in biomedical studies.<br /> <br /> 6. The training method resembles adversarial learning with gradient ascent, however, there is no evaluation of this method on adversarial examples. This is quite unusual considering the paper proposed a method for robust one-class classification, and can be a security threat in real life in critical applications.<br /> <br /> 7. The underlying idea behind OCLN is very similar to how neural networks are implemented in recommender systems and trained over positive/negative triplet models. In that case as well, due to the nature of implicit and explicit feedback, positive data tends to dominate the system. It would be interesting to see if insights from that area could be used to further boost the model presented in this paper.<br /> <br /> 8. The paper shows the performance of DROCC being evaluated for time series data. It is interesting to see high AUC scores for DROCC against baselines like nearest neighbours and REBMs.Because detecting abnormal data in time series datasets is not common to practise.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=47811 User:J46hou 2020-11-29T21:11:27Z <p>Z47shen: /* Conclusion and Future Work */</p> <hr /> <div>DROCC: Deep Robust One-Class Classification<br /> == Presented by == <br /> Jinjiang Lian, Yisheng Zhu, Jiawen Hou, Mingzhe Huang<br /> == Introduction ==<br /> In this paper, the “one-class” classification, whose goal is to obtain accurate discriminators for a special class, has been studied. Popular uses of this technique include anomaly detection which is widely used in detecting outliers. Anomaly detection is a well-studied area of research, which aims to learn a model that accurately describes &quot;normality&quot;. Its application ranges from fraud detection to medical diagnosis; however, the conventional approach of modeling with typical data using a simple function falls short when it comes to complex domains such as vision or speech. Another case where this would be useful is when recognizing “wake-word” while waking up AI systems such as Alexa. <br /> <br /> Deep learning based on anomaly detection methods attempts to learn features automatically but has some limitations. One approach is based on extending the classical data modeling techniques over the learned representations, but in this case, all the points may be mapped to a single point which makes the layer look &quot;perfect&quot;. The second approach is based on learning the salient geometric structure of data and training the discriminator to predict applied transformation. The result could be considered anomalous if the discriminator fails to predict the transformation accurately.<br /> <br /> Thus, in this paper, a new approach called Deep Robust One-Class Classification (DROCC) was presented to solve the above concerns. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. More specifically, we are presenting DROCC-LF which is an outlier-exposure style extension of DROCC. This extension combines the DROCC's anomaly detection loss with standard classification loss over the negative data and exploits the negative examples to learn a Mahalanobis distance.<br /> <br /> == Previous Work ==<br /> Traditional approaches for one-class problems include one-class SVM (Scholkopf et al., 1999) and Isolation Forest (Liu et al., 2008). One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of the art methodologies to tackle these kinds of problems are: <br /> <br /> 1. Approach based on prediction transformations (Golan &amp; El-Yaniv, 2018; Hendrycks et al.,2019a)  This work is based on learning the salient geometric structure of typical data by applying specific transformations to the input data and training the discriminator to preduct applied transformation. This approach has some shortcomings in the sense that it depends heavily on an appropriate domain-specific set of transformations that are in general hard to obtain. <br /> <br /> 2. Approach of minimizing a classical one-class loss on the learned final layer representations such as DeepSVDD. (Ruff et al.,2018) This such work has proposed some heuristics to mitigate issues like setting the bias to zero but it is often insufficient in practice. This method suffers from the fundamental drawback of representation collapse where the model is no longer being able to accurately recognize the feature representations.<br /> <br /> 3. Approach based on balancing unbalanced training data sets using methods such as SMOTE to synthetically create outlier data to train models on.<br /> <br /> == Motivation ==<br /> Anomaly detection is a well-studied problem with a large body of research (Aggarwal, 2016; Chandola et al., 2009) . The goal is to identify the outliers - the points not following a typical distribution. <br /> [[File:abnormal.jpeg | thumb | center | 1000px | Abnormal Data (Data Driven Investor, 2020)]]<br /> Classical approaches for anomaly detection are based on modeling the typical data using simple functions over the low-dimensional subspace or a tree-structured partition of the input space to detect anomalies (Sch¨olkopf et al., 1999; Liu et al., 2008; Lakhina et al., 2004) , such as constructing a minimum-enclosing ball around the typical data points (Tax &amp; Duin, 2004) . They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods, and Side-information based AD. While these techniques are well-suited when the input is featured appropriately, they struggle on complex domains like vision and speech, where hand-designing features are difficult.<br /> <br /> '''AD via Generative Modeling:''' involves deep autoencoders and GAN based methods and have been deeply studied. But, this method solves a much harder problem than required and reconstructs the entire input during the decoding step<br /> <br /> '''Deep One-Class SVM:''' Deep SVDD attempts to learn a neural network which maps data into a hypersphere. Mappings which fall within the hypersphere are considered &quot;normal&quot;. It was the first method to introduce deep one-class classification for the purpose of anomaly detection, but is impeded by representation collapse.<br /> <br /> '''Transformations based methods:''' Are more recent methods that are based on self-supervised training. The training process of these methods applies transformations to the regular points and training then trains the classifier to identify the transformations used. The model relies on the assumption that a point is normal iff the transformations applied to the point can be identified. Some proposed transformations are as simple as rotations and flips, or can be handcrafted and much more complicated. The various transformations that have been proposed are heavily domain dependent and are hard to design.<br /> <br /> '''Side-information based AD:''' incorporate labelled anomalous data or out-of-distribution samples. DROCC makes no assumptions regarding access to side-information.<br /> <br /> Another related problem is the one-class classification under limited negatives (OCLN). In this case, only a few negative samples are available. The goal is to find a classifier that would not misfire close negatives so that the false positive rate will be low. <br /> <br /> DROCC is robust to representation collapse by involving a discriminative component that is general and empirically accurate on most standard domains like tabular, time-series and vision without requiring any additional side information. DROCC is motivated by the key observation that generally, the typical data lies on a low-dimensional manifold, which is well-sampled in the training data. This is believed to be true even in complex domains such as vision, speech, and natural language (Pless &amp; Souvenir, 2009). <br /> <br /> == Model Explanation ==<br /> [[File:drocc_f1.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 1'''&lt;/div&gt;<br /> <br /> (a): A normal data manifold with red dots representing generated anomalous points in Ni(r). <br /> <br /> (b): Decision boundary learned by DROCC when applied to the data from (a). Blue represents points classified as normal and red points are classified as abnormal. We observe from here that DROCC is able to capture the manifold accurately; whereas the classical methods OC-SVM and DeepSVDD perform poorly as they both try to learn a minimum enclosing ball for the whole set of positive data points. <br /> <br /> (c), (d): First two dimensions of the decision boundary of DROCC and DROCC–LF, when applied to noisy data (Section 5.2). DROCC–LF is nearly optimal while DROCC’s decision boundary is inaccurate. Yellow color sine wave depicts the train data.<br /> <br /> == DROCC ==<br /> The model is based on the assumption that the true data lies on a manifold. As manifolds resemble Euclidean space locally, our discriminative component is based on classifying a point as anomalous if it is outside the union of small L2 norm balls around the training typical points (See Figure 1a, 1b for an illustration). Importantly, the above definition allows us to synthetically generate anomalous points, and we adaptively generate the most effective anomalous points while training via a gradient ascent phase reminiscent of adversarial training. In other words, DROCC has a gradient ascent phase to adaptively add anomalous points to our training set and a gradient descent phase to minimize the classification loss by learning a representation and a classifier on top of the representations to separate typical points from the generated anomalous points. In this way, DROCC automatically learns an appropriate representation (like DeepSVDD) but is robust to a representation collapse as mapping all points to the same value would lead to poor discrimination between normal points and the generated anomalous points.<br /> <br /> The algorithm that was used to train the model is laid out below in pseudocode.<br /> &lt;center&gt;<br /> [[File:DROCCtrain.png]]<br /> &lt;/center&gt;<br /> <br /> For a DNN &lt;math&gt;f_\theta: \mathbb{R}^d \to \mathbb{R}&lt;/math&gt; that is parameterized by a set of parameters &lt;math&gt;\theta&lt;/math&gt;, DROCC estimates &lt;math&gt;\theta^{dr} = \min_\theta\ell^{dr}(\theta)&lt;/math&gt; where <br /> $$\ell^{dr}(\theta) = \lambda\|\theta\|^2 + \sum_{i=1}^n[\ell(f_\theta(x_i),1)+\mu\max_{\tilde{x}_i \in N_i(r)}\ell(f_\theta(\tilde{x}_i),-1)]$$<br /> Here, &lt;math&gt;N_i(r) = \{\|\tilde{x}_i-x_i\|_2\leq\gamma\cdot r; r \leq \|\tilde{x}_i - x_j\|, \forall j=1,2,...n\}&lt;/math&gt; contains all the points that are at least distance &lt;math&gt;r&lt;/math&gt; from the training points. The &lt;math&gt;\gamma \geq 1&lt;/math&gt; is a regularization term, and &lt;math&gt;\ell:\mathbb{R} \times \mathbb{R} \to \mathbb{R}&lt;/math&gt; is a loss function. The &lt;math&gt;x_i&lt;/math&gt; are normal points that should be classified as positive and the &lt;math&gt;\tilde{x}_i&lt;/math&gt; are anomalous points that should be classified as negative. This formulation is a saddle point problem.<br /> <br /> == DROCC-LF ==<br /> To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) , DROCC–LF, an outlier-exposure style extension of DROCC was proposed. Intuitively, DROCC–LF combines DROCC’s anomaly detection loss (that is over only the positive data points) with standard classification loss over the negative data. In addition, DROCC–LF exploits the negative examples to learn a Mahalanobis distance to compare points over the manifold instead of using the standard Euclidean distance, which can be inaccurate for high-dimensional data with relatively fewer samples. (See Figure 1c, 1d for illustration)<br /> <br /> == Popular Dataset Benchmark Result ==<br /> <br /> [[File:drocc_auc.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 2: AUC result'''&lt;/div&gt;<br /> <br /> The CIFAR-10 dataset consists of 60000 32x32 color images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. The average AUC (with standard deviation) for one-vs-all anomaly detection on CIFAR-10 is shown in table 1. DROCC outperforms baselines on most classes, with gains as high as 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br /> <br /> [[File:drocc_f1score.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 3: F1-Score'''&lt;/div&gt;<br /> <br /> Figure 3 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from the UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about an 11.5% performance increase.<br /> Results on One-class Classification with Limited Negatives (OCLN): <br /> [[File:ocln.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''&lt;/div&gt;<br /> MNIST 0 vs. 1 Classification: <br /> We consider an experimental setup on the MNIST dataset, where the training data consists of Digit 0, the normal class, and Digit 1 as the anomaly. During the evaluation, in addition to samples from training distribution, we also have half zeros, which act as challenging OOD points (close negatives). These half zeros are generated by randomly masking 50% of the pixels (Figure 2). BCE performs poorly, with a recall of 54% only at a fixed FPR of 3%. DROCC–OE gives a recall value of 98:16% outperforming DeepSAD by a margin of 7%, which gives a recall value of 90:91%. DROCC–LF provides further improvement with a recall of 99:4% at 3% FPR. <br /> <br /> [[File:ocln_2.jpg | center]]<br /> &lt;div align=&quot;center&quot;&gt;'''Figure 5: OCLN on Audio Commands.'''&lt;/div&gt;<br /> Wake word Detection: <br /> Finally, we evaluate DROCC–LF on the practical problem of wake word detection with low FPR against arbitrary OOD negatives. To this end, we identify a keyword, say “Marvin” from the audio commands dataset (Warden, 2018)  as the positive class, and the remaining 34 keywords are labeled as the negative class. For training, we sample points uniformly at random from the above-mentioned dataset. However, for evaluation, we sample positives from the train distribution, but negatives contain a few challenging OOD points as well. Sampling challenging negatives itself is a hard task and is the key motivating reason for studying the problem. So, we manually list close-by keywords to Marvin such as Mar, Vin, Marvelous, etc. We then generate audio snippets for these keywords via a speech synthesis tool 2 with a variety of accents.<br /> Figure 3 shows that for 3% and 5% FPR settings, DROCC–LF is significantly more accurate than the baselines. For example, with FPR=3%, DROCC–LF is 10% more accurate than the baselines. We repeated the same experiment with the keyword: Seven, and observed a similar trend. In summary, DROCC–LF is able to generalize well against negatives that are “close” to the true positives even when such negatives were not supplied with the training data.<br /> <br /> == Conclusion and Future Work ==<br /> We introduced DROCC method for deep anomaly detection. It models normal data points using a low-dimensional manifold, these close points can be compared via Euclidean distance. Based on this intuition, DROCC’s optimization is formulated as a saddle point problem which is solved via a standard gradient descent-ascent algorithm. We then extended DROCC to OCLN problem where the goal is to generalize well against arbitrary negatives, assuming the positive class is well sampled and a small number of negative points are also available. Both the methods perform significantly better than strong baselines, in their respective problem settings. <br /> <br /> For computational efficiency, we simplified the projection set of both methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with the stricter set is an exciting research direction. Further, we would also like to rigorously analyze DROCC, assuming enough samples from a low-curvature manifold. Finally, as OCLN is an exciting problem that routinely comes up in a variety of real-world applications, we would like to apply DROCC–LF to a few high impact scenarios.<br /> <br /> The results of this study showed that DROCC is comparatively better for anomaly detection across many different areas, such as tabular data, images, audio, and time series, when compared to existing state-of-the-art techniques.<br /> <br /> It would be interesting to see how the DROCC method performs in situations where the anomaly is very rare, say detecting signals of volcanic explosion from seismic activity data. Such challenging anomalous situations will be a test of endurance for this method and can even help advance work in this area.<br /> <br /> == References ==<br /> : Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br /> <br /> : Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M¨uller, E., and Kloft, M. Deep one-class classification. In International Conference on Machine Learning (ICML), 2018.<br /> <br /> : Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br /> <br /> : Sch¨olkopf, B., Williamson, R., Smola, A., Shawe-Taylor, J., and Platt, J. Support vector method for novelty detection. In Proceedings of the 12th International Conference on Neural Information Processing Systems, 1999.<br /> <br /> : Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br /> <br /> : Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br /> <br /> : Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br /> <br /> : Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br /> <br /> : Liu, F. T., Ting, K. M., and Zhou, Z.-H. Isolation forest. In Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 2008.<br /> <br /> == Critiques/Insights ==<br /> <br /> 1. It would be interesting to see this implemented in self-driving cars, for instance, to detect unusual road conditions.<br /> <br /> 2. Figure 1 shows a good representation on how this model works. However, how can we know that this model is not prone to overfitting? There are many situations where there are valid points that lie outside of the line, especially new data that the model has never see before. An explanation on how this is avoided would be good.<br /> <br /> 3.In the introduction part, it should first explain what is &quot;one class&quot;, and then make a detailed application. Moreover, special definition words are used in many places in the text. No detailed explanation was given. In the end, the future application fields of DROCC and the research direction of the group can be explained.<br /> <br /> 4. The geometry of this technique (classification based on incidence outside of a ball centred at a known point &lt;math&gt;x&lt;/math&gt;) sounds quite similar to K-nearest neighbors. While the authors compared DROCC to single-nearest neighbor classification, choosing a higher K would result in a stronger, more regularized model. It would be interesting to see how DROCC compares to the general KNN classifier<br /> <br /> 5. This is a nice summary and the authors introduce clearly on the performance of DROCC. It is nice to use Alexa as an example to catch readers' attention. I think it will be nice to include the algorithm of the DROCC or the architecture of DROCC in this summary to help us know the whole view of this method. Maybe it will be interesting to apply DROCC in biomedical studies? since one-class classification is often used in biomedical studies.<br /> <br /> 6. The training method resembles adversarial learning with gradient ascent, however, there is no evaluation of this method on adversarial examples. This is quite unusual considering the paper proposed a method for robust one-class classification, and can be a security threat in real life in critical applications.<br /> <br /> 7. The underlying idea behind OCLN is very similar to how neural networks are implemented in recommender systems and trained over positive/negative triplet models. In that case as well, due to the nature of implicit and explicit feedback, positive data tends to dominate the system. It would be interesting to see if insights from that area could be used to further boost the model presented in this paper.<br /> <br /> 8. The paper shows the performance of DROCC being evaluated for time series data. It is interesting to see high AUC scores for DROCC against baselines like nearest neighbours and REBMs.Because detecting abnormal data in time series datasets is not common to practise.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Summary_for_survey_of_neural_networked-based_cancer_prediction_models_from_microarray_data&diff=47809 Summary for survey of neural networked-based cancer prediction models from microarray data 2020-11-29T21:06:45Z <p>Z47shen: /* Summary */</p> <hr /> <div>== Presented by == <br /> Rao Fu, Siqi Li, Yuqin Fang, Zeping Zhou<br /> <br /> == Introduction == <br /> Microarray technology can help researchers quickly detect genetic information and is widely used to analyze genetic diseases. Researchers use this technology to compare normal and abnormal cancerous tissues to gain insights into the pathology of cancer. <br /> <br /> However, due to the high dimensionality of the gene expressions, accuracy and computation time of the model might be affected. The following two approaches are adopted to cope with this problem: the feature selection method and the feature creating method. The formal one, similar to the well-known principle component analysis method, aims to focus on key features and ignore minor noises. On the other hand, the latter one, similar to scale invariant feature transformations, aims to combine existing features or map them to a new low-dimensional space.<br /> <br /> Comparing to neural network models presented by others, this paper is specifically designed for predicting cancer using gene expression data. Thus, we will review the latest neural network-based cancer prediction models by presenting the methodology of preprocessing, filtering, prediction, and clustering gene expressions.<br /> <br /> == Background == <br /> <br /> '''Neural Network''' &lt;br&gt;<br /> Neural networks are often used to solve non-linear complex problems. It is an operational model consisting of a large number of neurons connected to each other by different weights. In this network structure, each neuron is related to an activation function such as sigmoid or rectified linear activation functions. To train the network, the inputs are fed forward and the activation function value is calculated at every neuron. The difference between the output of the neural network and the actual value is what we call an error.<br /> The backpropagation mechanism is one of the most commonly used algorithms in solving neural network problems. By using this algorithm, we optimize the objective function by propagating back the generated error through the network to adjust the weights.<br /> In the next sections, we will use the above algorithm but with different network architectures and a different number of neurons to review the neural network-based cancer prediction models for learning the gene expression features.<br /> <br /> '''Cancer prediction models'''&lt;br&gt;<br /> Cancer prediction models often contain more than 1 method to achieve high prediction accuracy with a more accurate prognosis and it also aims to reduce the cost of patients.<br /> <br /> High dimensionality and spatial structure are the two main factors that can affect the accuracy of the cancer prediction models. They add irrelevant noisy features to our selected models. We have 3 ways to determine the accuracy of a model.<br /> <br /> The first is called the ROC curve. ROC curves, receiver operating characteristic curves, are graphs that show the true positive rate against the false-positive rate . It reflects the sensitivity of the response to the same signal stimulus under different criterias. To test its validity, we need to consider it with the confidence interval. Usually, a model is considered acceptable when its ROC is greater than 0.7. <br /> <br /> A different machine learning problem is predicting the survival time. The performance of a model that predicts survival time can be measured using two metrics. The problem of predicting survival time can be seen as a ranking problem, where survival times of different subjects are ranked against each other. CI (Concordance Index) is a measure of how good a model ranks survival times and explains the concordance probability of the predicted and observed survival. The closer its value to 0.7, the better the model is. We can express the ordering of survival times in an order graph &lt;math display=&quot;inline&quot;&gt;G = (V, E)&lt;/math&gt; where the vertices &lt;math display=&quot;inline&quot;&gt;V&lt;/math&gt; are the individual survival times, and the edges &lt;math display=&quot;inline&quot;&gt;E_{ij}&lt;/math&gt; from individual &lt;math display=&quot;inline&quot;&gt;i&lt;/math&gt; to &lt;math display=&quot;inline&quot;&gt;j&lt;/math&gt; indicate that &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt;, where &lt;math display=&quot;inline&quot;&gt;T_i, T_j&lt;/math&gt; are the survival times for individuals &lt;math display=&quot;inline&quot;&gt;i,j&lt;/math&gt; respectively. Then we can write &lt;math display=&quot;inline&quot;&gt;CI = \frac{1}{|E|}\sum_{i,j}I(f(i) &lt; f(j))&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;|E|&lt;/math&gt; is the number of edges in the order graph (ie. the total number of comparable pairs), and &lt;math display=&quot;inline&quot;&gt;I(f(i) &lt; f(j)) = 1&lt;/math&gt; if the predictor &lt;math display=&quot;inline&quot;&gt;f&lt;/math&gt; correctly ranks &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt; .<br /> <br /> Another metric is the Brier score, which measures the average difference between the observed and the estimated survival rate in a given period of time. It ranges from 0 to 1, and a lower score indicates higher accuracy. It is defined as &lt;math display=&quot;inline&quot;&gt;\frac{1}{n}\sum_{i=1}^n(f_i - o_i)^2&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;f_i&lt;/math&gt; is the predicted survival rate, and &lt;math display=&quot;inline&quot;&gt;o_i&lt;/math&gt; is the observed survival rate .<br /> <br /> == Neural network-based cancer prediction models ==<br /> An extensive search relevant to neural network-based cancer prediction was performed using Google scholar and other electronic databases namely PubMed and Scopus with keywords such as “Neural Networks AND Cancer Prediction” and “gene expression clustering”, and only articles between 2013 and 2018 with available accessibility were considered. The chosen papers covered cancer classification, discovery, survivability prediction, and statistical analysis models. The following figure 1 shows a graph representing the number of citations including filtering, predictive, and clustering for chosen papers. <br /> <br /> [[File:f1.png]]<br /> <br /> '''Datasets and preprocessing''' &lt;br&gt;<br /> Most studies investigating automatic cancer prediction and clustering used datasets such as the TCGA, UCI, NCBI Gene Expression Omnibus and Kentridge biomedical databases. There are a few techniques used in processing dataset including removing the genes that have zero expression across all samples, Normalization, filtering with p-value &gt; &lt;math&gt;10^{-5}&lt;/math&gt; to remove some unwanted technical variation and &lt;math&gt;\log_2&lt;/math&gt; transformations. Statistical methods, neural networks, were applied to reduce the dimensionality of the gene expressions by selecting a subset of genes. Principle Component Analysis (PCA) can also be used as an initial preprocessing step to extract the dataset's features. The PCA method linearly transforms the dataset features into lower dimensional space without capturing the complex relationships between the features. However, simply removing the genes that were not measured by the other datasets could not overcome the class imbalance problem. In that case, one research used Synthetic Minority Class Over Sampling method to generate synthetic minority class samples, which may lead to a sparse matrix problem. Clustering was also applied in some studies for labeling data by grouping the samples into high-risk, low-risk groups, and so on. <br /> <br /> The following table presents the dataset used by considered reference, the applied normalization technique, the cancer type and the dimensionality of the datasets.<br /> <br /> [[File:Datasets and preprocessing.png]]<br /> <br /> '''Neural network architecture''' &lt;br&gt;<br /> Most recent studies reveal that neural network methods are used for filtering, predicting and clustering in cancer prediction. <br /> <br /> *''filtering'': Filter the gene expressions to eliminate noise or reduce dimensionality. Then use the resulted features with statistical methods or machine learning classification and clustering tools as figure 2 indicates.<br /> <br /> *''predicting'': Extract features and improve the accuracy of prediction (classification).<br /> <br /> *''clustering'': Divide the gene expressions or samples based on similarity.<br /> <br /> [[File:filtering gane.png]]<br /> <br /> All the neurons in the neural network work together as feature detectors to learn the features from the input. In order to categorize a neural network as filtering, predicting, or clustering method, we looked at the overall role that network provided within the framework of cancer prediction. Filtering methods are trained to remove the input’s noise and to extract the most representative features that best describe the unlabeled gene expressions. Predicting methods are trained to extract the features that are significant to prediction, therefore its objective functions measure how accurately the network is able to predict the class of input. Clustering methods are trained to divide unlabeled samples into groups based on their similarities.<br /> <br /> '''Building neural networks-based approaches for gene expression prediction''' &lt;br&gt;<br /> According to our survey, the representative codes are generated by filtering methods with dimensionality M smaller or equal to N, where N is the dimensionality of the input. Some other machine learning algorithms such as naïve Bayes or k-means can be used together with the filtering.<br /> Predictive neural networks are supervised, which find the best classification accuracy; meanwhile, clustering methods are unsupervised, which group similar samples or genes together. <br /> The goal of training prediction is to enhance the classification capability, and the goal of training classification is to find the optimal group for a new test set with unknown labels.<br /> <br /> '''Neural network filters for cancer prediction''' &lt;br&gt;<br /> In the preprocessing step to classification, clustering, and statistical analysis, the autoencoders are more and more commonly-used, to extract generic genomic features. An autoencoder is composed of the encoder part and the decoder part. The encoder part is to learn the mapping between high-dimensional unlabeled input I(x) and the low-dimensional representations in the middle layer(s), and the decoder part is to learn the mapping from the middle layer’s representation to the high-dimensional output O(x). The reconstruction of the input can take the Root Mean Squared Error (RMSE) or the Logloss function as the objective function. <br /> <br /> $$RMSE = \sqrt{ \frac{\sum{(I(x)-O(x))^2}}{n} }$$<br /> <br /> $$Logloss = \sum{(I(x)\log(O(x)) + (1 - I(x))\log(1 - O(x)))}$$<br /> <br /> There are several types of autoencoders, such as stacked denoising autoencoders, contractive autoencoders, sparse autoencoders, regularized autoencoders, and variational autoencoders. The architecture of the networks varies in many parameters, such as depth and loss function. Each example of an autoencoder mentioned above has a different number of hidden layers, different activation functions (e.g. sigmoid function, exponential linear unit function), and different optimization algorithms (e.g. stochastic gradient descent optimization, Adam optimizer).<br /> <br /> Overfitting is a major problem that most autoencoders need to deal with to achieve high efficiency of the extracted features. Regularization, dropout, and sparsity are common solutions.<br /> <br /> The neural network filtering methods were used by different statistical methods and classifiers. The conventional methods include Cox regression model analysis, Support Vector Machine (SVM), K-means clustering, t-SNE and so on. The classifiers could be SVM or AdaBoost or others.<br /> <br /> By using neural network filtering methods, the model can be trained to learn low-dimensional representations, remove noises from the input, and gain better generalization performance by re-training the classifier with the newest output layer.<br /> <br /> '''Neural network prediction methods for cancer''' &lt;br&gt;<br /> The prediction based on neural networks can build a network that maps the input features to an output with a number of neurons, which could be one or two for binary classification or more for multi-class classification. It can also build several independent binary neural networks for the multi-class classification, where the technique called “one-hot encoding” is applied.<br /> <br /> The codeword is a binary string &lt;math&gt;C'k&lt;/math&gt; of length k whose j’th position is set to 1 for the j’th class, while other positions remain 0. The process of the neural networks is to map the input to the codeword iteratively, whose objective function is minimized in each iteration.<br /> <br /> Such cancer classifiers were applied to identify cancerous/non-cancerous samples, a specific cancer type, or the survivability risk. MLP models were used to predict the survival risk of lung cancer patients with several gene expressions as input. The deep generative model DeepCancer, the RBM-SVM and RBM-logistic regression models, the convolutional feedforward model DeepGene, Extreme Learning Machines (ELM), the one-dimensional convolutional framework model SE1DCNN, and GA-ANN model are all used for solving cancer issues mentioned above. This paper indicates that the performance of neural networks with MLP architecture as a classifier is better than those of SVM, logistic regression, naïve Bayes, classification trees, and KNN.<br /> <br /> '''Neural network clustering methods in cancer prediction''' &lt;br&gt;<br /> Neural network clustering belongs to unsupervised learning. The input data are divided into different groups according to their feature similarity.<br /> The single-layered neural network SOM, which is unsupervised and without a backpropagation mechanism, is one of the traditional model-based techniques to be applied to gene expression data. The measurement of its accuracy could be Rand Index (RI), which can be improved to Adjusted Random Index (ARI) and Normalized Mutation Information (NMI).<br /> <br /> $$RI=\frac{TP+TN}{TP+TN+FP+FN}$$<br /> <br /> In general, gene expression clustering considers either the relevance of samples-to-cluster assignment or that of gene-to-cluster assignment or both. The high dimensionality of gene expression samples poses a problem for traditional clustering algorithms such as k-means clustering, which uses a distance function to separate samples. Such an approach is not viable for high dimensional datasets. To solve the high dimensionality problem, there are two methods: clustering ensembles by running a single clustering algorithm several times, each of which has different initialization or number of parameters; and projective clustering by only considering a subset of the original features.<br /> <br /> SOM was applied on discriminating future tumor behavior using molecular alterations, whose results were not easy to be obtained by classic statistical models. Then this paper introduces two ensemble clustering frameworks: Random Double Clustering-based Cluster Ensembles (RDCCE) and Random Double Clustering-based Fuzzy Cluster Ensembles (RDCFCE). Their accuracies are high, but they have not taken the gene-to-cluster assignment into consideration.<br /> <br /> Also, the paper provides a double SOM based Clustering Ensemble Approach (SOM2CE) and double NG-based Clustering Ensemble Approach (NG2CE), which are robust to noisy genes. Moreover, Projective Clustering Ensemble (PCE) combines the advantages of both projective clustering and ensemble clustering, which is better than SOM and RDCFCE when there are irrelevant genes.<br /> <br /> == Summary ==<br /> <br /> Cancer is a disease with a high mortality rate that kills millions of people every year, and it’s essential to analyze gene expression for discovering gene abnormalities and increasing survivability as a consequence. The previous analysis in the paper reveals that neural networks are essentially used for filtering the gene expressions, predicting their class, or clustering them.<br /> <br /> Neural network filtering methods are used to reduce the dimensionality of the gene expressions and remove their noise. In the article, the authors recommended deep architectures in comparison to shallow architectures for best practice, as they combine many nonlinearities. <br /> <br /> Neural network prediction methods can be used for both binary and multi-class problems. In the binary case, the network architecture has only one or two output neurons that diagnose a given sample as cancerous or non-cancerous. In comparison, the number of the output neurons in multi-class problems is equal to the number of classes. The authors suggested that the deep architecture with convolution layers which was the most recently used model proved efficient capability in predicting cancer subtypes, as it captures the spatial correlations between gene expressions.<br /> Clustering is another analysis tool that is used to divide the gene expressions into groups. The authors indicated that a hybrid approach combining both the assembling, clustering and projective clustering is more accurate than using single-point clustering algorithms, such as SOM, since those methods do not have the capability to distinguish the noisy genes.<br /> <br /> ==Discussion==<br /> There are some technical problems that can be considered and improved for building new models. &lt;br&gt;<br /> <br /> 1. Overfitting: Since gene expression datasets are high dimensional and have a relatively small number of samples, it would be likely to properly fits the training data but not accurate for test samples due to the lack of generalization capability. The ways to avoid overfitting can be: (1). adding weight penalties using regularization; (2). using the average predictions from many models trained on different datasets; (3). dropout. (4) Augmentation of the dataset to produce more &quot;observations&quot;.&lt;br&gt;<br /> <br /> 2. Model configuration and training: In order to reduce both the computational and memory expenses but also with high prediction accuracy, it’s crucial to properly set the network parameters. The possible ways can be: (1). proper initialization; (2). pruning the unimportant connections by removing the zero-valued neurons; (3). using ensemble learning framework by training different models using different parameter settings or using different parts of the dataset for each base model; (4). Using SMOTE for dealing with class imbalance on the high dimensional level. &lt;br&gt;<br /> <br /> 3. Model evaluation: In Braga-Neto and Dougherty's research, they have investigated several model evaluation methods: cross-validation, substitution and bootstrap methods. The cross-validation was found to be unreliable for small size data since it displayed excessive variance. The bootstrap method proved more accurate predictability.&lt;br&gt;<br /> <br /> 4. Study producibility: A study needs to be reproducible to enhance research reliability so that others can replicate the results using the same algorithms, data and methodology. Hence, the query used for getting the dataset should be stated.<br /> <br /> ==Conclusion==<br /> This paper reviewed the most recent neural network-based cancer prediction models and gene expression analysis tools. The analysis indicates that the neural network methods are able to serve as filters, predictors, and clustering methods, and also showed that the role of the neural network determines its general architecture. The authors showed that Neural Network filtering methods are a way of reducing the dimensionality of the gene expressions, as well as removing their noise for better model fitting. To give suggestions for future neural network-based approaches, the authors highlighted some critical points that have to be considered such as overfitting and class imbalance, and suggest choosing different network parameters or combining two or more of the presented approaches. One of the biggest challenges for cancer prediction modelers is deciding on the network architecture (i.e. the number of hidden layers and neurons), as there are currently no guidelines to follow to obtain high prediction accuracy. The authors discovered that there is no algorithm available to concretely determine an optimal number of hidden layers or nodes and found that many papers simply implemented a trial and error method to reduce loss in the model.<br /> <br /> ==Critiques==<br /> <br /> While results indicate that the functionality of the neural network determines its general architecture, the decision on the number of hidden layers, neurons, hypermeters, and learning algorithms is made using trial-and-error techniques. Therefore improvements in this area of the model might need to be explored in order to obtain better results and in order to make more convincing statements.<br /> <br /> An issue that one must be mindful of is the underlying distribution of data. Cancer is an extremely complex genetic disease and the predictions would depend on so many variables, a number of which will not even be present in the dataset as they might have been collected. So there is a need for extensive validation when it comes to applying deep learning methods to cancer-related data.<br /> <br /> In the field of medical sciences and molecular biology, interpretability of results is imperative as often experts seek not just to solve the issue at hand but to understand the causal relationships. Having a high ROC value may not necessarily convince other experts on the validity of the finding because the underlying details of cancer symptoms have been abstracted in a complex neural network as a black box. However, the neural network clustering method suggested in this paper does offer a good compromise because it enables humans to visual low-level features but still gives experts the control on making various predictions using well-studied traditional techniques.<br /> <br /> With high dimensionality features, kernel SVM is another option for cancer prediction. Jiang et. al. developed a Hadamard Kernel for predicting breast cancer using gene expression data, and it utilizes the Kernel trick to avoid high computational efforts (link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5763304/). Compared against linear, quadratic, RBF and correlation kernels, Hadamard Kernel performs best with the highest averaged area under the ROC curve (AUC) value. It may be interesting to compare the performance and accuracy between the Hadamard Kernel and cancer prediction models with various number of hidden layers and neurons.<br /> <br /> Although the authors presented technical details about data processing, training approaches evaluation metric, and addressed many practical issues that can be considered for cancer prediction, no novel methods or models are proposed. It's more like a proof-of-concept about the feasibility of different models on cancer prediction.<br /> <br /> As the authors indicate neural networks would be a useful tool for cancer prediction models, the article is lacking an example for implementing neural networks to provide persuasive support for their arguments.<br /> <br /> The inheritance of cancer is complex and changeable. The predicted variables are therefore very complicated, so for the model of the learning data set, a more adequate training set is needed to learn. And multi-party verification of the learned model.<br /> <br /> The authors mentioned many different neural network models and compared them. It would be better if more details of a commonly applied model with relatively high accuracy could be given such as how the model is built. An article named Convolutional neural network models for cancer type prediction based on gene expression gives explanations of CNN in detail.<br /> <br /> The authors briefly discussed methods and algorithms being used in the presented paper in their summary. However, a very little amount of technical details were provided to the readers. The summary itself is lacking specific examples for the aforementioned algorithms, and datasets which were used in the original analysis were only introduced in one or two sentences. As a result, the summary and conclusion appear to be unconvincing to the readers.<br /> <br /> PCA can still be used as an initial preprocessing step even if it is used in a neural network whose data dimension is reduced. By merging the PCA component with a random number of original functions, some good techniques can be adopted to enable the network to capture more useful relationships<br /> <br /> ==Reference==<br />  Daoud, M., &amp; Mayo, M. (2019). A survey of neural network-based cancer prediction models from microarray data. Artificial Intelligence in Medicine, 97, 204–214.<br /> <br />  Brier GW. 1950. Verification of forecasts expressed in terms of probabilities. Monthly Weather Review 78: 1–3<br /> <br />  Harald Steck, Balaji Krishnapuram, Cary Dehing-oberije, Philippe Lambin, Vikas C. Raykar. On ranking in survival analysis: Bounds on the concordance index. In Advances in Neural Information Processing Systems (2008), pp. 1209-1216<br /> <br />  Google Developers. (2020 February 10). ''Classification: ROC Curve and AUC.'' Machine Learning Crash Course. https://developers.google.com/machine-learning/crash-course/classification/roc-and-auc<br /> <br />  Mostavi, M., Chiu, YC., Huang, Y. et al. Convolutional neural network models for cancer type prediction based on gene expression. ''BMC Med Genomics'' '''13''', 44 (2020). https://doi.org/10.1186/s12920-020-0677-2</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Summary_for_survey_of_neural_networked-based_cancer_prediction_models_from_microarray_data&diff=47805 Summary for survey of neural networked-based cancer prediction models from microarray data 2020-11-29T20:59:53Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Rao Fu, Siqi Li, Yuqin Fang, Zeping Zhou<br /> <br /> == Introduction == <br /> Microarray technology can help researchers quickly detect genetic information and is widely used to analyze genetic diseases. Researchers use this technology to compare normal and abnormal cancerous tissues to gain insights into the pathology of cancer. <br /> <br /> However, due to the high dimensionality of the gene expressions, accuracy and computation time of the model might be affected. The following two approaches are adopted to cope with this problem: the feature selection method and the feature creating method. The formal one, similar to the well-known principle component analysis method, aims to focus on key features and ignore minor noises. On the other hand, the latter one, similar to scale invariant feature transformations, aims to combine existing features or map them to a new low-dimensional space.<br /> <br /> Comparing to neural network models presented by others, this paper is specifically designed for predicting cancer using gene expression data. Thus, we will review the latest neural network-based cancer prediction models by presenting the methodology of preprocessing, filtering, prediction, and clustering gene expressions.<br /> <br /> == Background == <br /> <br /> '''Neural Network''' &lt;br&gt;<br /> Neural networks are often used to solve non-linear complex problems. It is an operational model consisting of a large number of neurons connected to each other by different weights. In this network structure, each neuron is related to an activation function such as sigmoid or rectified linear activation functions. To train the network, the inputs are fed forward and the activation function value is calculated at every neuron. The difference between the output of the neural network and the actual value is what we call an error.<br /> The backpropagation mechanism is one of the most commonly used algorithms in solving neural network problems. By using this algorithm, we optimize the objective function by propagating back the generated error through the network to adjust the weights.<br /> In the next sections, we will use the above algorithm but with different network architectures and a different number of neurons to review the neural network-based cancer prediction models for learning the gene expression features.<br /> <br /> '''Cancer prediction models'''&lt;br&gt;<br /> Cancer prediction models often contain more than 1 method to achieve high prediction accuracy with a more accurate prognosis and it also aims to reduce the cost of patients.<br /> <br /> High dimensionality and spatial structure are the two main factors that can affect the accuracy of the cancer prediction models. They add irrelevant noisy features to our selected models. We have 3 ways to determine the accuracy of a model.<br /> <br /> The first is called the ROC curve. ROC curves, receiver operating characteristic curves, are graphs that show the true positive rate against the false-positive rate . It reflects the sensitivity of the response to the same signal stimulus under different criterias. To test its validity, we need to consider it with the confidence interval. Usually, a model is considered acceptable when its ROC is greater than 0.7. <br /> <br /> A different machine learning problem is predicting the survival time. The performance of a model that predicts survival time can be measured using two metrics. The problem of predicting survival time can be seen as a ranking problem, where survival times of different subjects are ranked against each other. CI (Concordance Index) is a measure of how good a model ranks survival times and explains the concordance probability of the predicted and observed survival. The closer its value to 0.7, the better the model is. We can express the ordering of survival times in an order graph &lt;math display=&quot;inline&quot;&gt;G = (V, E)&lt;/math&gt; where the vertices &lt;math display=&quot;inline&quot;&gt;V&lt;/math&gt; are the individual survival times, and the edges &lt;math display=&quot;inline&quot;&gt;E_{ij}&lt;/math&gt; from individual &lt;math display=&quot;inline&quot;&gt;i&lt;/math&gt; to &lt;math display=&quot;inline&quot;&gt;j&lt;/math&gt; indicate that &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt;, where &lt;math display=&quot;inline&quot;&gt;T_i, T_j&lt;/math&gt; are the survival times for individuals &lt;math display=&quot;inline&quot;&gt;i,j&lt;/math&gt; respectively. Then we can write &lt;math display=&quot;inline&quot;&gt;CI = \frac{1}{|E|}\sum_{i,j}I(f(i) &lt; f(j))&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;|E|&lt;/math&gt; is the number of edges in the order graph (ie. the total number of comparable pairs), and &lt;math display=&quot;inline&quot;&gt;I(f(i) &lt; f(j)) = 1&lt;/math&gt; if the predictor &lt;math display=&quot;inline&quot;&gt;f&lt;/math&gt; correctly ranks &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt; .<br /> <br /> Another metric is the Brier score, which measures the average difference between the observed and the estimated survival rate in a given period of time. It ranges from 0 to 1, and a lower score indicates higher accuracy. It is defined as &lt;math display=&quot;inline&quot;&gt;\frac{1}{n}\sum_{i=1}^n(f_i - o_i)^2&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;f_i&lt;/math&gt; is the predicted survival rate, and &lt;math display=&quot;inline&quot;&gt;o_i&lt;/math&gt; is the observed survival rate .<br /> <br /> == Neural network-based cancer prediction models ==<br /> An extensive search relevant to neural network-based cancer prediction was performed using Google scholar and other electronic databases namely PubMed and Scopus with keywords such as “Neural Networks AND Cancer Prediction” and “gene expression clustering”, and only articles between 2013 and 2018 with available accessibility were considered. The chosen papers covered cancer classification, discovery, survivability prediction, and statistical analysis models. The following figure 1 shows a graph representing the number of citations including filtering, predictive, and clustering for chosen papers. <br /> <br /> [[File:f1.png]]<br /> <br /> '''Datasets and preprocessing''' &lt;br&gt;<br /> Most studies investigating automatic cancer prediction and clustering used datasets such as the TCGA, UCI, NCBI Gene Expression Omnibus and Kentridge biomedical databases. There are a few techniques used in processing dataset including removing the genes that have zero expression across all samples, Normalization, filtering with p-value &gt; &lt;math&gt;10^{-5}&lt;/math&gt; to remove some unwanted technical variation and &lt;math&gt;\log_2&lt;/math&gt; transformations. Statistical methods, neural networks, were applied to reduce the dimensionality of the gene expressions by selecting a subset of genes. Principle Component Analysis (PCA) can also be used as an initial preprocessing step to extract the dataset's features. The PCA method linearly transforms the dataset features into lower dimensional space without capturing the complex relationships between the features. However, simply removing the genes that were not measured by the other datasets could not overcome the class imbalance problem. In that case, one research used Synthetic Minority Class Over Sampling method to generate synthetic minority class samples, which may lead to a sparse matrix problem. Clustering was also applied in some studies for labeling data by grouping the samples into high-risk, low-risk groups, and so on. <br /> <br /> The following table presents the dataset used by considered reference, the applied normalization technique, the cancer type and the dimensionality of the datasets.<br /> <br /> [[File:Datasets and preprocessing.png]]<br /> <br /> '''Neural network architecture''' &lt;br&gt;<br /> Most recent studies reveal that neural network methods are used for filtering, predicting and clustering in cancer prediction. <br /> <br /> *''filtering'': Filter the gene expressions to eliminate noise or reduce dimensionality. Then use the resulted features with statistical methods or machine learning classification and clustering tools as figure 2 indicates.<br /> <br /> *''predicting'': Extract features and improve the accuracy of prediction (classification).<br /> <br /> *''clustering'': Divide the gene expressions or samples based on similarity.<br /> <br /> [[File:filtering gane.png]]<br /> <br /> All the neurons in the neural network work together as feature detectors to learn the features from the input. In order to categorize a neural network as filtering, predicting, or clustering method, we looked at the overall role that network provided within the framework of cancer prediction. Filtering methods are trained to remove the input’s noise and to extract the most representative features that best describe the unlabeled gene expressions. Predicting methods are trained to extract the features that are significant to prediction, therefore its objective functions measure how accurately the network is able to predict the class of input. Clustering methods are trained to divide unlabeled samples into groups based on their similarities.<br /> <br /> '''Building neural networks-based approaches for gene expression prediction''' &lt;br&gt;<br /> According to our survey, the representative codes are generated by filtering methods with dimensionality M smaller or equal to N, where N is the dimensionality of the input. Some other machine learning algorithms such as naïve Bayes or k-means can be used together with the filtering.<br /> Predictive neural networks are supervised, which find the best classification accuracy; meanwhile, clustering methods are unsupervised, which group similar samples or genes together. <br /> The goal of training prediction is to enhance the classification capability, and the goal of training classification is to find the optimal group for a new test set with unknown labels.<br /> <br /> '''Neural network filters for cancer prediction''' &lt;br&gt;<br /> In the preprocessing step to classification, clustering, and statistical analysis, the autoencoders are more and more commonly-used, to extract generic genomic features. An autoencoder is composed of the encoder part and the decoder part. The encoder part is to learn the mapping between high-dimensional unlabeled input I(x) and the low-dimensional representations in the middle layer(s), and the decoder part is to learn the mapping from the middle layer’s representation to the high-dimensional output O(x). The reconstruction of the input can take the Root Mean Squared Error (RMSE) or the Logloss function as the objective function. <br /> <br /> $$RMSE = \sqrt{ \frac{\sum{(I(x)-O(x))^2}}{n} }$$<br /> <br /> $$Logloss = \sum{(I(x)\log(O(x)) + (1 - I(x))\log(1 - O(x)))}$$<br /> <br /> There are several types of autoencoders, such as stacked denoising autoencoders, contractive autoencoders, sparse autoencoders, regularized autoencoders, and variational autoencoders. The architecture of the networks varies in many parameters, such as depth and loss function. Each example of an autoencoder mentioned above has a different number of hidden layers, different activation functions (e.g. sigmoid function, exponential linear unit function), and different optimization algorithms (e.g. stochastic gradient descent optimization, Adam optimizer).<br /> <br /> Overfitting is a major problem that most autoencoders need to deal with to achieve high efficiency of the extracted features. Regularization, dropout, and sparsity are common solutions.<br /> <br /> The neural network filtering methods were used by different statistical methods and classifiers. The conventional methods include Cox regression model analysis, Support Vector Machine (SVM), K-means clustering, t-SNE and so on. The classifiers could be SVM or AdaBoost or others.<br /> <br /> By using neural network filtering methods, the model can be trained to learn low-dimensional representations, remove noises from the input, and gain better generalization performance by re-training the classifier with the newest output layer.<br /> <br /> '''Neural network prediction methods for cancer''' &lt;br&gt;<br /> The prediction based on neural networks can build a network that maps the input features to an output with a number of neurons, which could be one or two for binary classification or more for multi-class classification. It can also build several independent binary neural networks for the multi-class classification, where the technique called “one-hot encoding” is applied.<br /> <br /> The codeword is a binary string &lt;math&gt;C'k&lt;/math&gt; of length k whose j’th position is set to 1 for the j’th class, while other positions remain 0. The process of the neural networks is to map the input to the codeword iteratively, whose objective function is minimized in each iteration.<br /> <br /> Such cancer classifiers were applied to identify cancerous/non-cancerous samples, a specific cancer type, or the survivability risk. MLP models were used to predict the survival risk of lung cancer patients with several gene expressions as input. The deep generative model DeepCancer, the RBM-SVM and RBM-logistic regression models, the convolutional feedforward model DeepGene, Extreme Learning Machines (ELM), the one-dimensional convolutional framework model SE1DCNN, and GA-ANN model are all used for solving cancer issues mentioned above. This paper indicates that the performance of neural networks with MLP architecture as a classifier is better than those of SVM, logistic regression, naïve Bayes, classification trees, and KNN.<br /> <br /> '''Neural network clustering methods in cancer prediction''' &lt;br&gt;<br /> Neural network clustering belongs to unsupervised learning. The input data are divided into different groups according to their feature similarity.<br /> The single-layered neural network SOM, which is unsupervised and without a backpropagation mechanism, is one of the traditional model-based techniques to be applied to gene expression data. The measurement of its accuracy could be Rand Index (RI), which can be improved to Adjusted Random Index (ARI) and Normalized Mutation Information (NMI).<br /> <br /> $$RI=\frac{TP+TN}{TP+TN+FP+FN}$$<br /> <br /> In general, gene expression clustering considers either the relevance of samples-to-cluster assignment or that of gene-to-cluster assignment or both. The high dimensionality of gene expression samples poses a problem for traditional clustering algorithms such as k-means clustering, which uses a distance function to separate samples. Such an approach is not viable for high dimensional datasets. To solve the high dimensionality problem, there are two methods: clustering ensembles by running a single clustering algorithm several times, each of which has different initialization or number of parameters; and projective clustering by only considering a subset of the original features.<br /> <br /> SOM was applied on discriminating future tumor behavior using molecular alterations, whose results were not easy to be obtained by classic statistical models. Then this paper introduces two ensemble clustering frameworks: Random Double Clustering-based Cluster Ensembles (RDCCE) and Random Double Clustering-based Fuzzy Cluster Ensembles (RDCFCE). Their accuracies are high, but they have not taken the gene-to-cluster assignment into consideration.<br /> <br /> Also, the paper provides a double SOM based Clustering Ensemble Approach (SOM2CE) and double NG-based Clustering Ensemble Approach (NG2CE), which are robust to noisy genes. Moreover, Projective Clustering Ensemble (PCE) combines the advantages of both projective clustering and ensemble clustering, which is better than SOM and RDCFCE when there are irrelevant genes.<br /> <br /> == Summary ==<br /> <br /> Cancer is a disease with a very high fatality rate that spreads worldwide, and it’s essential to analyze gene expression for discovering gene abnormalities and increasing survivability as a consequence. The previous analysis in the paper reveals that neural networks are essentially used for filtering the gene expressions, predicting their class, or clustering them.<br /> <br /> Neural network filtering methods are used to reduce the dimensionality of the gene expressions and remove their noise. In the article, the authors recommended deep architectures in comparison to shallow architectures for best practice, as they combine many nonlinearities. <br /> <br /> Neural network prediction methods can be used for both binary and multi-class problems. In the binary case, the network architecture has only one or two output neurons that diagnose a given sample as cancerous or non-cancerous. In comparison, the number of the output neurons in multi-class problems is equal to the number of classes. The authors suggested that the deep architecture with convolution layers which was the most recently used model proved efficient capability in predicting cancer subtypes, as it captures the spatial correlations between gene expressions.<br /> Clustering is another analysis tool that is used to divide the gene expressions into groups. The authors indicated that a hybrid approach combining both the assembling, clustering and projective clustering is more accurate than using single-point clustering algorithms, such as SOM, since those methods do not have the capability to distinguish the noisy genes.<br /> <br /> ==Discussion==<br /> There are some technical problems that can be considered and improved for building new models. &lt;br&gt;<br /> <br /> 1. Overfitting: Since gene expression datasets are high dimensional and have a relatively small number of samples, it would be likely to properly fits the training data but not accurate for test samples due to the lack of generalization capability. The ways to avoid overfitting can be: (1). adding weight penalties using regularization; (2). using the average predictions from many models trained on different datasets; (3). dropout. (4) Augmentation of the dataset to produce more &quot;observations&quot;.&lt;br&gt;<br /> <br /> 2. Model configuration and training: In order to reduce both the computational and memory expenses but also with high prediction accuracy, it’s crucial to properly set the network parameters. The possible ways can be: (1). proper initialization; (2). pruning the unimportant connections by removing the zero-valued neurons; (3). using ensemble learning framework by training different models using different parameter settings or using different parts of the dataset for each base model; (4). Using SMOTE for dealing with class imbalance on the high dimensional level. &lt;br&gt;<br /> <br /> 3. Model evaluation: In Braga-Neto and Dougherty's research, they have investigated several model evaluation methods: cross-validation, substitution and bootstrap methods. The cross-validation was found to be unreliable for small size data since it displayed excessive variance. The bootstrap method proved more accurate predictability.&lt;br&gt;<br /> <br /> 4. Study producibility: A study needs to be reproducible to enhance research reliability so that others can replicate the results using the same algorithms, data and methodology. Hence, the query used for getting the dataset should be stated.<br /> <br /> ==Conclusion==<br /> This paper reviewed the most recent neural network-based cancer prediction models and gene expression analysis tools. The analysis indicates that the neural network methods are able to serve as filters, predictors, and clustering methods, and also showed that the role of the neural network determines its general architecture. The authors showed that Neural Network filtering methods are a way of reducing the dimensionality of the gene expressions, as well as removing their noise for better model fitting. To give suggestions for future neural network-based approaches, the authors highlighted some critical points that have to be considered such as overfitting and class imbalance, and suggest choosing different network parameters or combining two or more of the presented approaches. One of the biggest challenges for cancer prediction modelers is deciding on the network architecture (i.e. the number of hidden layers and neurons), as there are currently no guidelines to follow to obtain high prediction accuracy. The authors discovered that there is no algorithm available to concretely determine an optimal number of hidden layers or nodes and found that many papers simply implemented a trial and error method to reduce loss in the model.<br /> <br /> ==Critiques==<br /> <br /> While results indicate that the functionality of the neural network determines its general architecture, the decision on the number of hidden layers, neurons, hypermeters, and learning algorithms is made using trial-and-error techniques. Therefore improvements in this area of the model might need to be explored in order to obtain better results and in order to make more convincing statements.<br /> <br /> An issue that one must be mindful of is the underlying distribution of data. Cancer is an extremely complex genetic disease and the predictions would depend on so many variables, a number of which will not even be present in the dataset as they might have been collected. So there is a need for extensive validation when it comes to applying deep learning methods to cancer-related data.<br /> <br /> In the field of medical sciences and molecular biology, interpretability of results is imperative as often experts seek not just to solve the issue at hand but to understand the causal relationships. Having a high ROC value may not necessarily convince other experts on the validity of the finding because the underlying details of cancer symptoms have been abstracted in a complex neural network as a black box. However, the neural network clustering method suggested in this paper does offer a good compromise because it enables humans to visual low-level features but still gives experts the control on making various predictions using well-studied traditional techniques.<br /> <br /> With high dimensionality features, kernel SVM is another option for cancer prediction. Jiang et. al. developed a Hadamard Kernel for predicting breast cancer using gene expression data, and it utilizes the Kernel trick to avoid high computational efforts (link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5763304/). Compared against linear, quadratic, RBF and correlation kernels, Hadamard Kernel performs best with the highest averaged area under the ROC curve (AUC) value. It may be interesting to compare the performance and accuracy between the Hadamard Kernel and cancer prediction models with various number of hidden layers and neurons.<br /> <br /> Although the authors presented technical details about data processing, training approaches evaluation metric, and addressed many practical issues that can be considered for cancer prediction, no novel methods or models are proposed. It's more like a proof-of-concept about the feasibility of different models on cancer prediction.<br /> <br /> As the authors indicate neural networks would be a useful tool for cancer prediction models, the article is lacking an example for implementing neural networks to provide persuasive support for their arguments.<br /> <br /> The inheritance of cancer is complex and changeable. The predicted variables are therefore very complicated, so for the model of the learning data set, a more adequate training set is needed to learn. And multi-party verification of the learned model.<br /> <br /> The authors mentioned many different neural network models and compared them. It would be better if more details of a commonly applied model with relatively high accuracy could be given such as how the model is built. An article named Convolutional neural network models for cancer type prediction based on gene expression gives explanations of CNN in detail.<br /> <br /> The authors briefly discussed methods and algorithms being used in the presented paper in their summary. However, a very little amount of technical details were provided to the readers. The summary itself is lacking specific examples for the aforementioned algorithms, and datasets which were used in the original analysis were only introduced in one or two sentences. As a result, the summary and conclusion appear to be unconvincing to the readers.<br /> <br /> PCA can still be used as an initial preprocessing step even if it is used in a neural network whose data dimension is reduced. By merging the PCA component with a random number of original functions, some good techniques can be adopted to enable the network to capture more useful relationships<br /> <br /> ==Reference==<br />  Daoud, M., &amp; Mayo, M. (2019). A survey of neural network-based cancer prediction models from microarray data. Artificial Intelligence in Medicine, 97, 204–214.<br /> <br />  Brier GW. 1950. Verification of forecasts expressed in terms of probabilities. Monthly Weather Review 78: 1–3<br /> <br />  Harald Steck, Balaji Krishnapuram, Cary Dehing-oberije, Philippe Lambin, Vikas C. Raykar. On ranking in survival analysis: Bounds on the concordance index. In Advances in Neural Information Processing Systems (2008), pp. 1209-1216<br /> <br />  Google Developers. (2020 February 10). ''Classification: ROC Curve and AUC.'' Machine Learning Crash Course. https://developers.google.com/machine-learning/crash-course/classification/roc-and-auc<br /> <br />  Mostavi, M., Chiu, YC., Huang, Y. et al. Convolutional neural network models for cancer type prediction based on gene expression. ''BMC Med Genomics'' '''13''', 44 (2020). https://doi.org/10.1186/s12920-020-0677-2</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Summary_for_survey_of_neural_networked-based_cancer_prediction_models_from_microarray_data&diff=47803 Summary for survey of neural networked-based cancer prediction models from microarray data 2020-11-29T20:56:45Z <p>Z47shen: /* Critiques */</p> <hr /> <div>== Presented by == <br /> Rao Fu, Siqi Li, Yuqin Fang, Zeping Zhou<br /> <br /> == Introduction == <br /> Microarray technology can help researchers quickly detect genetic information and is widely used to analyze genetic diseases. Researchers use this technology to compare normal and abnormal cancerous tissues to gain insights into the pathology of cancer. <br /> <br /> However, due to the high dimensionality of the gene expressions, accuracy and computation time of the model might be affected. The following two approaches are adopted to cope with this problem: the feature selection method and the feature creating method. The formal one, similar to the well-known principle component analysis method, aims to focus on key features and ignore minor noises. On the other hand, the latter one, similar to scale invariant feature transformations, aims to combine existing features or map them to a new low-dimensional space.<br /> <br /> Comparing to neural network models presented by others, this paper is specifically designed for predicting cancer using gene expression data. Thus, we will review the latest neural network-based cancer prediction models by presenting the methodology of preprocessing, filtering, prediction, and clustering gene expressions.<br /> <br /> == Background == <br /> <br /> '''Neural Network''' &lt;br&gt;<br /> Neural networks are often used to solve non-linear complex problems. It is an operational model consisting of a large number of neurons connected to each other by different weights. In this network structure, each neuron is related to an activation function such as sigmoid or rectified linear activation functions. To train the network, the inputs are fed forward and the activation function value is calculated at every neuron. The difference between the output of the neural network and the actual value is what we call an error.<br /> The backpropagation mechanism is one of the most commonly used algorithms in solving neural network problems. By using this algorithm, we optimize the objective function by propagating back the generated error through the network to adjust the weights.<br /> In the next sections, we will use the above algorithm but with different network architectures and a different number of neurons to review the neural network-based cancer prediction models for learning the gene expression features.<br /> <br /> '''Cancer prediction models'''&lt;br&gt;<br /> Cancer prediction models often contain more than 1 method to achieve high prediction accuracy with a more accurate prognosis and it also aims to reduce the cost of patients.<br /> <br /> High dimensionality and spatial structure are the two main factors that can affect the accuracy of the cancer prediction models. They add irrelevant noisy features to our selected models. We have 3 ways to determine the accuracy of a model.<br /> <br /> The first is called the ROC curve. ROC curves, receiver operating characteristic curves, are graphs that show the true positive rate against the false-positive rate . It reflects the sensitivity of the response to the same signal stimulus under different criterias. To test its validity, we need to consider it with the confidence interval. Usually, a model is considered acceptable when its ROC is greater than 0.7. <br /> <br /> A different machine learning problem is predicting the survival time. The performance of a model that predicts survival time can be measured using two metrics. The problem of predicting survival time can be seen as a ranking problem, where survival times of different subjects are ranked against each other. CI (Concordance Index) is a measure of how good a model ranks survival times and explains the concordance probability of the predicted and observed survival. The closer its value to 0.7, the better the model is. We can express the ordering of survival times in an order graph &lt;math display=&quot;inline&quot;&gt;G = (V, E)&lt;/math&gt; where the vertices &lt;math display=&quot;inline&quot;&gt;V&lt;/math&gt; are the individual survival times, and the edges &lt;math display=&quot;inline&quot;&gt;E_{ij}&lt;/math&gt; from individual &lt;math display=&quot;inline&quot;&gt;i&lt;/math&gt; to &lt;math display=&quot;inline&quot;&gt;j&lt;/math&gt; indicate that &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt;, where &lt;math display=&quot;inline&quot;&gt;T_i, T_j&lt;/math&gt; are the survival times for individuals &lt;math display=&quot;inline&quot;&gt;i,j&lt;/math&gt; respectively. Then we can write &lt;math display=&quot;inline&quot;&gt;CI = \frac{1}{|E|}\sum_{i,j}I(f(i) &lt; f(j))&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;|E|&lt;/math&gt; is the number of edges in the order graph (ie. the total number of comparable pairs), and &lt;math display=&quot;inline&quot;&gt;I(f(i) &lt; f(j)) = 1&lt;/math&gt; if the predictor &lt;math display=&quot;inline&quot;&gt;f&lt;/math&gt; correctly ranks &lt;math display=&quot;inline&quot;&gt;T_i &lt; T_j&lt;/math&gt; .<br /> <br /> Another metric is the Brier score, which measures the average difference between the observed and the estimated survival rate in a given period of time. It ranges from 0 to 1, and a lower score indicates higher accuracy. It is defined as &lt;math display=&quot;inline&quot;&gt;\frac{1}{n}\sum_{i=1}^n(f_i - o_i)^2&lt;/math&gt; where &lt;math display=&quot;inline&quot;&gt;f_i&lt;/math&gt; is the predicted survival rate, and &lt;math display=&quot;inline&quot;&gt;o_i&lt;/math&gt; is the observed survival rate .<br /> <br /> == Neural network-based cancer prediction models ==<br /> An extensive search relevant to neural network-based cancer prediction was performed using Google scholar and other electronic databases namely PubMed and Scopus with keywords such as “Neural Networks AND Cancer Prediction” and “gene expression clustering”, and only articles between 2013 and 2018 with available accessibility were considered. The chosen papers covered cancer classification, discovery, survivability prediction, and statistical analysis models. The following figure 1 shows a graph representing the number of citations including filtering, predictive, and clustering for chosen papers. <br /> <br /> [[File:f1.png]]<br /> <br /> '''Datasets and preprocessing''' &lt;br&gt;<br /> Most studies investigating automatic cancer prediction and clustering used datasets such as the TCGA, UCI, NCBI Gene Expression Omnibus and Kentridge biomedical databases. There are a few techniques used in processing dataset including removing the genes that have zero expression across all samples, Normalization, filtering with p-value &gt; &lt;math&gt;10^{-5}&lt;/math&gt; to remove some unwanted technical variation and &lt;math&gt;\log_2&lt;/math&gt; transformations. Statistical methods, neural networks, were applied to reduce the dimensionality of the gene expressions by selecting a subset of genes. Principle Component Analysis (PCA) can also be used as an initial preprocessing step to extract the dataset's features. The PCA method linearly transforms the dataset features into lower dimensional space without capturing the complex relationships between the features. However, simply removing the genes that were not measured by the other datasets could not overcome the class imbalance problem. In that case, one research used Synthetic Minority Class Over Sampling method to generate synthetic minority class samples, which may lead to a sparse matrix problem. Clustering was also applied in some studies for labeling data by grouping the samples into high-risk, low-risk groups, and so on. <br /> <br /> The following table presents the dataset used by considered reference, the applied normalization technique, the cancer type and the dimensionality of the datasets.<br /> <br /> [[File:Datasets and preprocessing.png]]<br /> <br /> '''Neural network architecture''' &lt;br&gt;<br /> Most recent studies reveal that neural network methods are used for filtering, predicting and clustering in cancer prediction. <br /> <br /> *''filtering'': Filter the gene expressions to eliminate noise or reduce dimensionality. Then use the resulted features with statistical methods or machine learning classification and clustering tools as figure 2 indicates.<br /> <br /> *''predicting'': Extract features and improve the accuracy of prediction (classification).<br /> <br /> *''clustering'': Divide the gene expressions or samples based on similarity.<br /> <br /> [[File:filtering gane.png]]<br /> <br /> All the neurons in the neural network work together as feature detectors to learn the features from the input. In order to categorize a neural network as filtering, predicting, or clustering method, we looked at the overall role that network provided within the framework of cancer prediction. Filtering methods are trained to remove the input’s noise and to extract the most representative features that best describe the unlabeled gene expressions. Predicting methods are trained to extract the features that are significant to prediction, therefore its objective functions measure how accurately the network is able to predict the class of input. Clustering methods are trained to divide unlabeled samples into groups based on their similarities.<br /> <br /> '''Building neural networks-based approaches for gene expression prediction''' &lt;br&gt;<br /> According to our survey, the representative codes are generated by filtering methods with dimensionality M smaller or equal to N, where N is the dimensionality of the input. Some other machine learning algorithms such as naïve Bayes or k-means can be used together with the filtering.<br /> Predictive neural networks are supervised, which find the best classification accuracy; meanwhile, clustering methods are unsupervised, which group similar samples or genes together. <br /> The goal of training prediction is to enhance the classification capability, and the goal of training classification is to find the optimal group for a new test set with unknown labels.<br /> <br /> '''Neural network filters for cancer prediction''' &lt;br&gt;<br /> In the preprocessing step to classification, clustering, and statistical analysis, the autoencoders are more and more commonly-used, to extract generic genomic features. An autoencoder is composed of the encoder part and the decoder part. The encoder part is to learn the mapping between high-dimensional unlabeled input I(x) and the low-dimensional representations in the middle layer(s), and the decoder part is to learn the mapping from the middle layer’s representation to the high-dimensional output O(x). The reconstruction of the input can take the Root Mean Squared Error (RMSE) or the Logloss function as the objective function. <br /> <br /> $$RMSE = \sqrt{ \frac{\sum{(I(x)-O(x))^2}}{n} }$$<br /> <br /> $$Logloss = \sum{(I(x)\log(O(x)) + (1 - I(x))\log(1 - O(x)))}$$<br /> <br /> There are several types of autoencoders, such as stacked denoising autoencoders, contractive autoencoders, sparse autoencoders, regularized autoencoders, and variational autoencoders. The architecture of the networks varies in many parameters, such as depth and loss function. Each example of an autoencoder mentioned above has a different number of hidden layers, different activation functions (e.g. sigmoid function, exponential linear unit function), and different optimization algorithms (e.g. stochastic gradient descent optimization, Adam optimizer).<br /> <br /> Overfitting is a major problem that most autoencoders need to deal with to achieve high efficiency of the extracted features. Regularization, dropout, and sparsity are common solutions.<br /> <br /> The neural network filtering methods were used by different statistical methods and classifiers. The conventional methods include Cox regression model analysis, Support Vector Machine (SVM), K-means clustering, t-SNE and so on. The classifiers could be SVM or AdaBoost or others.<br /> <br /> By using neural network filtering methods, the model can be trained to learn low-dimensional representations, remove noises from the input, and gain better generalization performance by re-training the classifier with the newest output layer.<br /> <br /> '''Neural network prediction methods for cancer''' &lt;br&gt;<br /> The prediction based on neural networks can build a network that maps the input features to an output with a number of neurons, which could be one or two for binary classification or more for multi-class classification. It can also build several independent binary neural networks for the multi-class classification, where the technique called “one-hot encoding” is applied.<br /> <br /> The codeword is a binary string &lt;math&gt;C'k&lt;/math&gt; of length k whose j’th position is set to 1 for the j’th class, while other positions remain 0. The process of the neural networks is to map the input to the codeword iteratively, whose objective function is minimized in each iteration.<br /> <br /> Such cancer classifiers were applied to identify cancerous/non-cancerous samples, a specific cancer type, or the survivability risk. MLP models were used to predict the survival risk of lung cancer patients with several gene expressions as input. The deep generative model DeepCancer, the RBM-SVM and RBM-logistic regression models, the convolutional feedforward model DeepGene, Extreme Learning Machines (ELM), the one-dimensional convolutional framework model SE1DCNN, and GA-ANN model are all used for solving cancer issues mentioned above. This paper indicates that the performance of neural networks with MLP architecture as a classifier is better than those of SVM, logistic regression, naïve Bayes, classification trees, and KNN.<br /> <br /> '''Neural network clustering methods in cancer prediction''' &lt;br&gt;<br /> Neural network clustering belongs to unsupervised learning. The input data are divided into different groups according to their feature similarity.<br /> The single-layered neural network SOM, which is unsupervised and without a backpropagation mechanism, is one of the traditional model-based techniques to be applied to gene expression data. The measurement of its accuracy could be Rand Index (RI), which can be improved to Adjusted Random Index (ARI) and Normalized Mutation Information (NMI).<br /> <br /> $$RI=\frac{TP+TN}{TP+TN+FP+FN}$$<br /> <br /> In general, gene expression clustering considers either the relevance of samples-to-cluster assignment or that of gene-to-cluster assignment or both. The high dimensionality of gene expression samples poses a problem for traditional clustering algorithms such as k-means clustering, which uses a distance function to separate samples. Such an approach is not viable for high dimensional datasets. To solve the high dimensionality problem, there are two methods: clustering ensembles by running a single clustering algorithm several times, each of which has different initialization or number of parameters; and projective clustering by only considering a subset of the original features.<br /> <br /> SOM was applied on discriminating future tumor behavior using molecular alterations, whose results were not easy to be obtained by classic statistical models. Then this paper introduces two ensemble clustering frameworks: Random Double Clustering-based Cluster Ensembles (RDCCE) and Random Double Clustering-based Fuzzy Cluster Ensembles (RDCFCE). Their accuracies are high, but they have not taken the gene-to-cluster assignment into consideration.<br /> <br /> Also, the paper provides a double SOM based Clustering Ensemble Approach (SOM2CE) and double NG-based Clustering Ensemble Approach (NG2CE), which are robust to noisy genes. Moreover, Projective Clustering Ensemble (PCE) combines the advantages of both projective clustering and ensemble clustering, which is better than SOM and RDCFCE when there are irrelevant genes.<br /> <br /> == Summary ==<br /> <br /> Cancer is a disease with a very high fatality rate that spreads worldwide, and it’s essential to analyze gene expression for discovering gene abnormalities and increasing survivability as a consequence. The previous analysis in the paper reveals that neural networks are essentially used for filtering the gene expressions, predicting their class, or clustering them.<br /> <br /> Neural network filtering methods are used to reduce the dimensionality of the gene expressions and remove their noise. In the article, the authors recommended deep architectures in comparison to shallow architectures for best practice, as they combine many nonlinearities. <br /> <br /> Neural network prediction methods can be used for both binary and multi-class problems. In the binary case, the network architecture has only one or two output neurons that diagnose a given sample as cancerous or non-cancerous. In comparison, the number of the output neurons in multi-class problems is equal to the number of classes. The authors suggested that the deep architecture with convolution layers which was the most recently used model proved efficient capability in predicting cancer subtypes, as it captures the spatial correlations between gene expressions.<br /> Clustering is another analysis tool that is used to divide the gene expressions into groups. The authors indicated that a hybrid approach combining both the assembling, clustering and projective clustering is more accurate than using single-point clustering algorithms, such as SOM, since those methods do not have the capability to distinguish the noisy genes.<br /> <br /> ==Discussion==<br /> There are some technical problems that can be considered and improved for building new models. &lt;br&gt;<br /> <br /> 1. Overfitting: Since gene expression datasets are high dimensional and have a relatively small number of samples, it would be likely to properly fits the training data but not accurate for test samples due to the lack of generalization capability. The ways to avoid overfitting can be: (1). adding weight penalties using regularization; (2). using the average predictions from many models trained on different datasets; (3). dropout. (4) Augmentation of the dataset to produce more &quot;observations&quot;.&lt;br&gt;<br /> <br /> 2. Model configuration and training: In order to reduce both the computational and memory expenses but also with high prediction accuracy, it’s crucial to properly set the network parameters. The possible ways can be: (1). proper initialization; (2). pruning the unimportant connections by removing the zero-valued neurons; (3). using ensemble learning framework by training different models using different parameter settings or using different parts of the dataset for each base model; (4). Using SMOTE for dealing with class imbalance on the high dimensional level. &lt;br&gt;<br /> <br /> 3. Model evaluation: In Braga-Neto and Dougherty's research, they have investigated several model evaluation methods: cross-validation, substitution and bootstrap methods. The cross-validation was found to be unreliable for small size data since it displayed excessive variance. The bootstrap method proved more accurate predictability.&lt;br&gt;<br /> <br /> 4. Study producibility: A study needs to be reproducible to enhance research reliability so that others can replicate the results using the same algorithms, data and methodology. Hence, the query used for getting the dataset should be stated.<br /> <br /> ==Conclusion==<br /> This paper reviewed the most recent neural network-based cancer prediction models and gene expression analysis tools. The analysis indicates that the neural network methods are able to serve as filters, predictors, and clustering methods, and also showed that the role of the neural network determines its general architecture. The authors showed that Neural Network filtering methods are a way of reducing the dimensionality of the gene expressions, as well as removing their noise for better model fitting. To give suggestions for future neural network-based approaches, the authors highlighted some critical points that have to be considered such as overfitting and class imbalance, and suggest choosing different network parameters or combining two or more of the presented approaches. One of the biggest challenges for cancer prediction modelers is deciding on the network architecture (i.e. the number of hidden layers and neurons), as there are currently no guidelines to follow to obtain high prediction accuracy. The authors discovered that there is no algorithm available to concretely determine an optimal number of hidden layers or nodes and found that many papers simply implemented a trial and error method to reduce loss in the model.<br /> <br /> ==Critiques==<br /> <br /> While results indicate that the functionality of the neural network determines its general architecture, the decision on the number of hidden layers, neurons, hypermeters, and learning algorithms is made using trial-and-error techniques. Therefore improvements in this area of the model might need to be explored in order to obtain better results and in order to make more convincing statements.<br /> <br /> An issue that one must be mindful of is the underlying distribution of data. Cancer is an extremely complex genetic disease and the predictions would depend on so many variables, a number of which will not even be present in the dataset as they might have been collected. So there is a need for extensive validation when it comes to applying deep learning methods to cancer-related data.<br /> <br /> In the field of medical sciences and molecular biology, interpretability of results is imperative as often experts seek not just to solve the issue at hand but to understand the causal relationships. Having a high ROC value may not necessarily convince other experts on the validity of the finding because the underlying details of cancer symptoms have been abstracted in a complex neural network as a black box. However, the neural network clustering method suggested in this paper does offer a good compromise because it enables humans to visual low-level features but still gives experts the control on making various predictions using well-studied traditional techniques.<br /> <br /> With high dimensionality features, kernel SVM is another option for cancer prediction. Jiang et. al. developed a Hadamard Kernel for predicting breast cancer using gene expression data, and it utilizes the Kernel trick to avoid high computational efforts (link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5763304/). Compared against linear, quadratic, RBF and correlation kernels, Hadamard Kernel performs best with the highest averaged area under the ROC curve (AUC) value. It may be interesting to compare the performance and accuracy between the Hadamard Kernel and cancer prediction models with various number of hidden layers and neurons.<br /> <br /> Although the authors presented technical details about data processing, training approaches evaluation metric, and addressed many practical issues that can be considered for cancer prediction, no novel methods or models are proposed. It's more like a proof-of-concept about the feasibility of different models on cancer prediction.<br /> <br /> As the authors indicate neural networks would be a useful tool for cancer prediction models, the article is lacking an example for implementing neural networks to provide persuasive support for their arguments.<br /> <br /> The inheritance of cancer is complex and changeable. The predicted variables are therefore very complicated, so for the model of the learning data set, a more adequate training set is needed to learn. And multi-party verification of the learned model.<br /> <br /> The authors mentioned many different neural network models and compared them. It would be better if more details of a commonly applied model with relatively high accuracy could be given such as how the model is built. An article named Convolutional neural network models for cancer type prediction based on gene expression gives explanations of CNN in detail.<br /> <br /> The authors briefly discussed methods and algorithms being used in the presented paper in their summary. However, a very little amount of technical details were provided to the readers. The summary itself is lacking specific examples for the aforementioned algorithms, and datasets which were used in the original analysis were only introduced in one or two sentences. As a result, the summary and conclusion appear to be unconvincing to the readers.<br /> <br /> By merging the PCA component with a random number of original functions, some good techniques can be adopted to enable the network to capture more useful relationships<br /> <br /> ==Reference==<br />  Daoud, M., &amp; Mayo, M. (2019). A survey of neural network-based cancer prediction models from microarray data. Artificial Intelligence in Medicine, 97, 204–214.<br /> <br />  Brier GW. 1950. Verification of forecasts expressed in terms of probabilities. Monthly Weather Review 78: 1–3<br /> <br />  Harald Steck, Balaji Krishnapuram, Cary Dehing-oberije, Philippe Lambin, Vikas C. Raykar. On ranking in survival analysis: Bounds on the concordance index. In Advances in Neural Information Processing Systems (2008), pp. 1209-1216<br /> <br />  Google Developers. (2020 February 10). ''Classification: ROC Curve and AUC.'' Machine Learning Crash Course. https://developers.google.com/machine-learning/crash-course/classification/roc-and-auc<br /> <br />  Mostavi, M., Chiu, YC., Huang, Y. et al. Convolutional neural network models for cancer type prediction based on gene expression. ''BMC Med Genomics'' '''13''', 44 (2020). https://doi.org/10.1186/s12920-020-0677-2</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan&diff=47802 User:Yktan 2020-11-29T20:46:30Z <p>Z47shen: /* Introduction */</p> <hr /> <div><br /> == Introduction ==<br /> <br /> Much of the success in training deep neural networks (DNNs) is due to the collection of large datasets with human-annotated labels. However, human annotation is a both time-consuming and expensive task, especially for the data that requires expertise such as medical data. Furthermore, certain datasets will be noisy due to the biases introduced by different annotators.<br /> <br /> There are a few existing approaches to use datasets with noisy labels. In learning with noisy labels (LNL), most methods take a loss correction approach. Other LNL methods estimate a noise transition matrix and employ it to correct the loss function. An example of a popular loss correction approach is the bootstrapping loss approach. Another approach to reduce annotation cost is semi-supervised learning (SSL), where the training data consists of labeled and unlabeled samples.<br /> <br /> This paper introduces DivideMix, which combines approaches from LNL and SSL. One unique thing about DivideMix is that it discards sample labels that are highly likely to be noisy and leverages these noisy samples as unlabeled data instead. This prevents the model from overfitting and improves generalization performance. Key contributions of this work are:<br /> 1) Co-divide, which trains two networks simultaneously, aims to improve generalization and avoiding confirmation bias.<br /> 2) During the SSL phase, an improvement is made on an existing method (MixMatch) by combining it with another method (MixUp).<br /> 3) Significant improvements to state-of-the-art results on multiple conditions are experimentally shown while using DivideMix. Extensive ablation study and qualitative results are also shown to examine the effect of different components.<br /> <br /> == Motivation ==<br /> <br /> While much has been achieved in training DNNs with noisy labels and SSL methods individually, not much progress has been made in exploring their underlying connections and building on top of the two approaches simultaneously. <br /> <br /> Existing LNL methods aim to correct the loss function by:<br /> &lt;ol&gt;<br /> &lt;li&gt; Treating all samples equally and correcting loss explicitly or implicitly through relabeling of the noisy samples<br /> &lt;li&gt; Reweighting training samples or separating clean and noisy samples, which results in correction of the loss function<br /> &lt;/ol&gt;<br /> <br /> A few examples of LNL methods include:<br /> &lt;ol&gt;<br /> &lt;li&gt; Estimating the noise transition matrix, which denote the probability of clean labels flipping to noisy labels, to correct the loss function<br /> &lt;li&gt; Leveraging DNNs to correct labels and using them to modify the loss<br /> &lt;li&gt; Reweighting samples so that noisy labels contribute less to the loss<br /> &lt;/ol&gt;<br /> <br /> However, these methods each have some downsides. For example, it is very challenging to correctly estimate the noise transition matrix in the first method; for the second method, DNNs tend to overfit to datasets with high noise ratio; for the third method, we need to be able to identify clean samples, which has also proven to be challenging.<br /> <br /> On the other hand, SSL methods mostly leverage unlabeled data using regularization to improve model performance. A recently proposed method, MixMatch incorporates the two classes of regularization – consistency regularization which enforces the model to produce consistent predictions on augmented input data, and entropy minimization which encourages the model to give high-confidence predictions on unlabeled data, as well as MixUp regularization. <br /> <br /> DivideMix partially adopts LNL in that it removes the labels that are highly likely to be noisy by using co-divide to avoid the confirmation bias problem. It then utilizes the noisy samples as unlabeled data and adopts an improved version of MixMatch (SSL) which accounts for the label noise during the label co-refinement and co-guessing phase. By incorporating SSL techniques into LNL and taking the best of both worlds, DivideMix aims to produce highly promising results in training DNNs by better addressing the confirmation bias problem, more accurately distinguishing and utilizing noisy samples, and performing well under high levels of noise.<br /> <br /> == Model Architecture and Algorithm ==<br /> <br /> DivideMix leverages semi-supervised learning to achieve effective modeling. The sample is first split into a labeled set and an unlabeled set. This is achieved by fitting a Gaussian Mixture Model as a per-sample loss distribution. The unlabeled set is made up of data points with discarded labels deemed noisy. Then, to avoid confirmation bias, which is typical when a model is self-training, two models are being trained simultaneously to filter error for each other. This is done by dividing the data using one model and then training the other model. This algorithm, known as Co-divide, keeps the two networks from converging when training, which avoids the bias from occurring. Being diverged also offers the two networks distrinct abilities to filter different types of error, making the model more robust to noise. Figure 1 describes the algorithm in graphical form.<br /> <br /> [[File:ModelArchitecture.PNG | center]]<br /> <br /> &lt;div align=&quot;center&quot;&gt;Figure 1: Model Architecture of DivideMix&lt;/div&gt;<br /> <br /> For each epoch, the network divides the dataset into a labeled set consisting of clean data, and an unlabeled set consisting of noisy data, which is then used as training data for the other network, where training is done in mini-batches. For each batch of the labelled samples, co-refinement is performed by using the ground truth label &lt;math&gt; y_b &lt;/math&gt;, the predicted label &lt;math&gt; p_b &lt;/math&gt;, and the posterior is used as the weight, &lt;math&gt; w_b &lt;/math&gt;. <br /> <br /> &lt;center&gt;&lt;math&gt; \bar{y}_b = w_b y_b + (1-w_b) p_b &lt;/math&gt;&lt;/center&gt; <br /> <br /> Then, a sharpening function is implemented on this weighted sum to produce the estimate, &lt;math&gt; \hat{y}_b &lt;/math&gt; Using all these predicted labels, the unlabeled samples will then be assigned a &quot;co-guessed&quot; label, which should produce a more accurate prediction.<br /> &lt;math&gt; \hat{y}_b=Sharpen(\bar{y}_b,T)={\bar{y}^{c{\frac{1}{T}}}_b}/{\sum_{c=1}^C\bar{y}^{c{\frac{1}{T}}}_b} &lt;/math&gt;, for c = 1, 2,....., C.<br /> Having calculated all these labels, MixMatch is applied to the combined mini-batch of labeled, &lt;math&gt; \hat{X} &lt;/math&gt; and unlabeled data, &lt;math&gt; \hat{U} &lt;/math&gt;, where, for a pair of samples and their labels, one new sample and new label is produced. More specifically, for a pair of samples &lt;math&gt; (x_1,x_2) &lt;/math&gt; and their labels &lt;math&gt; (p_1,p_2) &lt;/math&gt;, the mixed sample &lt;math&gt; (x',p') &lt;/math&gt; is:<br /> <br /> &lt;center&gt;<br /> &lt;math&gt;<br /> \begin{alignat}{2}<br /> <br /> \lambda &amp;\sim Beta(\alpha, \alpha) \\<br /> \lambda ' &amp;= max(\lambda, 1 - \lambda) \\<br /> x' &amp;= \lambda ' x_1 + (1 - \lambda ' ) x_2 \\<br /> p' &amp;= \lambda ' p_1 + (1 - \lambda ' ) p_2 \\<br /> <br /> \end{alignat}<br /> &lt;/math&gt;<br /> &lt;/center&gt; <br /> <br /> MixMatch transforms &lt;math&gt; \hat{X} &lt;/math&gt; and &lt;math&gt; \hat{U} &lt;/math&gt; into &lt;math&gt; X' &lt;/math&gt; and &lt;math&gt; U' &lt;/math&gt;. Then, the loss on &lt;math&gt; X' &lt;/math&gt;, &lt;math&gt; L_X &lt;/math&gt; (Cross-entropy loss) and the loss on &lt;math&gt; U' &lt;/math&gt;, &lt;math&gt; L_U &lt;/math&gt; (Mean Squared Error) are calculated. A regularization term, &lt;math&gt; L_{reg} &lt;/math&gt;, is introduced to regularize the model's average output across all samples in the mini-batch. Then, the total loss is calculated as:<br /> <br /> &lt;center&gt;&lt;math&gt; L = L_X + \lambda_u L_U + \lambda_r L_{reg} &lt;/math&gt;&lt;/center&gt; <br /> <br /> where &lt;math&gt; \lambda_r &lt;/math&gt; is set to 1, and &lt;math&gt; \lambda_u &lt;/math&gt; is used to control the unsupervised loss.<br /> <br /> Lastly, the stochastic gradient descent formula is updated with the calculated loss, &lt;math&gt; L &lt;/math&gt;, and the estimated parameters, &lt;math&gt; \boldsymbol{ \theta } &lt;/math&gt;.<br /> <br /> The full algorithm is shown below. [[File:dividemix.jpg|600px| | center]]<br /> &lt;div align=&quot;center&quot;&gt;Algorithm1: DivideMix. Line 4-8: co-divide; Line 17-18: label co-refinement; Line 20: co-guessing.&lt;/div&gt;<br /> <br /> The when the model is warmed up, it is trained on all data using standard cross-entropy to initially converge the model, but with a regulatory negative entropy term &lt;math&gt;\mathcal{H} = -\sum_{c}\text{p}^\text{c}_\text{model}(x;\theta)\log(\text{p}^\text{c}_\text{model}(x;\theta))&lt;/math&gt;, where &lt;math&gt;\text{p}^\text{c}_\text{model}&lt;/math&gt; is the softmax output probability for class c. This term penalizes confident predictions during the warm up to prevent overfitting to noise during the warm up, which can happen when there is asymmetric noise.<br /> <br /> == Results ==<br /> '''Applications'''<br /> <br /> The method was validated using four benchmark datasets: CIFAR-10, CIFAR100 (Krizhevsky &amp; Hinton, 2009) which contain 50K training images and 10K test images of size 32 × 32), Clothing1M (Xiao et al., 2015), and WebVision (Li et al., 2017a).<br /> Two types of label noise are used in the experiments: symmetric and asymmetric.<br /> An 18-layer PreAct Resnet (He et al., 2016) is trained using SGD with a momentum of 0.9, a weight decay of 0.0005, and a batch size of 128. The network is trained for 300 epochs. The initial learning rate was set to 0.02, and reduced by a factor of 10 after 150 epochs. Before applying the Co-divide and MixMatch strategies, the models were first independently trained over the entire dataset using cross-entropy loss during a &quot;warm-up&quot; period. Initially, training the models in this way prepares a more regular distribution of losses to improve upon in subsequent epochs. The warm-up period is 10 epochs for CIFAR-10 and 30 epochs for CIFAR-100. For all CIFAR experiments, we use the same hyperparameters M = 2, T = 0.5, and α = 4. τ is set as 0.5 except for 90% noise ratio when it is set as 0.6.<br /> <br /> <br /> '''Comparison of State-of-the-Art Methods'''<br /> <br /> The effectiveness of DivideMix was shown by comparing the test accuracy with the most recent state-of-the-art methods: <br /> Meta-Learning (Li et al., 2019) proposes a gradient-based method to find model parameters that are more noise-tolerant; <br /> Joint-Optim (Tanaka et al., 2018) and P-correction (Yi &amp; Wu, 2019) jointly optimize the sample labels and the network parameters;<br /> M-correction (Arazo et al., 2019) models sample loss with BMM and apply MixUp.<br /> The following are the results on CIFAR-10 and CIFAR-100 with different levels of symmetric label noise ranging from 20% to 90%. Both the best test accuracy across all epochs and the averaged test accuracy over the last 10 epochs were recorded in the following table:<br /> <br /> <br /> [[File:divideMixtable1.PNG | center]]<br /> <br /> From table 1, the author noticed that none of these methods can consistently outperform others across different datasets. M-correction excels at symmetric noise, whereas Meta-Learning performs better for asymmetric noise. DivideMix outperforms state-of-the-art methods by a large margin across all noise ratios. The improvement is substantial (∼10% of accuracy) for the more challenging CIFAR-100 with high noise ratios.<br /> <br /> DivideMix was compared with the state-of-the-art methods with the other two datasets: Clothing1M and WebVision. It also shows that DivideMix consistently outperforms state-of-the-art methods across all datasets with different types of label noise. For WebVision, DivideMix achieves more than 12% improvement in top-1 accuracy. <br /> <br /> <br /> '''Ablation Study'''<br /> <br /> The effect of removing different components to provide insights into what makes DivideMix successful. We analyze the results in Table 5 as follows.<br /> <br /> <br /> [[File:DivideMixtable5.PNG | center]]<br /> <br /> The authors find that both label refinement and input augmentation are beneficial for DivideMix. ''Label refinement'' is important for high noise ratio due because samples that are more noisy would be incorrectly divided into the labeled set. ''Augmentation'' upgrades model performance by creating more reliable predictions and by achieving consistency regularization. In addition, the performance drop seen in the ''DivideMix w/o co-training'' highlights the disadvantage of self-training; the model still has dataset division, label refinement and label guessing, but they are all performed by the same model.<br /> <br /> == Conclusion ==<br /> <br /> This paper provides a new and effective algorithm for learning with noisy labels by leveraging SSL. The DivideMix method trains two networks simultaneously and utilizes co-guessing and co-labeling effectively, therefore it is a robust approach to dealing with noise in datasets. DivideMix has also been tested using various datasets with the results consistently being one of the best when compared to other advanced methods.<br /> <br /> Future work of DivideMix is to create an adaptation for other applications such as Natural Language Processing, and incorporating the ideas of SSL and LNL into DivideMix architecture.<br /> <br /> == Critiques/ Insights ==<br /> <br /> 1. While combining both models makes the result better, the author did not show the relative time increase using this new combined methodology, which is very crucial considering training a large amount of data, especially for images. In addition, it seems that the author did not perform much on hyperparameters tuning for the combined model.<br /> <br /> 2. There is an interesting insight, which is when the noise ratio increases from 80% to 90%, the accuracy of DivideMix drops dramatically in both datasets.<br /> <br /> 3. There should be a further explanation of why the learning rate drops by a factor of 10 after 150 epochs.<br /> <br /> 4. It would be interesting to see the effectiveness of this method in other domains such as NLP. I am not aware of noisy training datasets available in NLP, but surely this is an important area to focus on, as much of the available data is collected from noisy sources from the web.<br /> <br /> 5. The paper implicitly assumes that a Gaussian mixture model (GMM) is sufficiently capable of identifying noise. Given the nature of a GMM, it would work well for noise that is distributed by a Gaussian distribution but for all other noise, it would probably be only asymptotic. The paper should present theoretical results on the noise that are Exponential, Rayleigh, etc. This is particularly important because the experiments were done on massive datasets, but they do not directly address the case when there are not many data points. <br /> <br /> 6. Comparing the training result on these benchmark datasets makes the algorithm quite comprehensive. This is a very insightful idea to maintain two networks to avoid bias from occurring.<br /> <br /> == References ==<br /> Eric Arazo, Diego Ortego, Paul Albert, Noel E. O’Connor, and Kevin McGuinness. Unsupervised<br /> label noise modeling and loss correction. In ICML, pp. 312–321, 2019.<br /> <br /> David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin<br /> Raffel. Mixmatch: A holistic approach to semi-supervised learning. NeurIPS, 2019.<br /> <br /> Yifan Ding, Liqiang Wang, Deliang Fan, and Boqing Gong. A semi-supervised two-stage approach<br /> to learning from noisy labels. In WACV, pp. 1215–1224, 2018.</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46125 User:T358wang 2020-11-23T20:54:48Z <p>Z47shen: /* Experiments and Analysis */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. Using this model, similar metrics to the state of the art model in the test were obtained and the inference time was found to be 15 times faster. Further, because of the efficient architecture, the system can serve in an online fashion. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of the model.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks. And we find that the sensitivity of “frequent” landmarks are much higher than “rare” landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==<br />  Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recogni- tion via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://arxiv.org/pdf/1908.10192.pdf 3357384.3357956<br /> <br />  FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br /> 2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br /> arXiv preprint arXiv:1803.11285 (2018).</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46102 User:T358wang 2020-11-23T18:35:26Z <p>Z47shen: /* Experiments and Analysis */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==<br />  Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recogni- tion via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://arxiv.org/pdf/1908.10192.pdf 3357384.3357956<br /> <br />  FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br /> 2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br /> arXiv preprint arXiv:1803.11285 (2018).</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46101 User:T358wang 2020-11-23T18:35:03Z <p>Z47shen: /* References */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==<br />  Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recogni- tion via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://arxiv.org/pdf/1908.10192.pdf 3357384.3357956<br /> <br />  FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br /> 2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br /> arXiv preprint arXiv:1803.11285 (2018).</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46096 User:T358wang 2020-11-23T18:33:56Z <p>Z47shen: /* References */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==<br />  Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recogni- tion via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://doi.org/10.1145/ 3357384.3357956<br /> <br />  FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br /> 2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br /> arXiv preprint arXiv:1803.11285 (2018).</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46095 User:T358wang 2020-11-23T18:33:45Z <p>Z47shen: /* References */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==<br />  Andrei Boiarov and Eduard Tyantov. 2019. Large Scale Landmark Recogni- tion via Deep Metric Learning. In The 28th ACM International Conference on Information and Knowledge Management (CIKM ’19), November 3–7, 2019, Beijing, China. ACM, New York, NY, USA, 10 pages. https://doi.org/10.1145/ 3357384.3357956<br />  FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br /> 2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br /> arXiv preprint arXiv:1803.11285 (2018).</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46088 User:T358wang 2020-11-23T18:20:17Z <p>Z47shen: /* Comparison */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46087 User:T358wang 2020-11-23T18:20:06Z <p>Z47shen: /* Comparison */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in the sensitivity&amp;specificity table), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46086 User:T358wang 2020-11-23T18:17:56Z <p>Z47shen: /* Experiments and Analysis */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in the table below. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in table 4), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46085 User:T358wang 2020-11-23T18:17:28Z <p>Z47shen: /* Experiments and Analysis */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in Table 4. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in the table below. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in table 4), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46084 User:T358wang 2020-11-23T18:16:42Z <p>Z47shen: /* Offline test and timing */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in Table 4. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in Table 4. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> ''' Offline test and timing '''<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in table 4), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46083 User:T358wang 2020-11-23T18:16:16Z <p>Z47shen: /* Comparison */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in Table 4. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in Table 4. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> === Offline test and timing ===<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in table 4), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46082 User:T358wang 2020-11-23T18:12:26Z <p>Z47shen: /* Experiments and Analysis */</p> <hr /> <div><br /> == Group ==<br /> Rui Chen, Zeren Shen, Zihao Guo, Taohao Wang<br /> <br /> == Introduction ==<br /> <br /> Landmark recognition is an image retrieval task with its own specific challenges and this paper provides a new and effective method to recognize landmark images. And this method has been successfully applied to actual images. In this way, statue buildings and characteristic objects can be effectively identified.<br /> <br /> There are many difficulties encountered in the development process:<br /> <br /> 1. The first problem is that the concept of landmarks cannot be strictly defined, because landmarks can be any object and building.<br /> <br /> 2. The second problem is that the same landmark can be photographed from different angles. The results of the multi-angle shooting will result in very different picture characteristics. But the system needs to accurately identify different landmarks. <br /> <br /> 3. The third problem is that the landmark recognition system must recognize a large number of landmarks, and the recognition must achieve high accuracy. <br /> <br /> These problems require that the system should have a very low false alarm rate and high recognition accuracy. <br /> There are also three potential problems:<br /> <br /> 1. The processed data set contains a little error content, the image content is not clean and the quantity is huge.<br /> <br /> 2. The algorithm for learning the training set must be fast and scalable.<br /> <br /> 3. While displaying high-quality judgment landmarks, there is no image geographic information mixed.<br /> <br /> The article describes the deep convolutional neural network (CNN) architecture, loss function, training method, and inference aspects. The results of quantitative experiments will be displayed through testing and deployment effect analysis to prove the effectiveness of our model. Finally, it introduces the comparison results between the method proposed in this paper and the latest model and gives a conclusion.<br /> <br /> == Related Work ==<br /> <br /> Landmark recognition can be regarded as one of the tasks of image retrieval, and a large number of documents are concentrated on image retrieval tasks. In the past two decades, the field of image retrieval has made significant progress, and the main methods can be divided into two categories. <br /> The first is a classic retrieval method using local features, a method based on local feature descriptors organized in bag-of-words, spatial verification, Hamming embedding, and query expansion. These methods are dominant in image retrieval. Later, until the rise of deep convolutional neural networks (CNN), deep convolutional neural networks (CNN) were used to generate global descriptors of input images.<br /> Another method is to selectively match the kernel Hamming embedding method extension. With the advent of deep convolutional neural networks, the most effective image retrieval method is based on training CNNs for specific tasks. Deep networks are very powerful for semantic feature representation, which allows us to effectively use them for landmark recognition. This method shows good results but brings additional memory and complexity costs. <br /> The DELF (DEep local feature) by Noh et al. proved promising results. This method combines the classic local feature method with deep learning. This allows us to extract local features from the input image and then use RANSAC for geometric verification. <br /> The goal of the project is to describe a method for accurate and fast large-scale landmark recognition using the advantages of deep convolutional neural networks.<br /> <br /> <br /> == Methodology ==<br /> <br /> This section will describe in detail the CNN architecture, loss function, training procedure, and inference implementation of the landmark recognition system. The figure below is an overview of the landmark recognition system.<br /> <br /> [[File:t358wang_landmark_recog_system.png |center|800px]]<br /> <br /> The landmark CNN consists of three parts including the main network, the embedding layer, and the classification layer. To obtain a CNN main network suitable for training landmark recognition model, fine-tuning is applied and several pre-trained backbones (Residual Networks) based on other similar datasets, including ResNet-50, ResNet-200, SE-ResNext-101, and Wide Residual Network (WRN-50-2), are evaluated based on inference quality and efficiency. Based on the evaluation results, WRN-50-2 is selected as the optimal backbone architecture.<br /> <br /> [[File:t358wang_backbones.png |center|600px]]<br /> <br /> For the embedding layer, as shown in figure x, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 &lt;math&gt;\times&lt;/math&gt; 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 &lt;math&gt;\times&lt;/math&gt; n layer is added as the classification layer. The below figure shows the overview of the CNN architecture of the landmark recognition system.<br /> <br /> [[File:t358wang_network_arch.png |center|800px]]<br /> <br /> To effectively determine the embedding vectors for each landmark class (centroids), the network needs to be trained to have the members of each class to be as close as possible to the centroids. Several suitable loss functions are evaluated including Contrastive Loss, Arcface, and Center loss. The center loss is selected since it achieves the optimal test results and it trains a center of embeddings of each class and penalizes distances between image embeddings as well as their class centers. In addition, the center loss is a simple addition to softmax loss and is trivial to implement.<br /> <br /> When implementing the loss function, a new additional class that includes all non-landmark instances needs to be added and the center loss function needs to be modified as follows: Let n be the number of landmark classes, m be the mini-batch size, &lt;math&gt;x_i \in R^d&lt;/math&gt; is the i-th embedding and &lt;math&gt;y_i&lt;/math&gt; is the corresponding label where &lt;math&gt;y_i \in&lt;/math&gt; {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote &lt;math&gt;W \in R^{d \times n}&lt;/math&gt; as the weights of the classifier layer, &lt;math&gt;W_j&lt;/math&gt; as its j-th column. Let &lt;math&gt;c_{y_i}&lt;/math&gt; be the &lt;math&gt;y_i&lt;/math&gt; th embeddings center from Center loss and &lt;math&gt;\lambda&lt;/math&gt; be the balancing parameter of Center loss. Then the final loss function will be: <br /> <br /> [[File:t358wang_loss_function.png |center|600px]]<br /> <br /> In the training procedure, the stochastic gradient descent(SGD) will be used as the optimizer with momentum=0.9 and weight decay = 5e-3. For the center loss function, the parameter &lt;math&gt;\lambda&lt;/math&gt; is set to 5e-5. Each image is resized to 256 &lt;math&gt;\times&lt;/math&gt; 256 and several data augmentations are applied to the dataset including random resized crop, color jitter and random flip. The training dataset is divided into four parts based on the geographical affiliation of cities where landmarks are located: Europe/Russia, North America/Australia/Oceania, Middle East/North Africa, and the Far East. <br /> <br /> The paper introduces curriculum learning for landmark recognition, which is shown in the below figure. The algorithm is trained for 30 epochs and the learning rate &lt;math&gt;\alpha_1, \alpha_2, \alpha_3&lt;/math&gt; will be reduced by a factor of 10 at the 12th epoch and 24th epoch.<br /> <br /> [[File:t358wang_algorithm1.png |center|600px]]<br /> <br /> In the inference phase, the paper introduces the term “centroids” which are embedding vectors that are calculated by averaging embeddings and are used to describe landmark classes. The calculation of centroids is significant to effectively determine whether a query image contains a landmark. The paper proposes two approaches to help the inference algorithm to calculate the centroids. First, instead of using the entire training data for each landmark, data cleaning is done to remove most of the redundant and irrelevant elements in the image. Second, since each landmark can have different shooting angles, it is more efficient to calculate a separate centroid for each shooting angle. Hence, a hierarchical agglomerative clustering algorithm is proposed to partition training data into several valid clusters for each landmark and the set of centroids for a landmark L can be represented by &lt;math&gt;\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v&lt;/math&gt; where v is the number of valid clusters for landmark L. <br /> <br /> Once the centroids are calculated for each landmark class, the system can make decisions whether there is any landmark in an image. The query image is passed through the landmark CNN and the resulting embedding vector is compared with all centroids by dot product similarity using approximate k-nearest neighbors (AKNN). To distinguish landmark classes from non-landmark, a threshold &lt;math&gt;\eta&lt;/math&gt; is set and it will be compared with the maximum similarity to determine if the image contains any landmarks.<br /> <br /> The full inference algorithm is described in the below figure.<br /> <br /> [[File:t358wang_algorithm2.png |center|600px]]<br /> <br /> == Experiments and Analysis ==<br /> <br /> '''Offline test'''<br /> <br /> In order to measure the quality of the model, an offline test set was collected and manually labeled. According to the calculations, photos containing landmarks make up 1 − 3% of the total number of photos on average. This distribution was emulated in an offline test, and the geo-information and landmark references weren’t used. <br /> The results of this test are presented in Table 4. Two metrics were used to measure the results of experiments: Sensitivity — the accuracy of a model on images with landmarks (also called Recall) and Specificity — the accuracy of a model on images without landmarks. Several types of DELF were evaluated, and the best results in terms of sensitivity and specificity were included in Table 4. The table also contains the results of the model trained only with Softmax loss, Softmax, and Center loss. Thus, the table below reflects improvements in our approach with the addition of new elements in it.<br /> <br /> [[File:t358wang_models_eval.png |center|600px]]<br /> <br /> It’s very important to understand how a model works on “rare” landmarks due to the small amount of data for them. Therefore, the behavior of the model was examined separately on “rare” and “frequent” landmarks in the table below. The column “Part from total number” shows what percentage of landmark examples in the offline test has the corresponding type of landmarks.<br /> <br /> [[File:t358wang_rare_freq.png |center|600px]]<br /> <br /> Analysis of the behavior of the model in different categories of landmarks in the offline test is presented in the table below. These results show that the model can successfully work with various categories of landmarks. Predictably better results (92% of sensitivity and 99.5% of specificity) could also be obtained when the offline test with geo-information was launched on the model.<br /> <br /> [[File:t358wang_landmark_category.png |center|600px]]<br /> <br /> '''Revisited Paris dataset'''<br /> <br /> Revisited Paris dataset (RPar) was also used to measure the quality of the landmark recognition approach. This dataset with Revisited Oxford (ROxf) is standard benchmarks for the comparison of image retrieval algorithms. In the recognition, it is important to determine the landmark, which is contained in the query image. Images of the same landmark can have different shooting angles or taken inside/outside the building. Thus, it is reasonable to measure the quality of the model in the standard and adapt it to the task settings. That means not all classes from queries are presented in the landmark dataset. For those images containing correct landmarks but taken from different shooting angles within the building, we transferred them to the “junk” category, which does not influence the final score and makes the test markup closer to our model’s goal. Results on RPar with and without distractors in medium and hard modes are presented in the table below. <br /> <br /> [[File:t358wang_methods_eval1.png |center|600px]]<br /> <br /> [[File:t358wang_methods_eval2.png |center|600px]]<br /> <br /> == Comparison ==<br /> <br /> Recent most efficient approaches to landmark recognition are built on fine-tuned CNN. We chose to compare our method to DELF on how well each performs on recognition tasks. A brief summary is given below:<br /> <br /> [[File:t358wang_comparison.png |center|600px]]<br /> <br /> <br /> Offline test and timing<br /> <br /> Both approaches obtained similar results for image retrieval in the offline test (shown in table 4), but the proposed approach is much faster on the inference stage and more memory efficient.<br /> <br /> To be more detailed, during the inference stage, DELF needs more forward passes through CNN, has to search the entire database, and performs the RANSAC method for geometric verification. All of them make it much more time-consuming than our proposed approach. Our approach mainly uses centroids, this makes it take less time and needs to store fewer elements.<br /> <br /> <br /> == Conclusion ==<br /> <br /> In this paper we were hoping to solve some difficulties emerging when trying to apply landmark recognition to the production level: there might not be a clean &amp; sufficiently large database for interesting tasks, algorithms should be fast, scalable, and should aim for low FP and high accuracy.<br /> <br /> While aiming for these goals, we presented a way of cleaning landmark data. And most importantly, we introduced the usage of embeddings of deep CNN to make recognition fast and scalable, trained by curriculum learning techniques with modified versions of Center loss. Compared to the state-of-the-art methods, this approach shows similar results but is much faster and suitable for implementation on a large scale.<br /> <br /> == References ==</div> Z47shen http://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat441F21&diff=42648 stat441F21 2020-10-09T02:02:36Z <p>Z47shen: /* 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 on 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 || 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Paper] || ||<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] || ||<br /> |-<br /> |Week of Nov 30 || || 21|| || || ||<br /> |-<br /> |Week of Nov 30 || || 22|| || || ||<br /> |-<br /> |Week of Nov 30 || || 23|| || || ||<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] || ||<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 || ||<br /> |-<br /> |Week of Nov 30 ||Zihui (Betty) Qin, Wenqi (Maggie) Zhao, Muyuan Yang, Amartya (Marty) Mukherjee || 26|| Deep Learning for Cardiologist-level Myocardial 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