http://wiki.math.uwaterloo.ca/statwiki/api.php?action=feedcontributions&user=Q58yu&feedformat=atomstatwiki - User contributions [US]2023-11-29T21:50:32ZUser contributionsMediaWiki 1.28.3http://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46972User:J46hou2020-11-27T04:04:42Z<p>Q58yu: /* 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; 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 looks "perfect". 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 transform 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodologies to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 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 />
<div align="center">'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46970User:J46hou2020-11-27T04:03:53Z<p>Q58yu: /* 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; 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 looks "perfect". 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 transform 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodologies to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 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 />
<div align="center">'''Figure 4: Sample positives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 the methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with more 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 volacanic 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46968User:J46hou2020-11-27T04:03:01Z<p>Q58yu: /* DROCC-LF */</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; 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 looks "perfect". 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 transform 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodologies to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 at 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br />
<br />
[[File:drocc_f1score.jpg | center]]<br />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about 11.5% performance increase.<br />
Results on One-class Classification with Limited Negatives (OCLN): <br />
[[File:ocln.jpg | center]]<br />
<div align="center">'''Figure 4: Sample postives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><br />
MNIST 0 vs. 1 Classification: <br />
We consider an experimental setup on 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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 the methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with more 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 volacanic 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46967User:J46hou2020-11-27T04:02:01Z<p>Q58yu: /* Previous 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; 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 looks "perfect". 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 transform 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodologies to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], we propose DROCC–LF, an outlier-exposure style extension of DROCC. 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 at 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br />
<br />
[[File:drocc_f1score.jpg | center]]<br />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about 11.5% performance increase.<br />
Results on One-class Classification with Limited Negatives (OCLN): <br />
[[File:ocln.jpg | center]]<br />
<div align="center">'''Figure 4: Sample postives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><br />
MNIST 0 vs. 1 Classification: <br />
We consider an experimental setup on 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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 the methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with more 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 volacanic 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46966User:J46hou2020-11-27T04:00:48Z<p>Q58yu: /* Introduction */</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; 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 looks "perfect". 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 transform 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodology to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], we propose DROCC–LF, an outlier-exposure style extension of DROCC. 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 at 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br />
<br />
[[File:drocc_f1score.jpg | center]]<br />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about 11.5% performance increase.<br />
Results on One-class Classification with Limited Negatives (OCLN): <br />
[[File:ocln.jpg | center]]<br />
<div align="center">'''Figure 4: Sample postives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><br />
MNIST 0 vs. 1 Classification: <br />
We consider an experimental setup on 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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 the methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with more 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 volacanic 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan&diff=46964User:Yktan2020-11-27T03:51:33Z<p>Q58yu: /* Introduction */</p>
<hr />
<div><br />
== Introduction ==<br />
<br />
Much of the success in training deep neural networks (DNNs) is thanks to the collection of large datasets with human-annotated labels. However, human annotation is both a 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 />
<ol><br />
<li> Treating all samples equally and correcting loss explicitly or implicitly through relabeling of the noisy samples<br />
<li> Reweighting training samples or separating clean and noisy samples, which results in correction of the loss function<br />
</ol><br />
<br />
A few examples of LNL methods include:<br />
<ol><br />
<li> Estimating the noise transition matrix to correct the loss function<br />
<li> Leveraging DNNs to correct labels and using them to modify the loss<br />
<li> Reweighting samples so that noisy labels contribute less to the loss<br />
</ol><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 ==<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. Figure 1 describes the algorithm in graphical form.<br />
<br />
[[File:ModelArchitecture.PNG | center]]<br />
<br />
<div align="center">Figure 1: Model Architecture of DivideMix</div><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 <math> y_b </math>, the predicted label <math> p_b </math>, and the posterior is used as the weight, <math> w_b </math>. <br />
<br />
<center><math> \bar{y}_b = w_b y_b + (1-w_b) p_b </math></center> <br />
<br />
Then, a sharpening function is implemented on this weighted sum to produce the estimate, <math> \hat{y}_b </math> Using all these predicted labels, the unlabeled samples will then be assigned a "co-guessed" label, which should produce a more accurate prediction. Having calculated all these labels, MixMatch is applied to the combined mini-batch of labeled, <math> \hat{X} </math> and unlabeled data, <math> \hat{U} </math>, where, for a pair of samples and their labels, one new sample and new label is produced. More specifically, for a pair of samples <math> (x_1,x_2) </math> and their labels <math> (p_1,p_2) </math>, the mixed sample <math> (x',p') </math> is:<br />
<br />
<center><br />
<math><br />
\begin{alignat}{2}<br />
<br />
\lambda &\sim Beta(\alpha, \alpha) \\<br />
\lambda ' &= max(\lambda, 1 - \lambda) \\<br />
x' &= \lambda ' x_1 + (1 - \lambda ' ) x_2 \\<br />
p' &= \lambda ' p_1 + (1 - \lambda ' ) p_2 \\<br />
<br />
\end{alignat}<br />
</math><br />
</center> <br />
<br />
MixMatch transforms <math> \hat{X} </math> and <math> \hat{U} </math> into <math> X' </math> and <math> U' </math>. Then, the loss on <math> X' </math>, <math> L_X </math> (Cross-entropy loss) and the loss on <math> U' </math>, <math> L_U </math> (Mean Squared Error) are calculated. A regularization term, <math> L_{reg} </math>, 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 />
<center><math> L = L_X + \lambda_u L_U + \lambda_r L_{reg} </math></center> <br />
<br />
where <math> \lambda_r </math> is set to 1, and <math> \lambda_u </math> is used to control the unsupervised loss.<br />
<br />
Lastly, the stochastic gradient descent formula is updated with the calculated loss, <math> L </math>, and the estimated parameters, <math> \boldsymbol{ \theta } </math>.<br />
<br />
== Results ==<br />
'''Applications'''<br />
<br />
The method was validated using four benchmark datasets: CIFAR-10, CIFAR100 (Krizhevsky & Hinton, 2009)(both 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 "warm-up" 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 & 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 table1, 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.<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 noise ratio increases from 80% to 90%, the accuracy of DivideMix drops dramatically in both datasets.<br />
<br />
3. There should be further explanation on 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 on 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 are distributed by a Gaussian distribution but for all other noise, it would probably be only asymptotic. The paper should present theoretical results on 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 />
== 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN&diff=46963Neural Speed Reading via Skim-RNN2020-11-27T03:50:12Z<p>Q58yu: /* Results */</p>
<hr />
<div>== Group ==<br />
<br />
Mingyan Dai, Jerry Huang, Daniel Jiang<br />
<br />
== Introduction ==<br />
<br />
Recurrent Neural Network (RNN) is the connection between artificial neural network nodes forming a directed graph along with time series and has time dynamic behavior. RNN is derived from a feedforward neural network and can use its memory to process variable-length input sequences. This makes it suitable for tasks such as unsegmented, connected handwriting recognition, and speech recognition.<br />
<br />
In Natural Language Processing, recurrent neural networks (RNNs) are a common architecture used to sequentially ‘read’ input tokens and output a distributed representation for each token. By recurrently updating the hidden state of the neural network, an RNN can inherently require the same computational cost across time. However, when it comes to processing input tokens, it is usually the case that some tokens are less important to the overall representation of a piece of text or a query when compared to others. In particular, when considering question answering, many times the neural network will encounter parts of a passage that is irrelevant when it comes to answering a query that is being asked.<br />
<br />
== Model ==<br />
<br />
In this paper, the authors introduce a model called 'skim-RNN', which takes advantage of ‘skimming’ less important tokens or pieces of text rather than ‘skipping’ them entirely. This models the human ability to skim through passages, or to spend less time reading parts that do not affect the reader’s main objective. While this leads to a loss in the comprehension rate of the text [1], it greatly reduces the amount of time spent reading by not focusing on areas that will not significantly affect efficiency when it comes to the reader's objective.<br />
<br />
'Skim-RNN' works by rapidly determining the significance of each input and spending less time processing unimportant input tokens by using a smaller RNN to update only a fraction of the hidden state. When the decision is to ‘fully read’, that is to not skim the text, Skim-RNN updates the entire hidden state with the default RNN cell. Since the hard decision function (‘skim’ or ‘read’) is non-differentiable, the authors use a gumbel-softmax [2] to estimate the gradient of the function, rather than traditional methods such as REINFORCE (policy gradient)[3]. The switching mechanism between the two RNN cells enables Skim-RNN to reduce the total number of float operations (Flop reduction, or Flop-R). When the skimming rate is high, which often leads to faster inference on CPUs, which makes it very useful for large-scale products and small devices.<br />
<br />
The Skim-RNN has the same input and output interfaces as standard RNNs, so it can be conveniently used to speed up RNNs in existing models. In addition, the speed of Skim-RNN can be dynamically controlled at inference time by adjusting a parameter for the threshold for the ‘skim’ decision.<br />
<br />
=== Implementation ===<br />
<br />
A Skim-RNN consists of two RNN cells, a default (big) RNN cell of hidden state size <math>d</math> and small RNN cell of hidden state size <math>d'</math>, where <math>d</math> and <math>d'</math> are parameters defined by the user and <math>d' \ll d</math>. This follows the fact that there should be a small RNN cell defined for when text is meant to be skimmed and a larger one for when the text should be processed as normal.<br />
<br />
Each RNN cell will have its own set of weights and bias as well as be any variant of an RNN. There is no requirement on how the RNN itself is structured, rather the core concept is to allow the model to dynamically make a decision as to which cell to use when processing input tokens. Note that skipping text can be incorporated by setting <math>d'</math> to 0, which means that when the input token is deemed irrelevant to a query or classification task, nothing about the information in the token is retained within the model.<br />
<br />
Experimental results suggest that this model is faster than using a single large RNN to process all input tokens, as the smaller RNN requires fewer floating-point operations to process the token. Additionally, higher accuracy and computational efficiency are achieved. <br />
<br />
==== Inference ====<br />
<br />
At each time step <math>t</math>, the Skim-RNN unit takes in an input <math>{\bf x}_t \in \mathbb{R}^d</math> as well as the previous hidden state <math>{\bf h}_{t-1} \in \mathbb{R}^d</math> and outputs the new state <math>{\bf h}_t </math> (although the dimensions of the hidden state and input are the same, this process holds for different sizes as well). In the Skim-RNN, there is a hard decision that needs to be made whether to read or skim the input, although there could be potential to include options for multiple levels of skimming.<br />
<br />
The decision to read or skim is done using a multinomial random variable <math>Q_t</math> over the probability distribution of choices <math>{\bf p}_t</math>, where<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>{\bf p}_t = \text{softmax}(\alpha({\bf x}_t, {\bf h}_{t-1})) = \text{softmax}({\bf W}[{\bf x}_t; {\bf h}_{t-1}]+{\bf b}) \in \mathbb{R}^k</math><br />
</div><br />
<br />
where <math>{\bf W} \in \mathbb{R}^{k \times 2d}</math>, <math>{\bf b} \in \mathbb{R}^{k}</math> are weights to be learned and <math>[{\bf x}_t; {\bf h}_{t-1}] \in \mathbb{R}^{2d}</math> indicates the row concatenation of the two vectors. In this case <math> \alpha </math> can have any form as long as the complexity of calculating it is less than <math> O(d^2)</math>. Letting <math>{\bf p}^1_t</math> indicate the probability for fully reading and <math>{\bf p}^2_t</math> indicate the probability for skimming the input at time <math> t</math>, it follows that the decision to read or skim can be modelled using a random variable <math> Q_t</math> by sampling from the distribution <math>{\bf p}_t</math> and<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>Q_t \sim \text{Multinomial}({\bf p}_t)</math><br />
</div><br />
<br />
Without loss of generality, we can define <math> Q_t = 1</math> to indicate that the input will be read while <math> Q_t = 2</math> indicates that it will be skimmed. Reading requires applying the full RNN on the input as well as the previous hidden state to modify the entire hidden state while skimming only modifies part of the prior hidden state.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \begin{cases}<br />
f({\bf x}_t, {\bf h}_{t-1}) & Q_t = 1\\<br />
[f'({\bf x}_t, {\bf h}_{t-1});{\bf h}_{t-1}(d'+1:d)] & Q_t = 2<br />
\end{cases}<br />
</math><br />
</div><br />
<br />
where <math> f </math> is a full RNN with output of dimension <math>d</math> and <math>f'</math> is a smaller RNN with <math>d'</math>-dimensional output. This has advantage that when the model decides to skim, then the computational complexity of that step is only <math>O(d'd)</math>, which is much smaller than <math>O(d^2)</math> due to previously defining <math> d' \ll d</math>.<br />
<br />
==== Training ====<br />
<br />
Since the expected loss/error of the model is a random variable that depends on the sequence of random variables <math> \{Q_t\} </math>, the loss is minimized with respect to the distribution of the variables. Defining the loss to be minimized while conditioning on a particular sequence of decisions<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L(\theta\vert Q)<br />
</math><br />
</div><br />
where <math>Q=Q_1\dots Q_T</math> is a sequence of decisions of length <math>T</math>, then the expected loss o ver the distribution of the sequence of decisions is<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
\mathbb{E}[L(\theta)] = \sum_{Q} L(\theta\vert Q)P(Q) = \sum_Q L(\theta\vert Q) \Pi_j {\bf p}_j^{Q_j}<br />
</math><br />
</div><br />
<br />
Since calculating <math>\delta \mathbb{E}_{Q_t}[L(\theta)]</math> directly is rather infeasible, it is possible to approximate the gradients with a gumbel-softmax distribution [2]. Reparameterizing <math> {\bf p}_t</math> as <math> {\bf r}_t</math>, then the back-propagation can flow to <math> {\bf p}_t</math> without being blocked by <math> Q_t</math> and the approximation can arbitrarily approach <math> Q_t</math> by controlling the parameters. The reparameterized distribution is therefore<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf r}_t^i = \frac{\text{exp}(\log({\bf p}_t^i + {g_t}^i)/\tau)}{\sum_j\text{exp}(\log({\bf p}_t^j + {g_t}^j)/\tau)}<br />
</math><br />
</div><br />
<br />
where <math>{g_t}^i</math> is an independent sample from a <math>\text{Gumbel}(0, 1) = -\log(-\log(\text{Uniform}(0, 1))</math> random variable and <math>\tau</math> is a parameter that represents a temperature. Then it can be rewritten that<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \sum_i {\bf r}_t^i {\bf \tilde{h}}_t<br />
</math><br />
</div><br />
<br />
where <math>{\bf \tilde{h}}_t</math> is the previous equation for <math>{\bf h}_t</math>. The temperature parameter gradually decreases with time, and <math>{\bf r}_t^i</math> becomes more discrete as it approaches 0.<br />
<br />
A final addition to the model is to encourage skimming when possible. Therefore an extra term related to the negative log probability of skimming and the sequence length. Therefore the final loss function used for the model is denoted by <br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L'(\theta) =L(\theta) + \gamma \cdot\frac{1}{T} \sum_i -\log({\bf \tilde{p}}^i_t)<br />
</math><br />
</div><br />
where <math> \gamma </math> is a parameter used to control the ratio between the main loss function and the negative log probability of skimming.<br />
<br />
== Experiment ==<br />
<br />
The effectiveness of Skim-RNN was measured in terms of accuracy and float operation reduction on four classification tasks and a question-answering task. These tasks were chosen because they do not require one’s full attention to every detail of the text, but rather ask for capturing the high-level information (classification) or focusing on a specific portion (QA) of the text, which a common context for speed reading. The tasks themselves are listed in the table below.<br />
<br />
[[File:Table1SkimRNN.png|center|1000px]]<br />
<br />
=== Classification Tasks ===<br />
<br />
In a language classification task, the input was a sequence of words and the output was the vector of categorical probabilities. Each word is embedded into a <math>d</math>-dimensional vector. We initialize the vector with GloVe [4] to form representations of the words and use those as the inputs for a long short-term memory (LSTM) architecture. A linear transformation on the last hidden state of the LSTM and then a softmax function was applied to obtain the classification probabilities. Adam [5] was used for optimization, with an initial learning rate of 0.0001. For Skim-LSTM, <math>\tau = \max(0.5, exp(−rn))</math> where <math>r = 1e-4</math> and <math>n</math> is the global training step, following [2]. We experiment on different sizes of big LSTM (<math>d \in \{100, 200\}</math>) and small LSTM (<math>d' \in \{5, 10, 20\}</math>) and the ratio between the model loss and the skim loss (<math>\gamma\in \{0.01, 0.02\}</math>) for Skim-LSTM. The batch sizes used were 32 for SST and Rotten Tomatoes, and 128 for others. For all models, early stopping was used when the validation accuracy did not increase for 3000 global steps.<br />
<br />
==== Results ====<br />
<br />
[[File:Table2SkimRNN.png|center|1000px]]<br />
<br />
[[File:Figure2SkimRNN.png|center|1000px]]<br />
<br />
Table 2 shows the accuracy and computational cost of the Skim-RNN model compared with other standard models. It is evident that the Skim-RNN model produces a speed-up on the computational complexity of the task while maintaining a high degree of accuracy. Also, it is interesting to know that the accuracy improvement over LSTM could be due to the increased stability of the hidden state, as the majority of the hidden state is not updated when skimming. Figure 2 meanwhile demonstrates the effect of varying the size of the small hidden state as well as the parameter <math>\gamma</math> on the accuracy and computational cost.<br />
<br />
[[File:Table3SkimRNN.png|center|1000px]]<br />
<br />
Table 3 shows an example of a classification task over a IMDb dataset, where Skim-RNN with <math>d = 200</math>, <math>d' = 10</math>, and <math>\gamma = 0.01</math> correctly classifies it with high skimming rate (92%). The goal was to classify the review as either positive or negative. The black words are skimmed, and the blue words are fully read. The skimmed words are clearly irrelevant and the model learns to only carefully read the important words, such as ‘liked’, ‘dreadful’, and ‘tiresome’.<br />
<br />
=== Question Answering Task ===<br />
<br />
In Stanford Question Answering Dataset, the task was to locate the answer span for a given question in a context paragraph. The effectiveness of Skim-RNN for SQuAD was evaluated using two different models: LSTM+Attention and BiDAF [6]. The first model was inspired by most then-present QA systems consisting of multiple LSTM layers and an attention mechanism. This type of model is complex enough to reach reasonable accuracy on the dataset and simple enough to run well-controlled analyses for the Skim-RNN. The second model was an open-source model designed for SQuAD, used primarily to show that Skim-RNN could replace RNN in existing complex systems.<br />
<br />
==== Training ==== <br />
<br />
Adam was used with an initial learning rate of 0.0005. For stable training, the model was pretrained with a standard LSTM for the first 5k steps, and then fine-tuned with Skim-LSTM.<br />
<br />
==== Results ====<br />
<br />
[[File:Table4SkimRNN.png|center|1000px]]<br />
<br />
Table 4 shows the accuracy (F1 and EM) of LSTM+Attention and Skim-LSTM+Attention models as well as VCRNN [7]. It can be observed from the table that the skimming models achieve higher or similar accuracy scores compared to the non-skimming models while also reducing the computational cost by more than 1.4 times. In addition, decreasing layers (1 layer) or hidden size (<math>d=5</math>) improved the computational cost but significantly decreases the accuracy compared to skimming. The table also shows that replacing LSTM with Skim-LSTM in an existing complex model (BiDAF) stably gives reduced computational cost without losing much accuracy (only 0.2% drop from 77.3% of BiDAF to 77.1% of Sk-BiDAF with <math>\gamma = 0.001</math>).<br />
<br />
An explanation for this trend that was given is that the model is more confident about which tokens are important in the second layer. Second, higher <math>\gamma</math> values lead to a higher skimming rate, which agrees with its intended functionality.<br />
<br />
Figure 4 shows the F1 score of LSTM+Attention model using standard LSTM and Skim LSTM, sorted in ascending order by Flop-R (computational cost). While models tend to perform better with larger computational cost, Skim LSTM (Red) outperforms standard LSTM (Blue) with a comparable computational cost. It can also be seen that the computational cost of Skim-LSTM is more stable across different configurations and computational cost. Moreover, increasing the value of <math>\gamma</math> for Skim-LSTM gradually increases the skipping rate and Flop-R, while it also led to reduced accuracy.<br />
<br />
=== Runtime Benchmark ===<br />
<br />
[[File:Figure6SkimRNN.png|center|1000px]]<br />
<br />
The details of the runtime benchmarks for LSTM and Skim-LSTM, which are used to estimate the speedup of Skim-LSTM-based models in the experiments, are also discussed. A CPU-based benchmark was assumed to be the default benchmark, which has a direct correlation with the number of float operations that can be performed per second. As mentioned previously, the speed-up results in Table 2 (as well as Figure 7) are benchmarked using Python (NumPy), instead of popular frameworks such as TensorFlow or PyTorch.<br />
<br />
Figure 7 shows the relative speed gain of Skim-LSTM compared to standard LSTM with varying hidden state size and skim rate. NumPy was used, with the inferences run on a single thread of CPU. The ratio between the reduction of the number of float operations (Flop-R) of LSTM and Skim-LSTM was plotted, with the ratio acting as a theoretical upper bound of the speed gain on CPUs. From here, it can be noticed that there is a gap between the actual gain and the theoretical gain in speed, with the gap being larger with more overhead of the framework or more parallelization. The gap also decreases as the hidden state size increases because the overhead becomes negligible with very large matrix operations. This indicates that Skim-RNN provides greater benefits for RNNs with larger hidden state size. However, combining Skim-RNN with a CPU-based framework can lead to substantially lower latency than GPUs.<br />
<br />
== Results ==<br />
<br />
The results clearly indicate that the Skim-RNN model provides features that are suitable for general reading tasks, which include classification and question answering. While the tables indicate that minor losses in accuracy occasionally did result when parameters were set at specific values, they were minor and were acceptable given the improvement in runtime.<br />
<br />
An important advantage of Skim-RNN is that the skim rate (and thus computational cost) can be dynamically controlled at inference time by adjusting the threshold for<br />
‘skim’ decision probability <math>{\bf p}^1_t</math>. Figure 5 shows the trade-off between the accuracy and computational cost for two settings, confirming the importance of skimming (<math>d' > 0</math>) compared to skipping (<math>d' = 0</math>).<br />
<br />
Figure 6 shows that the model does not skim when the input seems to be relevant to answering the question, which was as expected by the design of the model. In addition, the LSTM in the second layer skims more than that in the first layer mainly because the second layer is more confident about the importance of each token.<br />
<br />
== Conclusion ==<br />
<br />
A Skim-RNN can offer better latency results on a CPU compared to a standard RNN on a GPU, with lower computational cost, as demonstrated through the results of this study. Future work (as stated by the authors) involves using Skim-RNN for applications that require much higher hidden state size, such as video understanding, and using multiple small RNN cells for varying degrees of skimming. Further, since it has the same input and output interface as a regular RNN it can replace RNNs in existing applications.<br />
<br />
== Critiques ==<br />
<br />
1. It seems like Skim-RNN is using the not full RNN of processing words that are not important thus can increase speed in some very particular circumstances (ie, only small networks). The extra model complexity did slow down the speed while trying to "optimizing" the efficiency and sacrifice part of accuracy while doing so. It is only trying to target a very specific situation (classification/question-answering) and made comparisons only with the baseline LSTM model. It would be definitely more persuasive if the model can compare with some of the state of art nn models.<br />
<br />
2. This model of Skim-RNN is pretty good to extract binary classification type of text, thus it would be interesting for this to be applied to stock market news analyzing. For example a press release from a company can be analyzed quickly using this model and immediately give the trader a positive or negative summary of the news. Would be beneficial in trading since time and speed is an important factor when executing a trade.<br />
<br />
3. An appropriate application for Skim-RNN could be customer service chat bots as they can analyze a customer's message and skim associated company policies to craft a response. In this circumstance, quickly analyzing text is ideal to not waste customers time.<br />
<br />
4. This could be applied to news apps to improve readability by highlighting important sections.<br />
<br />
5. This summary describes an interesting and useful model which can save readers time for reading an article. I think it will be interesting that discuss more on training a model by Skim-RNN to highlight the important sections in very long textbooks. As a student, having highlights in the textbook is really helpful to study. But highlight the important parts in a time-consuming work for the author, maybe using Skim-RNN can provide a nice model to do this job.<br />
<br />
== Applications ==<br />
<br />
Recurrent architectures are used in many other applications, such as for processing video. Real-time video processing is an exceedingly demanding and resource-constrained task, particularly in edge settings. It would be interesting to see if this method could be applied to those cases for more efficient inference, such as on drones or self-driving cars.<br />
<br />
== References ==<br />
<br />
[1] Patricia Anderson Carpenter Marcel Adam Just. The Psychology of Reading and Language Comprehension. 1987.<br />
<br />
[2] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. In ICLR, 2017.<br />
<br />
[3] Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.<br />
<br />
[4] Jeffrey Pennington, Richard Socher, and Christopher D Manning. Glove: Global vectors for word representation. In EMNLP, 2014.<br />
<br />
[5] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
<br />
[6] Minjoon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. In ICLR, 2017a.<br />
<br />
[7] Yacine Jernite, Edouard Grave, Armand Joulin, and Tomas Mikolov. Variable computation in recurrent neural networks. In ICLR, 2017.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN&diff=46962Neural Speed Reading via Skim-RNN2020-11-27T03:49:47Z<p>Q58yu: /* Experiment */</p>
<hr />
<div>== Group ==<br />
<br />
Mingyan Dai, Jerry Huang, Daniel Jiang<br />
<br />
== Introduction ==<br />
<br />
Recurrent Neural Network (RNN) is the connection between artificial neural network nodes forming a directed graph along with time series and has time dynamic behavior. RNN is derived from a feedforward neural network and can use its memory to process variable-length input sequences. This makes it suitable for tasks such as unsegmented, connected handwriting recognition, and speech recognition.<br />
<br />
In Natural Language Processing, recurrent neural networks (RNNs) are a common architecture used to sequentially ‘read’ input tokens and output a distributed representation for each token. By recurrently updating the hidden state of the neural network, an RNN can inherently require the same computational cost across time. However, when it comes to processing input tokens, it is usually the case that some tokens are less important to the overall representation of a piece of text or a query when compared to others. In particular, when considering question answering, many times the neural network will encounter parts of a passage that is irrelevant when it comes to answering a query that is being asked.<br />
<br />
== Model ==<br />
<br />
In this paper, the authors introduce a model called 'skim-RNN', which takes advantage of ‘skimming’ less important tokens or pieces of text rather than ‘skipping’ them entirely. This models the human ability to skim through passages, or to spend less time reading parts that do not affect the reader’s main objective. While this leads to a loss in the comprehension rate of the text [1], it greatly reduces the amount of time spent reading by not focusing on areas that will not significantly affect efficiency when it comes to the reader's objective.<br />
<br />
'Skim-RNN' works by rapidly determining the significance of each input and spending less time processing unimportant input tokens by using a smaller RNN to update only a fraction of the hidden state. When the decision is to ‘fully read’, that is to not skim the text, Skim-RNN updates the entire hidden state with the default RNN cell. Since the hard decision function (‘skim’ or ‘read’) is non-differentiable, the authors use a gumbel-softmax [2] to estimate the gradient of the function, rather than traditional methods such as REINFORCE (policy gradient)[3]. The switching mechanism between the two RNN cells enables Skim-RNN to reduce the total number of float operations (Flop reduction, or Flop-R). When the skimming rate is high, which often leads to faster inference on CPUs, which makes it very useful for large-scale products and small devices.<br />
<br />
The Skim-RNN has the same input and output interfaces as standard RNNs, so it can be conveniently used to speed up RNNs in existing models. In addition, the speed of Skim-RNN can be dynamically controlled at inference time by adjusting a parameter for the threshold for the ‘skim’ decision.<br />
<br />
=== Implementation ===<br />
<br />
A Skim-RNN consists of two RNN cells, a default (big) RNN cell of hidden state size <math>d</math> and small RNN cell of hidden state size <math>d'</math>, where <math>d</math> and <math>d'</math> are parameters defined by the user and <math>d' \ll d</math>. This follows the fact that there should be a small RNN cell defined for when text is meant to be skimmed and a larger one for when the text should be processed as normal.<br />
<br />
Each RNN cell will have its own set of weights and bias as well as be any variant of an RNN. There is no requirement on how the RNN itself is structured, rather the core concept is to allow the model to dynamically make a decision as to which cell to use when processing input tokens. Note that skipping text can be incorporated by setting <math>d'</math> to 0, which means that when the input token is deemed irrelevant to a query or classification task, nothing about the information in the token is retained within the model.<br />
<br />
Experimental results suggest that this model is faster than using a single large RNN to process all input tokens, as the smaller RNN requires fewer floating-point operations to process the token. Additionally, higher accuracy and computational efficiency are achieved. <br />
<br />
==== Inference ====<br />
<br />
At each time step <math>t</math>, the Skim-RNN unit takes in an input <math>{\bf x}_t \in \mathbb{R}^d</math> as well as the previous hidden state <math>{\bf h}_{t-1} \in \mathbb{R}^d</math> and outputs the new state <math>{\bf h}_t </math> (although the dimensions of the hidden state and input are the same, this process holds for different sizes as well). In the Skim-RNN, there is a hard decision that needs to be made whether to read or skim the input, although there could be potential to include options for multiple levels of skimming.<br />
<br />
The decision to read or skim is done using a multinomial random variable <math>Q_t</math> over the probability distribution of choices <math>{\bf p}_t</math>, where<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>{\bf p}_t = \text{softmax}(\alpha({\bf x}_t, {\bf h}_{t-1})) = \text{softmax}({\bf W}[{\bf x}_t; {\bf h}_{t-1}]+{\bf b}) \in \mathbb{R}^k</math><br />
</div><br />
<br />
where <math>{\bf W} \in \mathbb{R}^{k \times 2d}</math>, <math>{\bf b} \in \mathbb{R}^{k}</math> are weights to be learned and <math>[{\bf x}_t; {\bf h}_{t-1}] \in \mathbb{R}^{2d}</math> indicates the row concatenation of the two vectors. In this case <math> \alpha </math> can have any form as long as the complexity of calculating it is less than <math> O(d^2)</math>. Letting <math>{\bf p}^1_t</math> indicate the probability for fully reading and <math>{\bf p}^2_t</math> indicate the probability for skimming the input at time <math> t</math>, it follows that the decision to read or skim can be modelled using a random variable <math> Q_t</math> by sampling from the distribution <math>{\bf p}_t</math> and<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>Q_t \sim \text{Multinomial}({\bf p}_t)</math><br />
</div><br />
<br />
Without loss of generality, we can define <math> Q_t = 1</math> to indicate that the input will be read while <math> Q_t = 2</math> indicates that it will be skimmed. Reading requires applying the full RNN on the input as well as the previous hidden state to modify the entire hidden state while skimming only modifies part of the prior hidden state.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \begin{cases}<br />
f({\bf x}_t, {\bf h}_{t-1}) & Q_t = 1\\<br />
[f'({\bf x}_t, {\bf h}_{t-1});{\bf h}_{t-1}(d'+1:d)] & Q_t = 2<br />
\end{cases}<br />
</math><br />
</div><br />
<br />
where <math> f </math> is a full RNN with output of dimension <math>d</math> and <math>f'</math> is a smaller RNN with <math>d'</math>-dimensional output. This has advantage that when the model decides to skim, then the computational complexity of that step is only <math>O(d'd)</math>, which is much smaller than <math>O(d^2)</math> due to previously defining <math> d' \ll d</math>.<br />
<br />
==== Training ====<br />
<br />
Since the expected loss/error of the model is a random variable that depends on the sequence of random variables <math> \{Q_t\} </math>, the loss is minimized with respect to the distribution of the variables. Defining the loss to be minimized while conditioning on a particular sequence of decisions<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L(\theta\vert Q)<br />
</math><br />
</div><br />
where <math>Q=Q_1\dots Q_T</math> is a sequence of decisions of length <math>T</math>, then the expected loss o ver the distribution of the sequence of decisions is<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
\mathbb{E}[L(\theta)] = \sum_{Q} L(\theta\vert Q)P(Q) = \sum_Q L(\theta\vert Q) \Pi_j {\bf p}_j^{Q_j}<br />
</math><br />
</div><br />
<br />
Since calculating <math>\delta \mathbb{E}_{Q_t}[L(\theta)]</math> directly is rather infeasible, it is possible to approximate the gradients with a gumbel-softmax distribution [2]. Reparameterizing <math> {\bf p}_t</math> as <math> {\bf r}_t</math>, then the back-propagation can flow to <math> {\bf p}_t</math> without being blocked by <math> Q_t</math> and the approximation can arbitrarily approach <math> Q_t</math> by controlling the parameters. The reparameterized distribution is therefore<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf r}_t^i = \frac{\text{exp}(\log({\bf p}_t^i + {g_t}^i)/\tau)}{\sum_j\text{exp}(\log({\bf p}_t^j + {g_t}^j)/\tau)}<br />
</math><br />
</div><br />
<br />
where <math>{g_t}^i</math> is an independent sample from a <math>\text{Gumbel}(0, 1) = -\log(-\log(\text{Uniform}(0, 1))</math> random variable and <math>\tau</math> is a parameter that represents a temperature. Then it can be rewritten that<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \sum_i {\bf r}_t^i {\bf \tilde{h}}_t<br />
</math><br />
</div><br />
<br />
where <math>{\bf \tilde{h}}_t</math> is the previous equation for <math>{\bf h}_t</math>. The temperature parameter gradually decreases with time, and <math>{\bf r}_t^i</math> becomes more discrete as it approaches 0.<br />
<br />
A final addition to the model is to encourage skimming when possible. Therefore an extra term related to the negative log probability of skimming and the sequence length. Therefore the final loss function used for the model is denoted by <br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L'(\theta) =L(\theta) + \gamma \cdot\frac{1}{T} \sum_i -\log({\bf \tilde{p}}^i_t)<br />
</math><br />
</div><br />
where <math> \gamma </math> is a parameter used to control the ratio between the main loss function and the negative log probability of skimming.<br />
<br />
== Experiment ==<br />
<br />
The effectiveness of Skim-RNN was measured in terms of accuracy and float operation reduction on four classification tasks and a question-answering task. These tasks were chosen because they do not require one’s full attention to every detail of the text, but rather ask for capturing the high-level information (classification) or focusing on a specific portion (QA) of the text, which a common context for speed reading. The tasks themselves are listed in the table below.<br />
<br />
[[File:Table1SkimRNN.png|center|1000px]]<br />
<br />
=== Classification Tasks ===<br />
<br />
In a language classification task, the input was a sequence of words and the output was the vector of categorical probabilities. Each word is embedded into a <math>d</math>-dimensional vector. We initialize the vector with GloVe [4] to form representations of the words and use those as the inputs for a long short-term memory (LSTM) architecture. A linear transformation on the last hidden state of the LSTM and then a softmax function was applied to obtain the classification probabilities. Adam [5] was used for optimization, with an initial learning rate of 0.0001. For Skim-LSTM, <math>\tau = \max(0.5, exp(−rn))</math> where <math>r = 1e-4</math> and <math>n</math> is the global training step, following [2]. We experiment on different sizes of big LSTM (<math>d \in \{100, 200\}</math>) and small LSTM (<math>d' \in \{5, 10, 20\}</math>) and the ratio between the model loss and the skim loss (<math>\gamma\in \{0.01, 0.02\}</math>) for Skim-LSTM. The batch sizes used were 32 for SST and Rotten Tomatoes, and 128 for others. For all models, early stopping was used when the validation accuracy did not increase for 3000 global steps.<br />
<br />
==== Results ====<br />
<br />
[[File:Table2SkimRNN.png|center|1000px]]<br />
<br />
[[File:Figure2SkimRNN.png|center|1000px]]<br />
<br />
Table 2 shows the accuracy and computational cost of the Skim-RNN model compared with other standard models. It is evident that the Skim-RNN model produces a speed-up on the computational complexity of the task while maintaining a high degree of accuracy. Also, it is interesting to know that the accuracy improvement over LSTM could be due to the increased stability of the hidden state, as the majority of the hidden state is not updated when skimming. Figure 2 meanwhile demonstrates the effect of varying the size of the small hidden state as well as the parameter <math>\gamma</math> on the accuracy and computational cost.<br />
<br />
[[File:Table3SkimRNN.png|center|1000px]]<br />
<br />
Table 3 shows an example of a classification task over a IMDb dataset, where Skim-RNN with <math>d = 200</math>, <math>d' = 10</math>, and <math>\gamma = 0.01</math> correctly classifies it with high skimming rate (92%). The goal was to classify the review as either positive or negative. The black words are skimmed, and the blue words are fully read. The skimmed words are clearly irrelevant and the model learns to only carefully read the important words, such as ‘liked’, ‘dreadful’, and ‘tiresome’.<br />
<br />
=== Question Answering Task ===<br />
<br />
In Stanford Question Answering Dataset, the task was to locate the answer span for a given question in a context paragraph. The effectiveness of Skim-RNN for SQuAD was evaluated using two different models: LSTM+Attention and BiDAF [6]. The first model was inspired by most then-present QA systems consisting of multiple LSTM layers and an attention mechanism. This type of model is complex enough to reach reasonable accuracy on the dataset and simple enough to run well-controlled analyses for the Skim-RNN. The second model was an open-source model designed for SQuAD, used primarily to show that Skim-RNN could replace RNN in existing complex systems.<br />
<br />
==== Training ==== <br />
<br />
Adam was used with an initial learning rate of 0.0005. For stable training, the model was pretrained with a standard LSTM for the first 5k steps, and then fine-tuned with Skim-LSTM.<br />
<br />
==== Results ====<br />
<br />
[[File:Table4SkimRNN.png|center|1000px]]<br />
<br />
Table 4 shows the accuracy (F1 and EM) of LSTM+Attention and Skim-LSTM+Attention models as well as VCRNN [7]. It can be observed from the table that the skimming models achieve higher or similar accuracy scores compared to the non-skimming models while also reducing the computational cost by more than 1.4 times. In addition, decreasing layers (1 layer) or hidden size (<math>d=5</math>) improved the computational cost but significantly decreases the accuracy compared to skimming. The table also shows that replacing LSTM with Skim-LSTM in an existing complex model (BiDAF) stably gives reduced computational cost without losing much accuracy (only 0.2% drop from 77.3% of BiDAF to 77.1% of Sk-BiDAF with <math>\gamma = 0.001</math>).<br />
<br />
An explanation for this trend that was given is that the model is more confident about which tokens are important in the second layer. Second, higher <math>\gamma</math> values lead to a higher skimming rate, which agrees with its intended functionality.<br />
<br />
Figure 4 shows the F1 score of LSTM+Attention model using standard LSTM and Skim LSTM, sorted in ascending order by Flop-R (computational cost). While models tend to perform better with larger computational cost, Skim LSTM (Red) outperforms standard LSTM (Blue) with a comparable computational cost. It can also be seen that the computational cost of Skim-LSTM is more stable across different configurations and computational cost. Moreover, increasing the value of <math>\gamma</math> for Skim-LSTM gradually increases the skipping rate and Flop-R, while it also led to reduced accuracy.<br />
<br />
=== Runtime Benchmark ===<br />
<br />
[[File:Figure6SkimRNN.png|center|1000px]]<br />
<br />
The details of the runtime benchmarks for LSTM and Skim-LSTM, which are used to estimate the speedup of Skim-LSTM-based models in the experiments, are also discussed. A CPU-based benchmark was assumed to be the default benchmark, which has a direct correlation with the number of float operations that can be performed per second. As mentioned previously, the speed-up results in Table 2 (as well as Figure 7) are benchmarked using Python (NumPy), instead of popular frameworks such as TensorFlow or PyTorch.<br />
<br />
Figure 7 shows the relative speed gain of Skim-LSTM compared to standard LSTM with varying hidden state size and skim rate. NumPy was used, with the inferences run on a single thread of CPU. The ratio between the reduction of the number of float operations (Flop-R) of LSTM and Skim-LSTM was plotted, with the ratio acting as a theoretical upper bound of the speed gain on CPUs. From here, it can be noticed that there is a gap between the actual gain and the theoretical gain in speed, with the gap being larger with more overhead of the framework or more parallelization. The gap also decreases as the hidden state size increases because the overhead becomes negligible with very large matrix operations. This indicates that Skim-RNN provides greater benefits for RNNs with larger hidden state size. However, combining Skim-RNN with a CPU-based framework can lead to substantially lower latency than GPUs.<br />
<br />
== Results ==<br />
<br />
The results clearly indicate that the Skim-RNN model provides features that are suitable for general reading tasks, which include classification and question answering. While the tables indicate that minor losses in accuracy occasionally did result when parameters were set at specific values, they were minor and were acceptable given the improvement in runtime.<br />
<br />
An important advantage of Skim-RNN is that the skim rate (and thus computational cost) can be dynamically controlled at inference time by adjusting the threshold for<br />
‘skim’ decision probability <math>{\bf p}^1_t</math>. Figure 5 shows the trade-off between the accuracy and computational cost for two settings, confirming the importance of skimming (<math>d' > 0</math>) compared to skipping (<math>d' = 0</math>).<br />
<br />
Figure 6 shows that the model does not skim when the input seems to be relevant to answering the question, which was as expected by the design of the model. In addition, the LSTM in second layer skims more than that in the first layer mainly because the second layer is more confident about the importance of each token.<br />
<br />
== Conclusion ==<br />
<br />
A Skim-RNN can offer better latency results on a CPU compared to a standard RNN on a GPU, with lower computational cost, as demonstrated through the results of this study. Future work (as stated by the authors) involves using Skim-RNN for applications that require much higher hidden state size, such as video understanding, and using multiple small RNN cells for varying degrees of skimming. Further, since it has the same input and output interface as a regular RNN it can replace RNNs in existing applications.<br />
<br />
== Critiques ==<br />
<br />
1. It seems like Skim-RNN is using the not full RNN of processing words that are not important thus can increase speed in some very particular circumstances (ie, only small networks). The extra model complexity did slow down the speed while trying to "optimizing" the efficiency and sacrifice part of accuracy while doing so. It is only trying to target a very specific situation (classification/question-answering) and made comparisons only with the baseline LSTM model. It would be definitely more persuasive if the model can compare with some of the state of art nn models.<br />
<br />
2. This model of Skim-RNN is pretty good to extract binary classification type of text, thus it would be interesting for this to be applied to stock market news analyzing. For example a press release from a company can be analyzed quickly using this model and immediately give the trader a positive or negative summary of the news. Would be beneficial in trading since time and speed is an important factor when executing a trade.<br />
<br />
3. An appropriate application for Skim-RNN could be customer service chat bots as they can analyze a customer's message and skim associated company policies to craft a response. In this circumstance, quickly analyzing text is ideal to not waste customers time.<br />
<br />
4. This could be applied to news apps to improve readability by highlighting important sections.<br />
<br />
5. This summary describes an interesting and useful model which can save readers time for reading an article. I think it will be interesting that discuss more on training a model by Skim-RNN to highlight the important sections in very long textbooks. As a student, having highlights in the textbook is really helpful to study. But highlight the important parts in a time-consuming work for the author, maybe using Skim-RNN can provide a nice model to do this job.<br />
<br />
== Applications ==<br />
<br />
Recurrent architectures are used in many other applications, such as for processing video. Real-time video processing is an exceedingly demanding and resource-constrained task, particularly in edge settings. It would be interesting to see if this method could be applied to those cases for more efficient inference, such as on drones or self-driving cars.<br />
<br />
== References ==<br />
<br />
[1] Patricia Anderson Carpenter Marcel Adam Just. The Psychology of Reading and Language Comprehension. 1987.<br />
<br />
[2] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. In ICLR, 2017.<br />
<br />
[3] Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.<br />
<br />
[4] Jeffrey Pennington, Richard Socher, and Christopher D Manning. Glove: Global vectors for word representation. In EMNLP, 2014.<br />
<br />
[5] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
<br />
[6] Minjoon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. In ICLR, 2017a.<br />
<br />
[7] Yacine Jernite, Edouard Grave, Armand Joulin, and Tomas Mikolov. Variable computation in recurrent neural networks. In ICLR, 2017.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN&diff=46961Neural Speed Reading via Skim-RNN2020-11-27T03:48:04Z<p>Q58yu: /* Model */</p>
<hr />
<div>== Group ==<br />
<br />
Mingyan Dai, Jerry Huang, Daniel Jiang<br />
<br />
== Introduction ==<br />
<br />
Recurrent Neural Network (RNN) is the connection between artificial neural network nodes forming a directed graph along with time series and has time dynamic behavior. RNN is derived from a feedforward neural network and can use its memory to process variable-length input sequences. This makes it suitable for tasks such as unsegmented, connected handwriting recognition, and speech recognition.<br />
<br />
In Natural Language Processing, recurrent neural networks (RNNs) are a common architecture used to sequentially ‘read’ input tokens and output a distributed representation for each token. By recurrently updating the hidden state of the neural network, an RNN can inherently require the same computational cost across time. However, when it comes to processing input tokens, it is usually the case that some tokens are less important to the overall representation of a piece of text or a query when compared to others. In particular, when considering question answering, many times the neural network will encounter parts of a passage that is irrelevant when it comes to answering a query that is being asked.<br />
<br />
== Model ==<br />
<br />
In this paper, the authors introduce a model called 'skim-RNN', which takes advantage of ‘skimming’ less important tokens or pieces of text rather than ‘skipping’ them entirely. This models the human ability to skim through passages, or to spend less time reading parts that do not affect the reader’s main objective. While this leads to a loss in the comprehension rate of the text [1], it greatly reduces the amount of time spent reading by not focusing on areas that will not significantly affect efficiency when it comes to the reader's objective.<br />
<br />
'Skim-RNN' works by rapidly determining the significance of each input and spending less time processing unimportant input tokens by using a smaller RNN to update only a fraction of the hidden state. When the decision is to ‘fully read’, that is to not skim the text, Skim-RNN updates the entire hidden state with the default RNN cell. Since the hard decision function (‘skim’ or ‘read’) is non-differentiable, the authors use a gumbel-softmax [2] to estimate the gradient of the function, rather than traditional methods such as REINFORCE (policy gradient)[3]. The switching mechanism between the two RNN cells enables Skim-RNN to reduce the total number of float operations (Flop reduction, or Flop-R). When the skimming rate is high, which often leads to faster inference on CPUs, which makes it very useful for large-scale products and small devices.<br />
<br />
The Skim-RNN has the same input and output interfaces as standard RNNs, so it can be conveniently used to speed up RNNs in existing models. In addition, the speed of Skim-RNN can be dynamically controlled at inference time by adjusting a parameter for the threshold for the ‘skim’ decision.<br />
<br />
=== Implementation ===<br />
<br />
A Skim-RNN consists of two RNN cells, a default (big) RNN cell of hidden state size <math>d</math> and small RNN cell of hidden state size <math>d'</math>, where <math>d</math> and <math>d'</math> are parameters defined by the user and <math>d' \ll d</math>. This follows the fact that there should be a small RNN cell defined for when text is meant to be skimmed and a larger one for when the text should be processed as normal.<br />
<br />
Each RNN cell will have its own set of weights and bias as well as be any variant of an RNN. There is no requirement on how the RNN itself is structured, rather the core concept is to allow the model to dynamically make a decision as to which cell to use when processing input tokens. Note that skipping text can be incorporated by setting <math>d'</math> to 0, which means that when the input token is deemed irrelevant to a query or classification task, nothing about the information in the token is retained within the model.<br />
<br />
Experimental results suggest that this model is faster than using a single large RNN to process all input tokens, as the smaller RNN requires fewer floating-point operations to process the token. Additionally, higher accuracy and computational efficiency are achieved. <br />
<br />
==== Inference ====<br />
<br />
At each time step <math>t</math>, the Skim-RNN unit takes in an input <math>{\bf x}_t \in \mathbb{R}^d</math> as well as the previous hidden state <math>{\bf h}_{t-1} \in \mathbb{R}^d</math> and outputs the new state <math>{\bf h}_t </math> (although the dimensions of the hidden state and input are the same, this process holds for different sizes as well). In the Skim-RNN, there is a hard decision that needs to be made whether to read or skim the input, although there could be potential to include options for multiple levels of skimming.<br />
<br />
The decision to read or skim is done using a multinomial random variable <math>Q_t</math> over the probability distribution of choices <math>{\bf p}_t</math>, where<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>{\bf p}_t = \text{softmax}(\alpha({\bf x}_t, {\bf h}_{t-1})) = \text{softmax}({\bf W}[{\bf x}_t; {\bf h}_{t-1}]+{\bf b}) \in \mathbb{R}^k</math><br />
</div><br />
<br />
where <math>{\bf W} \in \mathbb{R}^{k \times 2d}</math>, <math>{\bf b} \in \mathbb{R}^{k}</math> are weights to be learned and <math>[{\bf x}_t; {\bf h}_{t-1}] \in \mathbb{R}^{2d}</math> indicates the row concatenation of the two vectors. In this case <math> \alpha </math> can have any form as long as the complexity of calculating it is less than <math> O(d^2)</math>. Letting <math>{\bf p}^1_t</math> indicate the probability for fully reading and <math>{\bf p}^2_t</math> indicate the probability for skimming the input at time <math> t</math>, it follows that the decision to read or skim can be modelled using a random variable <math> Q_t</math> by sampling from the distribution <math>{\bf p}_t</math> and<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>Q_t \sim \text{Multinomial}({\bf p}_t)</math><br />
</div><br />
<br />
Without loss of generality, we can define <math> Q_t = 1</math> to indicate that the input will be read while <math> Q_t = 2</math> indicates that it will be skimmed. Reading requires applying the full RNN on the input as well as the previous hidden state to modify the entire hidden state while skimming only modifies part of the prior hidden state.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \begin{cases}<br />
f({\bf x}_t, {\bf h}_{t-1}) & Q_t = 1\\<br />
[f'({\bf x}_t, {\bf h}_{t-1});{\bf h}_{t-1}(d'+1:d)] & Q_t = 2<br />
\end{cases}<br />
</math><br />
</div><br />
<br />
where <math> f </math> is a full RNN with output of dimension <math>d</math> and <math>f'</math> is a smaller RNN with <math>d'</math>-dimensional output. This has advantage that when the model decides to skim, then the computational complexity of that step is only <math>O(d'd)</math>, which is much smaller than <math>O(d^2)</math> due to previously defining <math> d' \ll d</math>.<br />
<br />
==== Training ====<br />
<br />
Since the expected loss/error of the model is a random variable that depends on the sequence of random variables <math> \{Q_t\} </math>, the loss is minimized with respect to the distribution of the variables. Defining the loss to be minimized while conditioning on a particular sequence of decisions<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L(\theta\vert Q)<br />
</math><br />
</div><br />
where <math>Q=Q_1\dots Q_T</math> is a sequence of decisions of length <math>T</math>, then the expected loss o ver the distribution of the sequence of decisions is<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
\mathbb{E}[L(\theta)] = \sum_{Q} L(\theta\vert Q)P(Q) = \sum_Q L(\theta\vert Q) \Pi_j {\bf p}_j^{Q_j}<br />
</math><br />
</div><br />
<br />
Since calculating <math>\delta \mathbb{E}_{Q_t}[L(\theta)]</math> directly is rather infeasible, it is possible to approximate the gradients with a gumbel-softmax distribution [2]. Reparameterizing <math> {\bf p}_t</math> as <math> {\bf r}_t</math>, then the back-propagation can flow to <math> {\bf p}_t</math> without being blocked by <math> Q_t</math> and the approximation can arbitrarily approach <math> Q_t</math> by controlling the parameters. The reparameterized distribution is therefore<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf r}_t^i = \frac{\text{exp}(\log({\bf p}_t^i + {g_t}^i)/\tau)}{\sum_j\text{exp}(\log({\bf p}_t^j + {g_t}^j)/\tau)}<br />
</math><br />
</div><br />
<br />
where <math>{g_t}^i</math> is an independent sample from a <math>\text{Gumbel}(0, 1) = -\log(-\log(\text{Uniform}(0, 1))</math> random variable and <math>\tau</math> is a parameter that represents a temperature. Then it can be rewritten that<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \sum_i {\bf r}_t^i {\bf \tilde{h}}_t<br />
</math><br />
</div><br />
<br />
where <math>{\bf \tilde{h}}_t</math> is the previous equation for <math>{\bf h}_t</math>. The temperature parameter gradually decreases with time, and <math>{\bf r}_t^i</math> becomes more discrete as it approaches 0.<br />
<br />
A final addition to the model is to encourage skimming when possible. Therefore an extra term related to the negative log probability of skimming and the sequence length. Therefore the final loss function used for the model is denoted by <br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L'(\theta) =L(\theta) + \gamma \cdot\frac{1}{T} \sum_i -\log({\bf \tilde{p}}^i_t)<br />
</math><br />
</div><br />
where <math> \gamma </math> is a parameter used to control the ratio between the main loss function and the negative log probability of skimming.<br />
<br />
== Experiment ==<br />
<br />
The effectiveness of Skim-RNN was measured in terms of accuracy and float operation reduction on four classification tasks and a question answering task. These tasks were chosen because they do not require one’s full attention to every detail of the text, but rather ask for capturing the high-level information (classification) or focusing on specific portion (QA) of the text, which a common context for speed reading. The tasks themselves are listed in the table below.<br />
<br />
[[File:Table1SkimRNN.png|center|1000px]]<br />
<br />
=== Classification Tasks ===<br />
<br />
In a language classification task, the input was a sequence of words and the output was the vector of categorical probabilities. Each word is embedded into a <math>d</math>-dimensional vector. We initialize the vector with GloVe [4] to form representations of the words and use those as the inputs for a long short-term memory (LSTM) architecture. A linear transformation on the last hidden state of the LSTM and then a softmax function was applied to obtain the classification probabilities. Adam [5] was used for optimization, with initial learning rate of 0.0001. For Skim-LSTM, <math>\tau = \max(0.5, exp(−rn))</math> where <math>r = 1e-4</math> and <math>n</math> is the global training step, following [2]. We experiment on different sizes of big LSTM (<math>d \in \{100, 200\}</math>) and small LSTM (<math>d' \in \{5, 10, 20\}</math>) and the ratio between the model loss and the skim loss (<math>\gamma\in \{0.01, 0.02\}</math>) for Skim-LSTM. The batch sizes used were 32 for SST and Rotten Tomatoes, and 128 for others. For all models, early stopping was used when the validation accuracy did not increase for 3000 global steps.<br />
<br />
==== Results ====<br />
<br />
[[File:Table2SkimRNN.png|center|1000px]]<br />
<br />
[[File:Figure2SkimRNN.png|center|1000px]]<br />
<br />
Table 2 shows the accuracy and computational cost of the Skim-RNN model compared with other standard models. It is evident that the Skim-RNN model produces a speed-up on the computational complexity of the task while maintaining a high degree of accuracy. Also, it is interesting to know that the accuracy improvement over LSTM could be due to the increased stability of the hidden state, as the majority of the hidden state is not updated when skimming. Figure 2 meanwhile demonstrates the effect of varying the size of the small hidden state as well as the parameter <math>\gamma</math> on the accuracy and computational cost.<br />
<br />
[[File:Table3SkimRNN.png|center|1000px]]<br />
<br />
Table 3 shows an example of a classification task over a IMDb dataset, where Skim-RNN with <math>d = 200</math>, <math>d' = 10</math>, and <math>\gamma = 0.01</math> correctly classifies it with high skimming rate (92%). The goal was to classify the review as either positive or negative. The black words are skimmed, and blue words are fully read. The skimmed words are clearly irrelevant and the model learns to only carefully read the important words, such as ‘liked’, ‘dreadful’, and ‘tiresome’.<br />
<br />
=== Question Answering Task ===<br />
<br />
In Stanford Question Answering Dataset, the task was to locate the answer span for a given question in a context paragraph. The effectiveness of Skim-RNN for SQuAD was evaluated using two different models: LSTM+Attention and BiDAF [6]. The first model was inspired by most then-present QA systems consisting of multiple LSTM layers and an attention mechanism. This type of model is complex enough to reach reasonable accuracy on the dataset, and simple enough to run well-controlled analyses for the Skim-RNN. The second model wan an open-source model designed for SQuAD, used primarily to show that Skim-RNN could replace RNN in existing complex systems.<br />
<br />
==== Training ==== <br />
<br />
Adam was used with an initial learning rate of 0.0005. For stable training, the model was pretrained with a standard LSTM for the first 5k steps , and then fine-tuned with Skim-LSTM.<br />
<br />
==== Results ====<br />
<br />
[[File:Table4SkimRNN.png|center|1000px]]<br />
<br />
Table 4 shows the accuracy (F1 and EM) of LSTM+Attention and Skim-LSTM+Attention models as well as VCRNN [7]. It can be observed from the table that the skimming models achieve higher or similar accuracy scores compared to the non-skimming models while also reducing the computational cost by more than 1.4 times. In addition, decreasing layers (1 layer) or hidden size (<math>d=5</math>) improved the computational cost but significantly decreases the accuracy compared to skimming. The table also shows that replacing LSTM with Skim-LSTM in an existing complex model (BiDAF) stably gives reduced computational cost without losing much accuracy (only 0.2% drop from 77.3% of BiDAF to 77.1% of Sk-BiDAF with <math>\gamma = 0.001</math>).<br />
<br />
An explanation for this trend that was given is that the model is more confident about which tokens are important at the second layer. Second, higher <math>\gamma</math> values lead to higher skimming rate, which agrees with its intended functionality.<br />
<br />
Figure 4 shows the F1 score of LSTM+Attention model using standard LSTM and Skim LSTM, sorted in ascending order by Flop-R (computational cost). While models tend to perform better with larger computational cost, Skim LSTM (Red) outperforms standard LSTM (Blue) with comparable computational cost. It can also be seen that the computational cost of Skim-LSTM is more stable across different configurations and computational cost. Moreover, increasing the value of <math>\gamma</math> for Skim-LSTM gradually increases the skipping rate and Flop-R, while it also led to reduced accuracy.<br />
<br />
=== Runtime Benchmark ===<br />
<br />
[[File:Figure6SkimRNN.png|center|1000px]]<br />
<br />
The details of the runtime benchmarks for LSTM and Skim-LSTM, are used estimate the speed up of Skim-LSTM-based models in the experiments, are also discussed. A CPU-based benchmark was assumed to be the default benchmark, which has direct correlation with the number of float operations that can be performed per second. As mentioned previously, the speed-up results in Table 2 (as well as Figure 7) are benchmarked using Python (NumPy), instead of popular frameworks such as TensorFlow or PyTorch.<br />
<br />
Figure 7 shows the relative speed gain of Skim-LSTM compared to standard LSTM with varying hidden state size and skim rate. NumPy was used, with the inferences run on a single thread of CPU. The ratio between the reduction of the number of float operations (Flop-R) of LSTM and Skim-LSTM was plotted, with the ratio acting as a theoretical upper bound of the speed gain on CPUs. From here, it can be noticed that there is a gap between the actual gain and the theoretical gain in speed, with the gap being larger with more overhead of the framework, or more parallelization. The gap also decreases as the hidden state size increases because the the overhead becomes negligible with very large matrix operations. This indicates that Skim-RNN provide greater benefits for RNNs with larger hidden state size. However, combining Skim-RNN with CPU-based framework can lead to substantially lower latency than GPUs.<br />
<br />
== Results ==<br />
<br />
The results clearly indicate that the Skim-RNN model provides features that are suitable for general reading tasks, which include classification and question answering. While the tables indicate that minor losses in accuracy occasionally did result when parameters were set at specific values, they were minor and were acceptable given the improvement in runtime.<br />
<br />
An important advantage of Skim-RNN is that the skim rate (and thus computational cost) can be dynamically controlled at inference time by adjusting the threshold for<br />
‘skim’ decision probability <math>{\bf p}^1_t</math>. Figure 5 shows the trade-off between the accuracy and computational cost for two settings, confirming the importance of skimming (<math>d' > 0</math>) compared to skipping (<math>d' = 0</math>).<br />
<br />
Figure 6 shows that the model does not skim when the input seems to be relevant to answering the question, which was as expected by the design of the model. In addition, the LSTM in second layer skims more than that in the first layer mainly because the second layer is more confident about the importance of each token.<br />
<br />
== Conclusion ==<br />
<br />
A Skim-RNN can offer better latency results on a CPU compared to a standard RNN on a GPU, with lower computational cost, as demonstrated through the results of this study. Future work (as stated by the authors) involves using Skim-RNN for applications that require much higher hidden state size, such as video understanding, and using multiple small RNN cells for varying degrees of skimming. Further, since it has the same input and output interface as a regular RNN it can replace RNNs in existing applications.<br />
<br />
== Critiques ==<br />
<br />
1. It seems like Skim-RNN is using the not full RNN of processing words that are not important thus can increase speed in some very particular circumstances (ie, only small networks). The extra model complexity did slow down the speed while trying to "optimizing" the efficiency and sacrifice part of accuracy while doing so. It is only trying to target a very specific situation (classification/question-answering) and made comparisons only with the baseline LSTM model. It would be definitely more persuasive if the model can compare with some of the state of art nn models.<br />
<br />
2. This model of Skim-RNN is pretty good to extract binary classification type of text, thus it would be interesting for this to be applied to stock market news analyzing. For example a press release from a company can be analyzed quickly using this model and immediately give the trader a positive or negative summary of the news. Would be beneficial in trading since time and speed is an important factor when executing a trade.<br />
<br />
3. An appropriate application for Skim-RNN could be customer service chat bots as they can analyze a customer's message and skim associated company policies to craft a response. In this circumstance, quickly analyzing text is ideal to not waste customers time.<br />
<br />
4. This could be applied to news apps to improve readability by highlighting important sections.<br />
<br />
5. This summary describes an interesting and useful model which can save readers time for reading an article. I think it will be interesting that discuss more on training a model by Skim-RNN to highlight the important sections in very long textbooks. As a student, having highlights in the textbook is really helpful to study. But highlight the important parts in a time-consuming work for the author, maybe using Skim-RNN can provide a nice model to do this job.<br />
<br />
== Applications ==<br />
<br />
Recurrent architectures are used in many other applications, such as for processing video. Real-time video processing is an exceedingly demanding and resource-constrained task, particularly in edge settings. It would be interesting to see if this method could be applied to those cases for more efficient inference, such as on drones or self-driving cars.<br />
<br />
== References ==<br />
<br />
[1] Patricia Anderson Carpenter Marcel Adam Just. The Psychology of Reading and Language Comprehension. 1987.<br />
<br />
[2] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. In ICLR, 2017.<br />
<br />
[3] Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.<br />
<br />
[4] Jeffrey Pennington, Richard Socher, and Christopher D Manning. Glove: Global vectors for word representation. In EMNLP, 2014.<br />
<br />
[5] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
<br />
[6] Minjoon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. In ICLR, 2017a.<br />
<br />
[7] Yacine Jernite, Edouard Grave, Armand Joulin, and Tomas Mikolov. Variable computation in recurrent neural networks. In ICLR, 2017.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN&diff=46960Neural Speed Reading via Skim-RNN2020-11-27T03:46:34Z<p>Q58yu: /* Introduction */</p>
<hr />
<div>== Group ==<br />
<br />
Mingyan Dai, Jerry Huang, Daniel Jiang<br />
<br />
== Introduction ==<br />
<br />
Recurrent Neural Network (RNN) is the connection between artificial neural network nodes forming a directed graph along with time series and has time dynamic behavior. RNN is derived from a feedforward neural network and can use its memory to process variable-length input sequences. This makes it suitable for tasks such as unsegmented, connected handwriting recognition, and speech recognition.<br />
<br />
In Natural Language Processing, recurrent neural networks (RNNs) are a common architecture used to sequentially ‘read’ input tokens and output a distributed representation for each token. By recurrently updating the hidden state of the neural network, an RNN can inherently require the same computational cost across time. However, when it comes to processing input tokens, it is usually the case that some tokens are less important to the overall representation of a piece of text or a query when compared to others. In particular, when considering question answering, many times the neural network will encounter parts of a passage that is irrelevant when it comes to answering a query that is being asked.<br />
<br />
== Model ==<br />
<br />
In this paper, the authors introduce a model called 'skim-RNN', which takes advantage of ‘skimming’ less important tokens or pieces of text rather than ‘skipping’ them entirely. This models the human ability to skim through passages, or to spend less time reading parts do not affect the reader’s main objective. While this leads to a loss in the comprehension rate of the text [1], it greatly reduces the amount of time spent reading by not focusing on areas which will not significantly affect efficiency when it comes to the reader's objective.<br />
<br />
'Skim-RNN' works by rapidly determining the significance of each input and spending less time processing unimportant input tokens by using a smaller RNN to update only a fraction of the hidden state. When the decision is to ‘fully read’, that is to not skim the text, Skim-RNN updates the entire hidden state with the default RNN cell. Since the hard decision function (‘skim’ or ‘read’) is non-differentiable, the authors use a gumbel-softmax [2] to estimate the gradient of the function, rather than traditional methods such as REINFORCE (policy gradient)[3]. The switching mechanism between the two RNN cells enables Skim-RNN to reduce the total number of float operations (Flop reduction, or Flop-R). When the skimming rate is high, which often leads to faster inference on CPUs, which makes it very useful for large-scale products and small devices.<br />
<br />
The Skim-RNN has the same input and output interfaces as standard RNNs, so it can be conveniently used to speed up RNNs in existing models. In addition, the speed of Skim-RNN can be dynamically controlled at inference time by adjusting a parameter for the threshold for the ‘skim’ decision.<br />
<br />
=== Implementation ===<br />
<br />
A Skim-RNN consists of two RNN cells, a default (big) RNN cell of hidden state size <math>d</math> and small RNN cell of hidden state size <math>d'</math>, where <math>d</math> and <math>d'</math> are parameters defined by the user and <math>d' \ll d</math>. This follows the fact that there should be a small RNN cell defined for when text is meant to be skimmed and a larger one for when the text should be processed as normal.<br />
<br />
Each RNN cell will have its own set of weights and bias as well as be any variant of an RNN. There is no requirement on how the RNN itself is structured, rather the core concept is to allow the model to dynamically make a decision as to which cell to use when processing input tokens. Note that skipping text can be incorporated by setting <math>d'</math> to 0, which means that when the input token is deemed irrelevant to a query or classification task, nothing about the information in the token is retained within the model.<br />
<br />
Experimental results suggest that this model is faster than using a single large RNN to process all input tokens, as the smaller RNN requires fewer floating point operations to process the token. Additionally, higher accuracy and computational efficiency are achieved. <br />
<br />
==== Inference ====<br />
<br />
At each time step <math>t</math>, the Skim-RNN unit takes in an input <math>{\bf x}_t \in \mathbb{R}^d</math> as well as the previous hidden state <math>{\bf h}_{t-1} \in \mathbb{R}^d</math> and outputs the new state <math>{\bf h}_t </math> (although the dimensions of the hidden state and input are the same, this process holds for different sizes as well). In the Skim-RNN, there is a hard decision that needs to be made whether to read or skim the input, although there could be potential to include options for multiple levels of skimming.<br />
<br />
The decision to read or skim is done using a multinomial random variable <math>Q_t</math> over the probability distribution of choices <math>{\bf p}_t</math>, where<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>{\bf p}_t = \text{softmax}(\alpha({\bf x}_t, {\bf h}_{t-1})) = \text{softmax}({\bf W}[{\bf x}_t; {\bf h}_{t-1}]+{\bf b}) \in \mathbb{R}^k</math><br />
</div><br />
<br />
where <math>{\bf W} \in \mathbb{R}^{k \times 2d}</math>, <math>{\bf b} \in \mathbb{R}^{k}</math> are weights to be learned and <math>[{\bf x}_t; {\bf h}_{t-1}] \in \mathbb{R}^{2d}</math> indicates the row concatenation of the two vectors. In this case <math> \alpha </math> can have any form as long as the complexity of calculating it is less than <math> O(d^2)</math>. Letting <math>{\bf p}^1_t</math> indicate the probability for fully reading and <math>{\bf p}^2_t</math> indicate the probability for skimming the input at time <math> t</math>, it follows that the decision to read or skim can be modelled using a random variable <math> Q_t</math> by sampling from the distribution <math>{\bf p}_t</math> and<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math>Q_t \sim \text{Multinomial}({\bf p}_t)</math><br />
</div><br />
<br />
Without loss of generality, we can define <math> Q_t = 1</math> to indicate that the input will be read while <math> Q_t = 2</math> indicates that it will be skimmed. Reading requires applying the full RNN on the input as well as the previous hidden state to modify the entire hidden state, while skimming only modifies part of the prior hidden state.<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \begin{cases}<br />
f({\bf x}_t, {\bf h}_{t-1}) & Q_t = 1\\<br />
[f'({\bf x}_t, {\bf h}_{t-1});{\bf h}_{t-1}(d'+1:d)] & Q_t = 2<br />
\end{cases}<br />
</math><br />
</div><br />
<br />
where <math> f </math> is a full RNN with output of dimension <math>d</math> and <math>f'</math> is a smaller RNN with <math>d'</math>-dimensional output. This has advantage that when the model decides to skim, then the computational complexity of that step is only <math>O(d'd)</math>, which is much smaller than <math>O(d^2)</math> due to previously defining <math> d' \ll d</math>.<br />
<br />
==== Training ====<br />
<br />
Since the expected loss/error of the model is a random variable that depends on the sequence of random variables <math> \{Q_t\} </math>, the loss is minimized with respect to the distribution of the variables. Defining the loss to be minimized while conditioning on a particular sequence of decisions<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L(\theta\vert Q)<br />
</math><br />
</div><br />
where <math>Q=Q_1\dots Q_T</math> is a sequence of decisions of length <math>T</math>, then the expected loss o ver the distribution of the sequence of decisions is<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
\mathbb{E}[L(\theta)] = \sum_{Q} L(\theta\vert Q)P(Q) = \sum_Q L(\theta\vert Q) \Pi_j {\bf p}_j^{Q_j}<br />
</math><br />
</div><br />
<br />
Since calculating <math>\delta \mathbb{E}_{Q_t}[L(\theta)]</math> directly is rather infeasible, it is possible to approximate the gradients with a gumbel-softmax distribution [2]. Reparameterizing <math> {\bf p}_t</math> as <math> {\bf r}_t</math>, then the back-propagation can flow to <math> {\bf p}_t</math> without being blocked by <math> Q_t</math> and the approximation can arbitrarily approach <math> Q_t</math> by controlling the parameters. The reparameterized distribution is therefore<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf r}_t^i = \frac{\text{exp}(\log({\bf p}_t^i + {g_t}^i)/\tau)}{\sum_j\text{exp}(\log({\bf p}_t^j + {g_t}^j)/\tau)}<br />
</math><br />
</div><br />
<br />
where <math>{g_t}^i</math> is an independent sample from a <math>\text{Gumbel}(0, 1) = -\log(-\log(\text{Uniform}(0, 1))</math> random variable and <math>\tau</math> is a parameter that represents a temperature. Then it can be rewritten that<br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
{\bf h}_t = \sum_i {\bf r}_t^i {\bf \tilde{h}}_t<br />
</math><br />
</div><br />
<br />
where <math>{\bf \tilde{h}}_t</math> is the previous equation for <math>{\bf h}_t</math>. The temperature parameter gradually decreases with time, and <math>{\bf r}_t^i</math> becomes more discrete as it approaches 0.<br />
<br />
A final addition to the model is to encourage skimming when possible. Therefore an extra term related to the negative log probability of skimming and the sequence length. Therefore the final loss function used for the model is denoted by <br />
<br />
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><br />
<math><br />
L'(\theta) =L(\theta) + \gamma \cdot\frac{1}{T} \sum_i -\log({\bf \tilde{p}}^i_t)<br />
</math><br />
</div><br />
where <math> \gamma </math> is a parameter used to control the ratio between the main loss function and the negative log probability of skimming.<br />
<br />
== Experiment ==<br />
<br />
The effectiveness of Skim-RNN was measured in terms of accuracy and float operation reduction on four classification tasks and a question answering task. These tasks were chosen because they do not require one’s full attention to every detail of the text, but rather ask for capturing the high-level information (classification) or focusing on specific portion (QA) of the text, which a common context for speed reading. The tasks themselves are listed in the table below.<br />
<br />
[[File:Table1SkimRNN.png|center|1000px]]<br />
<br />
=== Classification Tasks ===<br />
<br />
In a language classification task, the input was a sequence of words and the output was the vector of categorical probabilities. Each word is embedded into a <math>d</math>-dimensional vector. We initialize the vector with GloVe [4] to form representations of the words and use those as the inputs for a long short-term memory (LSTM) architecture. A linear transformation on the last hidden state of the LSTM and then a softmax function was applied to obtain the classification probabilities. Adam [5] was used for optimization, with initial learning rate of 0.0001. For Skim-LSTM, <math>\tau = \max(0.5, exp(−rn))</math> where <math>r = 1e-4</math> and <math>n</math> is the global training step, following [2]. We experiment on different sizes of big LSTM (<math>d \in \{100, 200\}</math>) and small LSTM (<math>d' \in \{5, 10, 20\}</math>) and the ratio between the model loss and the skim loss (<math>\gamma\in \{0.01, 0.02\}</math>) for Skim-LSTM. The batch sizes used were 32 for SST and Rotten Tomatoes, and 128 for others. For all models, early stopping was used when the validation accuracy did not increase for 3000 global steps.<br />
<br />
==== Results ====<br />
<br />
[[File:Table2SkimRNN.png|center|1000px]]<br />
<br />
[[File:Figure2SkimRNN.png|center|1000px]]<br />
<br />
Table 2 shows the accuracy and computational cost of the Skim-RNN model compared with other standard models. It is evident that the Skim-RNN model produces a speed-up on the computational complexity of the task while maintaining a high degree of accuracy. Also, it is interesting to know that the accuracy improvement over LSTM could be due to the increased stability of the hidden state, as the majority of the hidden state is not updated when skimming. Figure 2 meanwhile demonstrates the effect of varying the size of the small hidden state as well as the parameter <math>\gamma</math> on the accuracy and computational cost.<br />
<br />
[[File:Table3SkimRNN.png|center|1000px]]<br />
<br />
Table 3 shows an example of a classification task over a IMDb dataset, where Skim-RNN with <math>d = 200</math>, <math>d' = 10</math>, and <math>\gamma = 0.01</math> correctly classifies it with high skimming rate (92%). The goal was to classify the review as either positive or negative. The black words are skimmed, and blue words are fully read. The skimmed words are clearly irrelevant and the model learns to only carefully read the important words, such as ‘liked’, ‘dreadful’, and ‘tiresome’.<br />
<br />
=== Question Answering Task ===<br />
<br />
In Stanford Question Answering Dataset, the task was to locate the answer span for a given question in a context paragraph. The effectiveness of Skim-RNN for SQuAD was evaluated using two different models: LSTM+Attention and BiDAF [6]. The first model was inspired by most then-present QA systems consisting of multiple LSTM layers and an attention mechanism. This type of model is complex enough to reach reasonable accuracy on the dataset, and simple enough to run well-controlled analyses for the Skim-RNN. The second model wan an open-source model designed for SQuAD, used primarily to show that Skim-RNN could replace RNN in existing complex systems.<br />
<br />
==== Training ==== <br />
<br />
Adam was used with an initial learning rate of 0.0005. For stable training, the model was pretrained with a standard LSTM for the first 5k steps , and then fine-tuned with Skim-LSTM.<br />
<br />
==== Results ====<br />
<br />
[[File:Table4SkimRNN.png|center|1000px]]<br />
<br />
Table 4 shows the accuracy (F1 and EM) of LSTM+Attention and Skim-LSTM+Attention models as well as VCRNN [7]. It can be observed from the table that the skimming models achieve higher or similar accuracy scores compared to the non-skimming models while also reducing the computational cost by more than 1.4 times. In addition, decreasing layers (1 layer) or hidden size (<math>d=5</math>) improved the computational cost but significantly decreases the accuracy compared to skimming. The table also shows that replacing LSTM with Skim-LSTM in an existing complex model (BiDAF) stably gives reduced computational cost without losing much accuracy (only 0.2% drop from 77.3% of BiDAF to 77.1% of Sk-BiDAF with <math>\gamma = 0.001</math>).<br />
<br />
An explanation for this trend that was given is that the model is more confident about which tokens are important at the second layer. Second, higher <math>\gamma</math> values lead to higher skimming rate, which agrees with its intended functionality.<br />
<br />
Figure 4 shows the F1 score of LSTM+Attention model using standard LSTM and Skim LSTM, sorted in ascending order by Flop-R (computational cost). While models tend to perform better with larger computational cost, Skim LSTM (Red) outperforms standard LSTM (Blue) with comparable computational cost. It can also be seen that the computational cost of Skim-LSTM is more stable across different configurations and computational cost. Moreover, increasing the value of <math>\gamma</math> for Skim-LSTM gradually increases the skipping rate and Flop-R, while it also led to reduced accuracy.<br />
<br />
=== Runtime Benchmark ===<br />
<br />
[[File:Figure6SkimRNN.png|center|1000px]]<br />
<br />
The details of the runtime benchmarks for LSTM and Skim-LSTM, are used estimate the speed up of Skim-LSTM-based models in the experiments, are also discussed. A CPU-based benchmark was assumed to be the default benchmark, which has direct correlation with the number of float operations that can be performed per second. As mentioned previously, the speed-up results in Table 2 (as well as Figure 7) are benchmarked using Python (NumPy), instead of popular frameworks such as TensorFlow or PyTorch.<br />
<br />
Figure 7 shows the relative speed gain of Skim-LSTM compared to standard LSTM with varying hidden state size and skim rate. NumPy was used, with the inferences run on a single thread of CPU. The ratio between the reduction of the number of float operations (Flop-R) of LSTM and Skim-LSTM was plotted, with the ratio acting as a theoretical upper bound of the speed gain on CPUs. From here, it can be noticed that there is a gap between the actual gain and the theoretical gain in speed, with the gap being larger with more overhead of the framework, or more parallelization. The gap also decreases as the hidden state size increases because the the overhead becomes negligible with very large matrix operations. This indicates that Skim-RNN provide greater benefits for RNNs with larger hidden state size. However, combining Skim-RNN with CPU-based framework can lead to substantially lower latency than GPUs.<br />
<br />
== Results ==<br />
<br />
The results clearly indicate that the Skim-RNN model provides features that are suitable for general reading tasks, which include classification and question answering. While the tables indicate that minor losses in accuracy occasionally did result when parameters were set at specific values, they were minor and were acceptable given the improvement in runtime.<br />
<br />
An important advantage of Skim-RNN is that the skim rate (and thus computational cost) can be dynamically controlled at inference time by adjusting the threshold for<br />
‘skim’ decision probability <math>{\bf p}^1_t</math>. Figure 5 shows the trade-off between the accuracy and computational cost for two settings, confirming the importance of skimming (<math>d' > 0</math>) compared to skipping (<math>d' = 0</math>).<br />
<br />
Figure 6 shows that the model does not skim when the input seems to be relevant to answering the question, which was as expected by the design of the model. In addition, the LSTM in second layer skims more than that in the first layer mainly because the second layer is more confident about the importance of each token.<br />
<br />
== Conclusion ==<br />
<br />
A Skim-RNN can offer better latency results on a CPU compared to a standard RNN on a GPU, with lower computational cost, as demonstrated through the results of this study. Future work (as stated by the authors) involves using Skim-RNN for applications that require much higher hidden state size, such as video understanding, and using multiple small RNN cells for varying degrees of skimming. Further, since it has the same input and output interface as a regular RNN it can replace RNNs in existing applications.<br />
<br />
== Critiques ==<br />
<br />
1. It seems like Skim-RNN is using the not full RNN of processing words that are not important thus can increase speed in some very particular circumstances (ie, only small networks). The extra model complexity did slow down the speed while trying to "optimizing" the efficiency and sacrifice part of accuracy while doing so. It is only trying to target a very specific situation (classification/question-answering) and made comparisons only with the baseline LSTM model. It would be definitely more persuasive if the model can compare with some of the state of art nn models.<br />
<br />
2. This model of Skim-RNN is pretty good to extract binary classification type of text, thus it would be interesting for this to be applied to stock market news analyzing. For example a press release from a company can be analyzed quickly using this model and immediately give the trader a positive or negative summary of the news. Would be beneficial in trading since time and speed is an important factor when executing a trade.<br />
<br />
3. An appropriate application for Skim-RNN could be customer service chat bots as they can analyze a customer's message and skim associated company policies to craft a response. In this circumstance, quickly analyzing text is ideal to not waste customers time.<br />
<br />
4. This could be applied to news apps to improve readability by highlighting important sections.<br />
<br />
5. This summary describes an interesting and useful model which can save readers time for reading an article. I think it will be interesting that discuss more on training a model by Skim-RNN to highlight the important sections in very long textbooks. As a student, having highlights in the textbook is really helpful to study. But highlight the important parts in a time-consuming work for the author, maybe using Skim-RNN can provide a nice model to do this job.<br />
<br />
== Applications ==<br />
<br />
Recurrent architectures are used in many other applications, such as for processing video. Real-time video processing is an exceedingly demanding and resource-constrained task, particularly in edge settings. It would be interesting to see if this method could be applied to those cases for more efficient inference, such as on drones or self-driving cars.<br />
<br />
== References ==<br />
<br />
[1] Patricia Anderson Carpenter Marcel Adam Just. The Psychology of Reading and Language Comprehension. 1987.<br />
<br />
[2] Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. In ICLR, 2017.<br />
<br />
[3] Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992.<br />
<br />
[4] Jeffrey Pennington, Richard Socher, and Christopher D Manning. Glove: Global vectors for word representation. In EMNLP, 2014.<br />
<br />
[5] Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In ICLR, 2015.<br />
<br />
[6] Minjoon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. In ICLR, 2017a.<br />
<br />
[7] Yacine Jernite, Edouard Grave, Armand Joulin, and Tomas Mikolov. Variable computation in recurrent neural networks. In ICLR, 2017.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=46959Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence2020-11-27T03:41:34Z<p>Q58yu: /* Motivation */</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 being easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) has become an important part of human’s life. People can share their experiences in a location, 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) it is difficult to incorporate 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 self-attentive encoder while NAD stands for the neighbor-aware decoder. 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 [1] 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 [4]. 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 is consist 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[2], Foursquare [3], and Yelp[3]. 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 />
== 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 x_u to hidden representation A_u using weight matrix W^1 and the activation function softmax and tanh. The 0's and 1's in x_u indicates whether the user has been to a certain POI. The weight matrix W_a assigns different weights on various features of POIs.<br />
<br />
[[File:encoder.JPG|center]]<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 is able to 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 in food delivery service apps to suggest new restaurants to customers.<br />
<br />
It would be nice if the author could 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.<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, I do not have a clear understanding of how important each component is to the recommendation quality.<br />
<br />
== References ==<br />
[1] 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 />
[2] 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 />
[3] 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 />
[4] 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 />
[5] 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 />
[6] Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br />
<br />
[7] Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667. [12] Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br />
<br />
[8] 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 />
[9] 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 />
[10] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=46958Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence2020-11-27T03:39:58Z<p>Q58yu: /* Previous Work */</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 being easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) has become an important part of human’s life. People can share their experiences in a location, 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) it is difficult to incorporate 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 self-attentive encoder while NAD stands for the neighbor-aware decoder. 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 [1] 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 [4]. 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 is constructed by 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[2], Foursquare [3], and Yelp[3]. 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 />
== 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 x_u to hidden representation A_u using weight matrix W^1 and the activation function softmax and tanh. The 0's and 1's in x_u indicates whether the user has been to a certain POI. The weight matrix W_a assigns different weights on various features of POIs.<br />
<br />
[[File:encoder.JPG|center]]<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 is able to 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 in food delivery service apps to suggest new restaurants to customers.<br />
<br />
It would be nice if the author could 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.<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, I do not have a clear understanding of how important each component is to the recommendation quality.<br />
<br />
== References ==<br />
[1] 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 />
[2] 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 />
[3] 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 />
[4] 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 />
[5] 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 />
[6] Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br />
<br />
[7] Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667. [12] Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br />
<br />
[8] 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 />
[9] 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 />
[10] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Point-of-Interest_Recommendation:_Exploiting_Self-Attentive_Autoencoders_with_Neighbor-Aware_Influence&diff=46957Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence2020-11-27T03:37:14Z<p>Q58yu: /* Introduction */</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 being easier and more efficient. Precisely because of this development, Location-based Social Networks (LBSNs) has become an important part of human’s life. People can share their experiences in a location, 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) it is difficult to incorporate 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 self-attentive encoder while NAD stands for the neighbor-aware decoder. 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. But 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 [1] adopted weighted regularized MF to serve people on POI. So, machine learning is popular in this area. POI recommendation is an important topic in the domain of recommender systems [4]. 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 is constructed by 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[2], Foursquare [3], and Yelp[3]. 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 />
== 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 x_u to hidden representation A_u using weight matrix W^1 and the activation function softmax and tanh. The 0's and 1's in x_u indicates whether the user has been to a certain POI. The weight matrix W_a assigns different weights on various features of POIs.<br />
<br />
[[File:encoder.JPG|center]]<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 is able to 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 in food delivery service apps to suggest new restaurants to customers.<br />
<br />
It would be nice if the author could 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.<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, I do not have a clear understanding of how important each component is to the recommendation quality.<br />
<br />
== References ==<br />
[1] 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 />
[2] 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 />
[3] 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 />
[4] 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 />
[5] 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 />
[6] Yifan Hu, Yehuda Koren, and Chris Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In ICDM. IEEE Computer Society, 263–272.<br />
<br />
[7] Santosh Kabbur, Xia Ning, and George Karypis. 2013. FISM: factored item similarity models for top-N recommender systems. In KDD. ACM, 659–667. [12] Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. CoRR abs/1412.6980 (2014).<br />
<br />
[8] 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 />
[9] 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 />
[10] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou&diff=46933User:J46hou2020-11-27T02:38:51Z<p>Q58yu: /* Introduction */</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 work, we study “one-class” classification, where the goal is to obtain accurate discriminators for a special class. Popular uses of this technique include anomaly detection where we are interested in detecting outliers. Anomaly detection is a well-studied area of research; 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 looks "perfect". 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 transform accurately.<br />
<br />
Thus, in this paper, we are presenting a new approach called Deep Robust One-Class Classification (DROCC) 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)[9]. One drawback of these approaches is that they involve careful feature engineering when applied to structured domains like images. The current state of art methodology to tackle this kind of problems are: <br />
<br />
1. Approach based on prediction transformations (Golan & El-Yaniv, 2018; Hendrycks et al.,2019a) [1] 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)[2] 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) [3]. 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) [4], such as constructing a minimum-enclosing ball around the typical data points (Tax & Duin, 2004) [5]. They broadly fall into three categories: AD via generative modeling, Deep Once Class SVM, Transformations based methods. 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 />
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 & Souvenir, 2009). [6]<br />
<br />
== Model Explanation ==<br />
[[File:drocc_f1.jpg | center]]<br />
<div align="center">'''Figure 1'''</div><br />
<br />
Explanation of Figure1:<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 />
== DROCC-LF ==<br />
To especially tackle problems such as anomaly detection and outlier exposure (Hendrycks et al., 2019a) [7], we propose DROCC–LF, an outlier-exposure style extension of DROCC. 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 />
<div align="center">'''Figure 2: AUC result'''</div><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 at 20%, and notably, nearest neighbors (NN) beats all the baselines on 2 classes.<br />
<br />
[[File:drocc_f1score.jpg | center]]<br />
<div align="center">'''Figure 3: F1-Score'''</div><br />
<br />
Table 2 shows F1-Score (with standard deviation) for one-vs-all anomaly detection on Thyroid, Arrhythmia, and Abalone datasets from UCI Machine Learning Repository. DROCC outperforms the baselines on all three datasets by a minimum of 0.07 which is about 11.5% performance increase.<br />
Results on One-class Classification with Limited Negatives (OCLN): <br />
[[File:ocln.jpg | center]]<br />
<div align="center">'''Figure 4: Sample postives, negatives and close negatives for MNIST digit 0 vs 1 experiment (OCLN).'''</div><br />
MNIST 0 vs. 1 Classification: <br />
We consider an experimental setup on 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 />
<div align="center">'''Figure 5: OCLN on Audio Commands.'''</div><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) [8] 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 and hence can compare close points 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 the methods which can perhaps slow down the convergence of the two methods. Designing optimization algorithms that can work with more 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 volacanic 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 />
[1]: Golan, I. and El-Yaniv, R. Deep anomaly detection using geometric transformations. In Advances in Neural Information Processing Systems (NeurIPS), 2018.<br />
<br />
[2]: 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 />
[3]: Aggarwal, C. C. Outlier Analysis. Springer Publishing Company, Incorporated, 2nd edition, 2016. ISBN 3319475770.<br />
<br />
[4]: 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 />
[5]: Tax, D. M. and Duin, R. P. Support vector data description. Machine Learning, 54(1), 2004.<br />
<br />
[6]: Pless, R. and Souvenir, R. A survey of manifold learning for images. IPSJ Transactions on Computer Vision and Applications, 1, 2009.<br />
<br />
[7]: Hendrycks, D., Mazeika, M., and Dietterich, T. Deep anomaly detection with outlier exposure. In International Conference on Learning Representations (ICLR), 2019a.<br />
<br />
[8]: Warden, P. Speech commands: A dataset for limited vocabulary speech recognition, 2018. URL https: //arxiv.org/abs/1804.03209.<br />
<br />
[9]: 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 "one class", 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 <math>x</math>) 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification%E2%80%94%E2%80%94via_Convolution_Neural_Network&diff=46931Semantic Relation Classification——via Convolution Neural Network2020-11-27T02:36:37Z<p>Q58yu: /* Introduction */</p>
<hr />
<div><br />
<br />
<br />
== Presented by ==<br />
Rui Gong, Xinqi Ling, Di Ma,Xuetong Wang<br />
<br />
== Introduction ==<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 finally 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 />
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.<br />
<br />
<br />
After the embeddings, the model will transform the embedded sentence to 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 <math> N </math>, 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 />
is given to a weight matrix <math> W\in\mathbb{R}^{(d^{w}+2d^{wp})\times k}</math> 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 <math> k </math> 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 <math> \hat{c}=max\{c\} </math> was picked.<br />
With different weight filter, different mapped feature vectors can be obtained. Finally, the original <br />
sentence <math> e </math> can be converted into a new representation <math> r_{x} </math> with a fixed length. For example, if there are 5 filters,<br />
then there are 5 features (<math> \hat{c} </math>) picked to create <math> r_{x} </math> for each <math> x </math>.<br />
<br />
Then, the score vector <br />
$$s(x)=W^{classes}r_{x}$$<br />
is obtained which represented the score for each class, given <math> x </math>'s entities' relation will be classified as <br />
the one with the highest score. The <math> W^{classes} </math> here is the model being trained.<br />
<br />
To improve the performance, “Negative Sampling" was used. Given the trained data point <br />
<math> \tilde{x} </math>, and its correct class <math> \tilde{y} </math>. Let <math> I=Y\setminus\{\tilde{y}\} </math> represent the <br />
incorrect labels for <math> x </math>. 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 <math> m_{+} </math>, <math> m_{-} </math>, and penalty scale factor <math> \gamma </math>.<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 in order 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 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. Because 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 did not<br />
use the cross-validation as the test set. Instead, it runs a constant number of<br />
training epochs, and it can be chosen by cross-validation based on the training data. The best submission for the training set 1.2 is the first submission which<br />
extracted 10% of the training data as validation accuracy on the test set predictions.<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 together 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, linear classifiers, sequential random forest, LSTM, and CNN models are tested. Variations are applied to the models. Among all variations, vanilla CNN with negative sampling and ACL-embedding 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 />
- In the section of previous work, the author mentioned 9 natural language relationship 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 details.<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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Semantic_Relation_Classification%E2%80%94%E2%80%94via_Convolution_Neural_Network&diff=46928Semantic Relation Classification——via Convolution Neural Network2020-11-27T02:26:43Z<p>Q58yu: /* Results */</p>
<hr />
<div><br />
<br />
<br />
== Presented by ==<br />
Rui Gong, Xinqi Ling, Di Ma,Xuetong Wang<br />
<br />
== Introduction ==<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 />
Data comes from 350 scientific paper abstracts, which has 1228 and 1248 annotated sentences for two tasks. 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 CNN model category performed the best, so the article specifically submitted the final submission for this model. 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 />
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.<br />
<br />
<br />
After the embeddings, the model will transform the embedded sentence to 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 <math> N </math>, 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 />
is given to a weight matrix <math> W\in\mathbb{R}^{(d^{w}+2d^{wp})\times k}</math> 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 <math> k </math> 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 <math> \hat{c}=max\{c\} </math> was picked.<br />
With different weight filter, different mapped feature vectors can be obtained. Finally, the original <br />
sentence <math> e </math> can be converted into a new representation <math> r_{x} </math> with a fixed length. For example, if there are 5 filters,<br />
then there are 5 features (<math> \hat{c} </math>) picked to create <math> r_{x} </math> for each <math> x </math>.<br />
<br />
Then, the score vector <br />
$$s(x)=W^{classes}r_{x}$$<br />
is obtained which represented the score for each class, given <math> x </math>'s entities' relation will be classified as <br />
the one with the highest score. The <math> W^{classes} </math> here is the model being trained.<br />
<br />
To improve the performance, “Negative Sampling" was used. Given the trained data point <br />
<math> \tilde{x} </math>, and its correct class <math> \tilde{y} </math>. Let <math> I=Y\setminus\{\tilde{y}\} </math> represent the <br />
incorrect labels for <math> x </math>. 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 <math> m_{+} </math>, <math> m_{-} </math>, and penalty scale factor <math> \gamma </math>.<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 in order 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 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. Because 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 did not<br />
use the cross-validation as the test set. Instead, it runs a constant number of<br />
training epochs, and it can be chosen by cross-validation based on the training data. The best submission for the training set 1.2 is the first submission which<br />
extracted 10% of the training data as validation accuracy on the test set predictions.<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 together 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, linear classifiers, sequential random forest, LSTM, and CNN models are tested. Variations are applied to the models. Among all variations, vanilla CNN with negative sampling and ACL-embedding 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 />
- In the section of previous work, the author mentioned 9 natural language relationship 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 details.<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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=46927Superhuman AI for Multiplayer Poker2020-11-27T02:23:22Z<p>Q58yu: /* Theoretical Analysis */</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. 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 (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<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 opponents 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, by shifting away from the Nash equilibrium strategy, it 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 />
<div align="center">Figure 1: Lemonade Stand Example</div><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 (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 builtin 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 <br />
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 />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><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 is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy overall iterations converges 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 leads to the strategy 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 by anonymizing the players by providing each of them 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 played. <br />
<br />
The second format included 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 />
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, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"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."</div> <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 reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 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 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.<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 has 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 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 more applications in other area? 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 />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
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 (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). 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., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=46926Superhuman AI for Multiplayer Poker2020-11-27T02:20:11Z<p>Q58yu: /* Nash Equilibrium in Multiplayer Games */</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. 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 (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<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 opponents 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, by shifting away from the Nash equilibrium strategy, it 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 />
<div align="center">Figure 1: Lemonade Stand Example</div><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 (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 builtin 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 <br />
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 />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><br />
<br />
At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by 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, 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 decision and zero regret indicates that you are indifferent.<br />
<br />
The value of counter factual 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 is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy over all iterations converges 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 leads to the strategy 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 by anonymizing the players by providing each of them 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 played. <br />
<br />
The second format included 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 />
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, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"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."</div> <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 reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 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 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.<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 has 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 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 more applications in other area? 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 />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
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 (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). 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., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Superhuman_AI_for_Multiplayer_Poker&diff=46924Superhuman AI for Multiplayer Poker2020-11-27T02:15:23Z<p>Q58yu: /* Nash Equilibrium in Multiplayer Games */</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. 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 (for example, in the "Prisoner's dilemma" the Nash equilibrium of both players betraying each other is not the optimal strategy).<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 opponents 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, by shifting away from the Nash equilibrium strategy, it 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 problem itself. If we can efficiently compute a Nash equilibrium in games with more than two players, it is 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 />
<div align="center">Figure 1: Lemonade Stand Example</div><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 (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 builtin 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 <br />
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 />
<div align="center">Figure 1: Kuhn Poker (Simpler form of Poker) </div><br />
<br />
At the start of each iteration, MCCFR stimulates a hand of poker randomly (Cards held by 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, 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 decision and zero regret indicates that you are indifferent.<br />
<br />
The value of counter factual 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 is chosen with higher probability. CFR minimizes regret over many iterations until the average strategy over all iterations converges 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 leads to the strategy 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 by anonymizing the players by providing each of them 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 played. <br />
<br />
The second format included 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 />
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, and significance tests were run at a 95% significance level with one-tailed t-tests as a check for Pluribus’s performance in being profitable.<br />
<br />
Applying AIVAT the following were the results:<br />
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"<br />
! scope="col" | Format !! scope="col" | Average mbb/game !! scope="col" | Standard Error in mbb/game !! scope="col" | P-value of being profitable <br />
|-<br />
! scope="row" | 5H+1AI <br />
| 48 || 25 || 0.028 <br />
|-<br />
! scope="row" | 1H+5AI <br />
| 32 || 15 || 0.014<br />
|}<br />
[[File:top.PNG| 950px | x450px |left]]<br />
<br />
<br />
<div align="center">"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."</div> <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 reduces the computational power required. Hence it was computed in 8 days and required less than 512 GB of memory, and costs about $144 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 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.<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 has 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 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 more applications in other area? 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 />
== Conclusion ==<br />
<br />
As Pluribus’s strategy was not developed with any human data and was trained by self-play only, it is an unbiased and different perspective on how optimal play can be attained.<br />
Developing a superhuman AI for multiplayer poker was a widely recognized<br />
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 (12 Jul 1994). A Course in Game Theory. Cambridge, MA: MIT. p. 14.<br />
<br />
Justin Sermeno. (2020, November 17). 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., & Gong, Q. (2020). Combining deep reinforcement learning and search for imperfect-information games. Advances in Neural Information Processing Systems, 33.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Graph_Structure_of_Neural_Networks&diff=46192Graph Structure of Neural Networks2020-11-24T04:16:29Z<p>Q58yu: /* Top architectures can be identified efficiently */</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 "computational graph", 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 layer and all the way to the output neurons.<br />
<br />
In Neural Networks research, it is often important to build a relation between a neural network’s accuracy and its underlying graph structure. A natural choice is to use computational graph representation, but this has many limitations including a lack of generality and disconnection with biology/neuroscience. This disconnection between biology/neuroscience makes knowledge less transferable and interdisciplinary research more difficult.<br />
<br />
Thus, we develop a new way of representing a neural network as a graph, called a relational graph. The key insight 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 for the systematic exploration of 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.<br />
<br />
= Neural Network as Relational Graph =<br />
<br />
The author proposes the concept of relational graph to study the graphical structure of neural network. Each relational graph is based on an undirected graph <math>G =(V; E)</math>, where <math>V =\{v_1,...,v_n\}</math> is the set of all the nodes, and <math>E \subseteq \{(v_i,v_j)|v_i,v_j\in V\}</math> is the set of all edges that connect nodes. Note that for the graph used here, all nodes have self edges, that is <math>(v_i,v_i)\in E</math>. <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 <math>G</math>. First, a feature quantity <math>x_v</math> is associated with each node. The quantity <math>x_v</math> might be a scalar, vector or tensor depending on different types of neural networks (see the Table at the end of the section). Then a message function <math>f_{uv}(·)</math> is associated with every edge in the graph. A message function specifically takes a node’s feature as the input and then output a message. An aggregation function <math>{\rm AGG}_v(·)</math> then takes a set of messages (the outputs of message function) and outputs the updated node feature. <br />
<br />
A relation graph is a graph <math>G</math> associated with several rounds of message exchange, which transform the feature quantity <math>x_v</math> with the message function <math>f_{uv}(·)</math> and the aggregation function <math>{\rm AGG}_v(·)</math>. 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 <math>r-1</math> rounds of message exchange, then the <math>r^{th}</math> round of message exchange for a node <math>v</math> can be described as<br />
<br />
<div style="text-align:center;"><math>\mathbf{x}_v^{(r+1)}= {\rm AGG}^{(r)}(\{f_v^{(r)}(\textbf{x}_u^{(r)}), \forall u\in N(v)\})</math></div> <br />
<br />
where <math>\mathbf{x}^{(r+1)}</math> is the feature of of the <math>v</math> node in the relational graph after the <math>r^{th}</math> round of update. <math>u,v</math> are nodes in Graph <math>G</math>. <math>N(u)=\{u|(u,v)\in E\}</math> is the set of all the neighbor nodes of <math>u</math> in graph <math>G</math>.<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 <math>r^{th}</math> layer of an MLP takes <math>x^{(r)}</math> as input and <math>x^{(r+1)}</math> as output, then a neuron computes <br />
<br />
<div style="text-align:center;"><math>x_i^{(r+1)}= \sigma(\Sigma_jw_{ij}^{(r)}x_j^{(r)})</math>.</div> <br />
<br />
where <math>w_{ij}^{(r)}</math> is the trainable weight and <math>\sigma</math> is the non-linearity function. Let's first consider the special case where the input and output of all the layers <math>x^{(r)}</math>, <math>1 \leq r \leq R </math> have the same feature dimensions <math>d</math>. In this scenario, we can have <math>d</math> nodes in the Graph <math>G</math> 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 <math>R</math> rounds of message exchange in total. The aggregation function here will be the summation with non-linearity transform <math>\sigma(\Sigma)</math>, 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 <math>x_v</math> connects to all the other nodes in <math>G</math>, that is neighborhood set <math>N(v) = V</math> for each node <math>v</math>. The figure below shows the correspondence between the complete relation graph with a 5-layer 4-dimension fully-connected MLP.<br />
<br />
<div style="text-align:center;">[[File:fully_connnected_MLP.png]]</div><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 />
<div style="text-align:center;">[[File:otherMLP.png]]</div><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 <math>\textbf{x}_j^{(r)}</math> 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 change 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. The representation of these more complicated networks are described in detail in the paper, and the correspondence between different networks and their relational graph properties is summarized in the table below. <br />
<br />
<div style="text-align:center;">[[File:relational_specification.png]]</div><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 neighbourhood, 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 shows as below:<br />
<br />
<div style="text-align:center;">[[File:3.2 graph generator.png]]</div><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 />
<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 & Le, 2019)<br />
<br />
*8-layer CNN with 3×3 convolution<br />
<br />
= Discussions and Conclusions =<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 are always exists graph structure that has higher predictive accuracy under Top-1 error compare to the complete graph<br />
<br />
* There is a sweet spot that the graph structure near the sweet spot usually outperform the base graph<br />
<br />
* The predictive accuracy under top-1 error can be represented by a smooth function of Average Path Length <math> (L) </math> and Clustering Coefficient <math> (C) </math><br />
<br />
* The Experiments is consistent across multiple datasets and multiple graph structure with similar Average Path Length and Clustering Coefficient.<br />
<br />
* The best graph structure can be identified easily.<br />
<br />
* There is a similarity between best artificial neurons and biological neurons.<br />
<br />
----<br />
<br />
<br />
<br />
[[File:Result2_441_2020Group16.png]]<br />
<br />
$$\text{Figure - Results from Experiments}$$<br />
<br />
== Neural networks performance depends on its structure ==<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 />
Compare with the complete graph which has parameter <math> L = 1 </math> and <math> C = 1 </math>, 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 />
== Sweet spot where performance is significantly improved ==<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 <math>[0.1,0.7]</math> and average path length within <math>[1.5,3]</math>.<br />
<br />
== Relationship between neural network’s performance and parameters == <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 />
== Consistency among many different tasks and datasets ==<br />
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 <math>[0.1,0.7]</math> and average path length within <math>[1.5,3]</math> 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 <math>0.658</math>, the p-value for the Null hypothesis is less than <math>10^{-8}</math>.<br />
<br />
== Top architectures can be identified efficiently ==<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 />
== Well-performing neural networks have graph structure surprisingly similar to those of real biological neural networks==<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 />
= 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 "sweet spot" we talked about might be a special feature for the given data set only which is 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 staked 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.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=46188Task Understanding from Confusing Multi-task Data2020-11-24T03:17:45Z<p>Q58yu: /* 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 human 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. 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, a system that allows the machine to learn 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. 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. Thus, 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, assuming the risk measure is mean squared error (MSE), the expected risk functional is<br />
<br />
$$ R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x $$<br />
<br />
where <math>p(x)</math> is the prior distribution of the input variable <math>x</math>. In practice, model optimizations are performed using the empirical risk<br />
<br />
$$ R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2 $$<br />
<br />
When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let <math>f_j(x)</math> be the true ground-truth function for each task <math> j </math>. Therefore, for some input variable <math> x_i </math>, an ideal model <math>g</math> would predict <math> g(x_i) = f_j(x_i) </math>. With this, the risk functional 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 <math> (f_j(x) - g(x))^2 p(f_j) </math> the '''confusing multiple mappings'''. Then the optimal solution <math>g^*(x)</math> to the mapping is <math>\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)</math> under this risk functional. 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 <math>f_u(x) \neq f_v(x)</math> for some input <math>x</math> and <math>u \neq v</math>, <math>R(g^*) > 0</math> 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''' &mdash; allocation of which samples come from the same task<br />
* '''Mapping function''' &mdash; mapping relation from input to output of every learned task<br />
<br />
Suppose there are <math>n</math> ground-truth mappings <math>\{f_j : 1 \leq j \leq n\}</math> that we wish to approximate with a set of mapping functions <math>\{g_k : 1 \leq k \leq l\}</math>. The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determines whether the sample is assigned to task <math>g_k</math>. Under the CSL framework, the risk functional (mean squared 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 />
== 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 <math>k=1,..., n</math> that makes the expected risk function of the CSL problem zero.''<br />
<br />
'''Theorem 2 (Error Bound of CSL)'''<br />
''With probability at least <math>1 - \eta</math> simultaneously with finite VC dimension <math>\tau</math> 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 <math>\alpha</math> is the total parameters of learning functions <math>g, h</math>, <math>B</math> is the upper bound of one sample's risk, <math>m</math> is the size of training data and''<br />
$$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<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 <math>g_k</math>, where <math>y_k = g_k(x)</math> represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample <math>(x,y)</math> and output is an n-dimensional one-hot vector. This output vector determines which task the sample <math>(x,y)</math> 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 resulting 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 is 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 <math>g_k</math> with its corresponding sample <math>(x_i^k, y_i^k)</math>. The optimization problem becomes: <math>\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2</math>. 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 <math>(x, y)</math> will be assigned to <math>g_k</math> that is closest to label y among all different <math>k</math>s. Mapping-net thus provides a temporary solution for deconfusing-net: <math>\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2</math>. The optimization becomes: <math>\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2</math>. 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 <math>(x_i,y_i),i=1,...,m</math> pairs. However, unlike typical regression problems, there are multiple <math>f_j(x),j=1,...,n</math> mapping functions, so the goal is to recover both the mapping functions <math>f_j</math> as well as determine which mapping function corresponds to each of the <math>m</math> 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 (<math>x_i</math>) and either the color, or the digit it represents (<math>y_i</math>). The goal is to recover the classification task ("color" or "digit") for each observation and construct the 2 classifiers for both tasks. <br />
<br />
'''Kaggle Fashion Product''': This data set has more observations than the "colored-MNIST" data and consists of pictures labelled 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 labelling and the accuracy of the learned mapping function. <br />
<br />
'''Task Prediction Accuracy''': <math>\alpha_T(j)</math> is the average number of times the learned deconfusing function <math>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <math>j</math>.<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 <math>k</math> is taken because we need to determine which learned task corresponds to which ground-truth task.<br />
<br />
'''Label Prediction Accuracy''': <math>\alpha_L(j)</math> again chooses <math>f_k</math>, the learned mapping function that is closest to the ground-truth of task <math>j</math>, and measures its average absolute accuracy compared to the ground-truth of task <math>j</math>, <math>f_j</math>, across all <math>m</math> 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 />
==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 <math>\alpha_L</math> scores of around 95%, compared to <math>\alpha_L</math> 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''': In order to "correctly" partition the observations into the correct tasks, a 5-shot warm-up was used. In this situaion, the CSL methods work well 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 <math>h</math>.<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 <math>(x_i,y_i)</math>, where <math>y_i</math> is a <math>n</math>-long indicator vector for whether the image <math>(x_i,y_i)</math> corresponds to each of the <math>n</math> labels<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 "refund", "order didn't arrive", "order damaged", "how good the item is" 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 a 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 task. For data with high noise, oscillations may severely prolong the time needed for 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 to 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 "Application of Multi-label Learning" section.<br />
<br />
= References =<br />
<br />
[1] Su, Xin, et al. "Task Understanding from Confusing Multi-task Data."<br />
<br />
[2] Caruana, R. (1997) "Multi-task learning"<br />
<br />
[3] 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 />
[4] 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 />
[5] Chavdarova, Tatjana, and François Fleuret. "Sgan: An alternative training of generative adversarial networks." In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=46187Task Understanding from Confusing Multi-task Data2020-11-24T03:08:28Z<p>Q58yu: /* Limitations */</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 human 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. 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, a system that allows the machine to learn 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. 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. Thus, 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, assuming the risk measure is mean squared error (MSE), the expected risk functional is<br />
<br />
$$ R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x $$<br />
<br />
where <math>p(x)</math> is the prior distribution of the input variable <math>x</math>. In practice, model optimizations are performed using the empirical risk<br />
<br />
$$ R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2 $$<br />
<br />
When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let <math>f_j(x)</math> be the true ground-truth function for each task <math> j </math>. Therefore, for some input variable <math> x_i </math>, an ideal model <math>g</math> would predict <math> g(x_i) = f_j(x_i) </math>. With this, the risk functional 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 <math> (f_j(x) - g(x))^2 p(f_j) </math> the '''confusing multiple mappings'''. Then the optimal solution <math>g^*(x)</math> to the mapping is <math>\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)</math> under this risk functional. 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 <math>f_u(x) \neq f_v(x)</math> for some input <math>x</math> and <math>u \neq v</math>, <math>R(g^*) > 0</math> 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''' &mdash; allocation of which samples come from the same task<br />
* '''Mapping function''' &mdash; mapping relation from input to output of every learned task<br />
<br />
Suppose there are <math>n</math> ground-truth mappings <math>\{f_j : 1 \leq j \leq n\}</math> that we wish to approximate with a set of mapping functions <math>\{g_k : 1 \leq k \leq l\}</math>. The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determines whether the sample is assigned to task <math>g_k</math>. Under the CSL framework, the risk functional (mean squared 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 />
== 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 <math>k=1,..., n</math> that makes the expected risk function of the CSL problem zero.''<br />
<br />
'''Theorem 2 (Error Bound of CSL)'''<br />
''With probability at least <math>1 - \eta</math> simultaneously with finite VC dimension <math>\tau</math> 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 <math>\alpha</math> is the total parameters of learning functions <math>g, h</math>, <math>B</math> is the upper bound of one sample's risk, <math>m</math> is the size of training data and''<br />
$$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<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 <math>g_k</math>, where <math>y_k = g_k(x)</math> represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample <math>(x,y)</math> and output is an n-dimensional one-hot vector. This output vector determines which task the sample <math>(x,y)</math> 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 resulting 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 is 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 <math>g_k</math> with its corresponding sample <math>(x_i^k, y_i^k)</math>. The optimization problem becomes: <math>\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2</math>. 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 <math>(x, y)</math> will be assigned to <math>g_k</math> that is closest to label y among all different <math>k</math>s. Mapping-net thus provides a temporary solution for deconfusing-net: <math>\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2</math>. The optimization becomes: <math>\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2</math>. 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 <math>(x_i,y_i),i=1,...,m</math> pairs. However, unlike typical regression problems, there are multiple <math>f_j(x),j=1,...,n</math> mapping functions, so the goal is to recover both the mapping functions <math>f_j</math> as well as determine which mapping function corresponds to each of the <math>m</math> 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 (<math>x_i</math>) and either the color, or the digit it represents (<math>y_i</math>). The goal is to recover the classification task ("color" or "digit") for each observation and construct the 2 classifiers for both tasks. <br />
<br />
'''Kaggle Fashion Product''': This data set has more observations than the "colored-MNIST" data and consists of pictures labelled 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 labelling and the accuracy of the learned mapping function. <br />
<br />
'''Task Prediction Accuracy''': <math>\alpha_T(j)</math> is the average number of times the learned deconfusing function <math>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <math>j</math>.<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 <math>k</math> is taken because we need to determine which learned task corresponds to which ground-truth task.<br />
<br />
'''Label Prediction Accuracy''': <math>\alpha_L(j)</math> again chooses <math>f_k</math>, the learned mapping function that is closest to the ground-truth of task <math>j</math>, and measures its average absolute accuracy compared to the ground-truth of task <math>j</math>, <math>f_j</math>, across all <math>m</math> 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 />
==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 <math>\alpha_L</math> scores of around 95%, compared to <math>\alpha_L</math> 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''': In order to "correctly" partition the observations into the correct tasks, a 5-shot warm-up was used. In this situaion, the CSL methods work well 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 <math>h</math>.<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 <math>(x_i,y_i)</math>, where <math>y_i</math> is a <math>n</math>-long indicator vector for whether the image <math>(x_i,y_i)</math> corresponds to each of the <math>n</math> labels<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 "refund", "order didn't arrive", "order damaged", "how good the item is" 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 a 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 task. For data with high noise, oscillations may severely prolong the time needed for 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 to different types of data.<br />
<br />
= References =<br />
<br />
[1] Su, Xin, et al. "Task Understanding from Confusing Multi-task Data."<br />
<br />
[2] Caruana, R. (1997) "Multi-task learning"<br />
<br />
[3] 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 />
[4] 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 />
[5] Chavdarova, Tatjana, and François Fleuret. "Sgan: An alternative training of generative adversarial networks." In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=46185Task Understanding from Confusing Multi-task Data2020-11-24T03:01:20Z<p>Q58yu: /* Limitations */</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 human 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. 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, a system that allows the machine to learn 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. 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. Thus, 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, assuming the risk measure is mean squared error (MSE), the expected risk functional is<br />
<br />
$$ R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x $$<br />
<br />
where <math>p(x)</math> is the prior distribution of the input variable <math>x</math>. In practice, model optimizations are performed using the empirical risk<br />
<br />
$$ R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2 $$<br />
<br />
When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let <math>f_j(x)</math> be the true ground-truth function for each task <math> j </math>. Therefore, for some input variable <math> x_i </math>, an ideal model <math>g</math> would predict <math> g(x_i) = f_j(x_i) </math>. With this, the risk functional 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 <math> (f_j(x) - g(x))^2 p(f_j) </math> the '''confusing multiple mappings'''. Then the optimal solution <math>g^*(x)</math> to the mapping is <math>\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)</math> under this risk functional. 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 <math>f_u(x) \neq f_v(x)</math> for some input <math>x</math> and <math>u \neq v</math>, <math>R(g^*) > 0</math> 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''' &mdash; allocation of which samples come from the same task<br />
* '''Mapping function''' &mdash; mapping relation from input to output of every learned task<br />
<br />
Suppose there are <math>n</math> ground-truth mappings <math>\{f_j : 1 \leq j \leq n\}</math> that we wish to approximate with a set of mapping functions <math>\{g_k : 1 \leq k \leq l\}</math>. The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determines whether the sample is assigned to task <math>g_k</math>. Under the CSL framework, the risk functional (mean squared 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 />
== 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 <math>k=1,..., n</math> that makes the expected risk function of the CSL problem zero.''<br />
<br />
'''Theorem 2 (Error Bound of CSL)'''<br />
''With probability at least <math>1 - \eta</math> simultaneously with finite VC dimension <math>\tau</math> 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 <math>\alpha</math> is the total parameters of learning functions <math>g, h</math>, <math>B</math> is the upper bound of one sample's risk, <math>m</math> is the size of training data and''<br />
$$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<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 <math>g_k</math>, where <math>y_k = g_k(x)</math> represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample <math>(x,y)</math> and output is an n-dimensional one-hot vector. This output vector determines which task the sample <math>(x,y)</math> 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 resulting 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 is 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 <math>g_k</math> with its corresponding sample <math>(x_i^k, y_i^k)</math>. The optimization problem becomes: <math>\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2</math>. 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 <math>(x, y)</math> will be assigned to <math>g_k</math> that is closest to label y among all different <math>k</math>s. Mapping-net thus provides a temporary solution for deconfusing-net: <math>\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2</math>. The optimization becomes: <math>\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2</math>. 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 <math>(x_i,y_i),i=1,...,m</math> pairs. However, unlike typical regression problems, there are multiple <math>f_j(x),j=1,...,n</math> mapping functions, so the goal is to recover both the mapping functions <math>f_j</math> as well as determine which mapping function corresponds to each of the <math>m</math> 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 (<math>x_i</math>) and either the color, or the digit it represents (<math>y_i</math>). The goal is to recover the classification task ("color" or "digit") for each observation and construct the 2 classifiers for both tasks. <br />
<br />
'''Kaggle Fashion Product''': This data set has more observations than the "colored-MNIST" data and consists of pictures labelled 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 labelling and the accuracy of the learned mapping function. <br />
<br />
'''Task Prediction Accuracy''': <math>\alpha_T(j)</math> is the average number of times the learned deconfusing function <math>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <math>j</math>.<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 <math>k</math> is taken because we need to determine which learned task corresponds to which ground-truth task.<br />
<br />
'''Label Prediction Accuracy''': <math>\alpha_L(j)</math> again chooses <math>f_k</math>, the learned mapping function that is closest to the ground-truth of task <math>j</math>, and measures its average absolute accuracy compared to the ground-truth of task <math>j</math>, <math>f_j</math>, across all <math>m</math> 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 />
==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 <math>\alpha_L</math> scores of around 95%, compared to <math>\alpha_L</math> 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''': In order to "correctly" partition the observations into the correct tasks, a 5-shot warm-up was used. In this situaion, the CSL methods work well 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 <math>h</math>.<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 <math>(x_i,y_i)</math>, where <math>y_i</math> is a <math>n</math>-long indicator vector for whether the image <math>(x_i,y_i)</math> corresponds to each of the <math>n</math> labels<br />
<br />
==Limitations==<br />
<br />
'''Number of Tasks''': The authors want to find a better way of deciding the number of tasks than increasing it one by one and seeing which is the minimum number of tasks that gives the smallest risk. They propose adding low-quality constraints to deconfusing-net.<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 "refund", "order didn't arrive", "order damaged", "how good the item is" 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 a 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 task. For data with high noise, oscillations may severely prolong the time needed for 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 to different types of data.<br />
<br />
= References =<br />
<br />
[1] Su, Xin, et al. "Task Understanding from Confusing Multi-task Data."<br />
<br />
[2] Caruana, R. (1997) "Multi-task learning"<br />
<br />
[3] 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 />
[4] 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 />
[5] Chavdarova, Tatjana, and François Fleuret. "Sgan: An alternative training of generative adversarial networks." In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data&diff=46175Task Understanding from Confusing Multi-task Data2020-11-24T02:24:11Z<p>Q58yu: /* Introduction */</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 human in a narrowly defined task, for example, self-driving cars and Google assistant. 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, a system that allows the machine to learn 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. 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. Thus, 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, assuming the risk measure is mean squared error (MSE), the expected risk functional is<br />
<br />
$$ R(g) = \int_x (f(x) - g(x))^2 p(x) \; \mathrm{d}x $$<br />
<br />
where <math>p(x)</math> is the prior distribution of the input variable <math>x</math>. In practice, model optimizations are performed using the empirical risk<br />
<br />
$$ R_e(g) = \sum_{i=1}^n (y_i - g(x_i))^2 $$<br />
<br />
When the problem involves different tasks, the model should optimize for each data point depending on the given task. Let <math>f_j(x)</math> be the true ground-truth function for each task <math> j </math>. Therefore, for some input variable <math> x_i </math>, an ideal model <math>g</math> would predict <math> g(x_i) = f_j(x_i) </math>. With this, the risk functional 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 <math> (f_j(x) - g(x))^2 p(f_j) </math> the '''confusing multiple mappings'''. Then the optimal solution <math>g^*(x)</math> to the mapping is <math>\bar{f}(x) = \sum_{j=1}^n p(f_j) f_j(x)</math> under this risk functional. 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 <math>f_u(x) \neq f_v(x)</math> for some input <math>x</math> and <math>u \neq v</math>, <math>R(g^*) > 0</math> 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''' &mdash; allocation of which samples come from the same task<br />
* '''Mapping function''' &mdash; mapping relation from input to output of every learned task<br />
<br />
Suppose there are <math>n</math> ground-truth mappings <math>\{f_j : 1 \leq j \leq n\}</math> that we wish to approximate with a set of mapping functions <math>\{g_k : 1 \leq k \leq l\}</math>. The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determines whether the sample is assigned to task <math>g_k</math>. Under the CSL framework, the risk functional (mean squared 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 />
== 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 <math>k=1,..., n</math> that makes the expected risk function of the CSL problem zero.''<br />
<br />
'''Theorem 2 (Error Bound of CSL)'''<br />
''With probability at least <math>1 - \eta</math> simultaneously with finite VC dimension <math>\tau</math> 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 <math>\alpha</math> is the total parameters of learning functions <math>g, h</math>, <math>B</math> is the upper bound of one sample's risk, <math>m</math> is the size of training data and''<br />
$$\epsilon(m) = 4 \; \frac{\tau (\ln \frac{2m}{\tau} + 1) - \ln \eta / 4}{m}$$<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 <math>g_k</math>, where <math>y_k = g_k(x)</math> represents the output of one certain task. The deconfusing-net is corresponding to function h, whose input is a sample <math>(x,y)</math> and output is an n-dimensional one-hot vector. This output vector determines which task the sample <math>(x,y)</math> 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 resulting 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 is 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 <math>g_k</math> with its corresponding sample <math>(x_i^k, y_i^k)</math>. The optimization problem becomes: <math>\displaystyle \min_{g_k} L_{map}(g_k) = \sum_{i=1}^{m_k} \mid y_i^k - g_k(x_i^k)\mid^2</math>. 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 <math>(x, y)</math> will be assigned to <math>g_k</math> that is closest to label y among all different <math>k</math>s. Mapping-net thus provides a temporary solution for deconfusing-net: <math>\hat{h}(x_i, y_i) = arg \displaystyle\min_{k} \mid y_i - g_k(x_i)\mid^2</math>. The optimization becomes: <math>\displaystyle \min_{h} L_{dec}(h) = \sum_{i=1}^{m} \mid {h}(x_i, y_i) - \hat{h}(x_i, y_i)\mid^2</math>. 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 <math>(x_i,y_i),i=1,...,m</math> pairs. However, unlike typical regression problems, there are multiple <math>f_j(x),j=1,...,n</math> mapping functions, so the goal is to recover both the mapping functions <math>f_j</math> as well as determine which mapping function corresponds to each of the <math>m</math> 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 (<math>x_i</math>) and either the color, or the digit it represents (<math>y_i</math>). The goal is to recover the classification task ("color" or "digit") for each observation and construct the 2 classifiers for both tasks. <br />
<br />
'''Kaggle Fashion Product''': This data set has more observations than the "colored-MNIST" data and consists of pictures labelled 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 labelling and the accuracy of the learned mapping function. <br />
<br />
'''Task Prediction Accuracy''': <math>\alpha_T(j)</math> is the average number of times the learned deconfusing function <math>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <math>j</math>.<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 <math>k</math> is taken because we need to determine which learned task corresponds to which ground-truth task.<br />
<br />
'''Label Prediction Accuracy''': <math>\alpha_L(j)</math> again chooses <math>f_k</math>, the learned mapping function that is closest to the ground-truth of task <math>j</math>, and measures its average absolute accuracy compared to the ground-truth of task <math>j</math>, <math>f_j</math>, across all <math>m</math> 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 />
==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 <math>\alpha_L</math> scores of around 95%, compared to <math>\alpha_L</math> 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''': In order to "correctly" partition the observations into the correct tasks, a 5-shot warm-up was used. In this situaion, the CSL methods work well 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 <math>h</math>.<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 <math>(x_i,y_i)</math>, where <math>y_i</math> is a <math>n</math>-long indicator vector for whether the image <math>(x_i,y_i)</math> corresponds to each of the <math>n</math> labels<br />
<br />
==Limitations==<br />
<br />
'''Number of Tasks''': The authors want to find a better way of deciding the number of tasks than increasing it one by one and seeing which is the minimum number of tasks that gives the smallest risk. They propose adding low-quality constraints to deconfusing-net.<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.<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 "refund", "order didn't arrive", "order damaged", "how good the item is" 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 a 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 task. For data with high noise, oscillations may severely prolong the time needed for 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 to different types of data.<br />
<br />
= References =<br />
<br />
[1] Su, Xin, et al. "Task Understanding from Confusing Multi-task Data."<br />
<br />
[2] Caruana, R. (1997) "Multi-task learning"<br />
<br />
[3] 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 />
[4] 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 />
[5] Chavdarova, Tatjana, and François Fleuret. "Sgan: An alternative training of generative adversarial networks." In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9407-9415. 2018.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46137User:T358wang2020-11-23T22:03:08Z<p>Q58yu: /* Related Work */</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. This paper provides a new and effective method to recognize landmark images, which has been successfully applied to actual images. In this way, statues, 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. Random Sample Consensus (RANSAC) is a method to smooth data containing a significant percentage of errors, which is ideally suited for applications in automated image analysis where interpretation is based on the data generated by error-prone feature detectors. 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 />
== 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 the below figure, the last fully-connected layer after the averaging pool is removed. Instead, a fully-connected 2048 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> 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, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> 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 <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 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 <math>\alpha_1, \alpha_2, \alpha_3</math> 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 <math>\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v</math> 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 <math>\eta</math> 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)[2] 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&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 & 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 />
[1] 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 />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46135User:T358wang2020-11-23T21:39:31Z<p>Q58yu: /* Introduction */</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. This paper provides a new and effective method to recognize landmark images, which has been successfully applied to actual images. In this way, statues, 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 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> 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, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> 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 <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 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 <math>\alpha_1, \alpha_2, \alpha_3</math> 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 <math>\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v</math> 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 <math>\eta</math> 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)[2] 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&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 & 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 />
[1] 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 />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46133User:T358wang2020-11-23T21:37:55Z<p>Q58yu: /* Introduction */</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, statues, 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 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> 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, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> 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 <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 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 <math>\alpha_1, \alpha_2, \alpha_3</math> 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 <math>\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v</math> 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 <math>\eta</math> 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)[2] 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&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 & 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 />
[1] 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 />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:T358wang&diff=46132User:T358wang2020-11-23T21:37:17Z<p>Q58yu: /* Introduction */</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 <math>\times</math> 512 layer and a batch normalization are added as the embedding layer. After the batch norm, a fully-connected 512 <math>\times</math> 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, <math>x_i \in R^d</math> is the i-th embedding and <math>y_i</math> is the corresponding label where <math>y_i \in</math> {1,...,n,n+1}, n+1 is the label of the non-landmark class. Denote <math>W \in R^{d \times n}</math> as the weights of the classifier layer, <math>W_j</math> as its j-th column. Let <math>c_{y_i}</math> be the <math>y_i</math> th embeddings center from Center loss and <math>\lambda</math> 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 <math>\lambda</math> is set to 5e-5. Each image is resized to 256 <math>\times</math> 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 <math>\alpha_1, \alpha_2, \alpha_3</math> 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 <math>\mu_{l_j} = \frac{1}{v} \sum_{i \in C_j} x_i, j \in 1,...,v</math> 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 <math>\eta</math> 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)[2] 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&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 & 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 />
[1] 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 />
[2] FilipRadenović,AhmetIscen,GiorgosTolias,YannisAvrithis,andOndřejChum.<br />
2018. Revisiting Oxford and Paris: Large-Scale Image Retrieval Benchmarking.<br />
arXiv preprint arXiv:1803.11285 (2018).</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=46129User:Cvmustat2020-11-23T21:03:50Z<p>Q58yu: /* CRNN Model Architecture */</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.[1] 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 />
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 embedding of words together, and it is able to capture both local and position invariant features of the text.[2] 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. [3] 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. In addition, 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.[4] 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 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. The 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. The architecture combines these two matrix representations to classify the text as well as offer the importance information of each word for the prediction which can help with the interpretation of 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.<br />
<br />
'''20 Newsgroups:''' a news categorization dataset, again using only 4 large classes from the dataset.<br />
<br />
'''Sogou News:''' a Chinese news categorization dataset, using the 4 largest classes from the dataset.<br />
<br />
'''Yahoo! Answers:''' a topic classification dataset, with 10 classes.<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, to obtain the following results:<br />
<br />
[[File:table of results.png|550px]]<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 />
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]]<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 />
'''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 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: <math> \hat{y}_{t} </math> and <math> h_t </math>. For a time step <math> t </math>, <math> h_t </math> is fed back into the layer to compute <math> \hat{y}_{t+1} </math> and <math> h_{t+1} </math>. <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 memorizing 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 are 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 <math>h_{t-1} \in \mathbb{R}^m, x_t \in \mathbb{R}^d </math> be the inputs, and let <math>\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}</math> be trainable weight matrices. Then the following equations describe the update and reset gates:<br />
<br />
<math><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 />
</math><br />
<br />
Note that <math> \sigma, \text{tanh}, \circ </math> are all element-wise functions. The above equations do the following:<br />
<br />
<ol><br />
<li> <math>h_{t-1}</math> carries information from the previous iteration and <math>x_t</math> is the current input </li><br />
<li> the update gate <math>z_t</math> controls how much past information should be forwarded to the next hidden state </li><br />
<li> the rest gate <math>r_t</math> controls how much past information is forgotten or reset </li><br />
<li> new memory <math>\tilde{h}_t</math> contains the relevant past memory as instructed by <math>r_t</math> and current information from the input <math>x_t</math> </li><br />
<li> then <math>z_t</math> is used to control what is passed on from <math>h_{t-1}</math> and <math>(1-z_t)</math> controls the new memory that is passed on<br />
</ol><br />
<br />
We treat <math>h_0</math> and <math> h_{n+1} </math> as zero vectors in the method. Thus, each <math>h_t</math> can be computed as above to yield results for the bi-directional RNN. The resulting hidden states <math>\overrightarrow{h_t}</math> and <math>\overleftarrow{h_t}</math> contain contextual information around the <math> t</math>-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, <math>V^i </math>, we compute a new representation that aggregates meanings from the forward and backward hidden states more accurately as follows:<br />
<br />
<math> <br />
[\hat{h_t}]_i = tanh(\overrightarrow{h_t}V^i\overleftarrow{h_t} + b_i) <br />
</math><br />
<br />
Where <math>V^i \in \mathbb{R}^{m \times m} </math> is the learned tensor layer, and <math> b_i \in \mathbb{R} </math> is the bias.We repeat this <math> m </math> times with different <math>V^i </math> matrices and <math> b_i </math> vectors. Through the neural tensor layer, each element in <math> [\hat{h_t}]_i </math> can be viewed as a different type of intersection between the forward and backward hidden states. In the model, <math> [\hat{h_t}]_i </math> 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 />
<math><br />
\overleftrightarrow{h_t} = [\overrightarrow{h_t}^T,\overleftarrow{h_t}^T,\hat{h_t}]^T <br />
</math><br />
<br />
We calculate this vector for every word in the text and then stack them all into matrix <math> H </math> with shape <math>n</math>-by-<math>3m</math>.<br />
<br />
<math><br />
H = [\overleftrightarrow{h_1};...\overleftrightarrow{h_n}]<br />
</math><br />
<br />
This <math>H</math> 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 />
<ol><br />
<li> Given a sequence of words, each word is converted into a word vector using the word2vec algorithm which gives matrix X. <br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
<ul><br />
<li> 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 />
<li> Temporal dimension example: convolve words from 1 to K, then convolve words 2 to K+1, etc<br />
</li><br />
</ul><br />
<br />
<li> 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 />
</li><br />
<br />
<li> Each linear combination of the K-gram representations gives the relative word importance based on the aspect that the linear combination encodes.<br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
</ol><br />
<br />
[[File:Group12_Figure1.png |center]]<br />
<br />
<div align="center">Figure 1: The architecture of CRNN.</div><br />
<br />
== Merging RNN & 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 <math>S=A^TH</math> which has shape <math>z \times 3m</math> and is essentially a linear combination of the hidden states. The concatenated rows of S results in a vector in <math>\mathbb{R}^{3zm}</math>, 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 />
<ul><br />
<li> Use cross-entropy loss as the loss function </li><br />
<li> Perform dropout on random columns in matrix C in the CNN pipeline </li><br />
<li> Perform L2 regularization on all parameters </li><br />
<li> Use stochastic gradient descent with a learning rate of 0.001 </li><br />
</ul><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]]<br />
<br />
== Conclusion & 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 different aspects and stores it into a weight matrix. The Recurrent Neural Network learns each words contextual representation through the combination of the forward and backward context informations that are 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 analysis. In the future, one can explore the features that extracted from the model and use them to potentially learn new methods such as model space. [5]<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 />
== References ==<br />
----<br />
<br />
[1] 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 />
[2] N. Kalchbrenner, E. Grefenstette, and P. Blunsom, “A convolutional neural network for modelling sentences,”<br />
arXiv preprint arXiv:1404.2188, 2014.<br />
<br />
[3] 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 />
[4] 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 />
[5] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=46127User:Cvmustat2020-11-23T20:57:44Z<p>Q58yu: /* CRNN Model Architecture */</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.[1] 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 />
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 embedding of words together, and it is able to capture both local and position invariant features of the text.[2] 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. [3] 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. In addition, 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.[4] 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 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. The 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. The architecture combines these two matrix representations to classify the text as well as offer the importance information of each word for the prediction which can help with the interpretation of 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.<br />
<br />
'''20 Newsgroups:''' a news categorization dataset, again using only 4 large classes from the dataset.<br />
<br />
'''Sogou News:''' a Chinese news categorization dataset, using the 4 largest classes from the dataset.<br />
<br />
'''Yahoo! Answers:''' a topic classification dataset, with 10 classes.<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, to obtain the following results:<br />
<br />
[[File:table of results.png|550px]]<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 />
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]]<br />
<br />
== CRNN Model Architecture ==<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 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: <math> \hat{y}_{t} </math> and <math> h_t </math>. For a time step <math> t </math>, <math> h_t </math> is fed back into the layer to compute <math> \hat{y}_{t+1} </math> and <math> h_{t+1} </math>. <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 memorizing 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 are 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 <math>h_{t-1} \in \mathbb{R}^m, x_t \in \mathbb{R}^d </math> be the inputs, and let <math>\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}</math> be trainable weight matrices. Then the following equations describe the update and reset gates:<br />
<br />
<math><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 />
</math><br />
<br />
Note that <math> \sigma, \text{tanh}, \circ </math> are all element-wise functions. The above equations do the following:<br />
<br />
<ol><br />
<li> <math>h_{t-1}</math> carries information from the previous iteration and <math>x_t</math> is the current input </li><br />
<li> the update gate <math>z_t</math> controls how much past information should be forwarded to the next hidden state </li><br />
<li> the rest gate <math>r_t</math> controls how much past information is forgotten or reset </li><br />
<li> new memory <math>\tilde{h}_t</math> contains the relevant past memory as instructed by <math>r_t</math> and current information from the input <math>x_t</math> </li><br />
<li> then <math>z_t</math> is used to control what is passed on from <math>h_{t-1}</math> and <math>(1-z_t)</math> controls the new memory that is passed on<br />
</ol><br />
<br />
We treat <math>h_0</math> and <math> h_{n+1} </math> as zero vectors in the method. Thus, each <math>h_t</math> can be computed as above to yield results for the bi-directional RNN. The resulting hidden states <math>\overrightarrow{h_t}</math> and <math>\overleftarrow{h_t}</math> contain contextual information around the <math> t</math>-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, <math>V^i </math>, we compute a new representation that aggregates meanings from the forward and backward hidden states more accurately as follows:<br />
<br />
<math> <br />
[\hat{h_t}]_i = tanh(\overrightarrow{h_t}V^i\overleftarrow{h_t} + b_i) <br />
</math><br />
<br />
Where <math>V^i \in \mathbb{R}^{m \times m} </math> is the learned tensor layer, and <math> b_i \in \mathbb{R} </math> is the bias.We repeat this <math> m </math> times with different <math>V^i </math> matrices and <math> b_i </math> vectors. Through the neural tensor layer, each element in <math> [\hat{h_t}]_i </math> can be viewed as a different type of intersection between the forward and backward hidden states. In the model, <math> [\hat{h_t}]_i </math> 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 />
<math><br />
\overleftrightarrow{h_t} = [\overrightarrow{h_t}^T,\overleftarrow{h_t}^T,\hat{h_t}]^T <br />
</math><br />
<br />
We calculate this vector for every word in the text and then stack them all into matrix <math> H </math> with shape <math>n</math>-by-<math>3m</math>.<br />
<br />
<math><br />
H = [\overleftrightarrow{h_1};...\overleftrightarrow{h_n}]<br />
</math><br />
<br />
This <math>H</math> 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 />
<ol><br />
<li> Given a sequence of words, each word is converted into a word vector using the word2vec algorithm which gives matrix X. <br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
<ul><br />
<li> 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 />
<li> Temporal dimension example: convolve words from 1 to K, then convolve words 2 to K+1, etc<br />
</li><br />
</ul><br />
<br />
<li> 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 />
</li><br />
<br />
<li> Each linear combination of the K-gram representations gives the relative word importance based on the aspect that the linear combination encodes.<br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
</ol><br />
<br />
[[File:Group12_Figure1.png |center]]<br />
<br />
<div align="center">Figure 1: The architecture of CRNN.</div><br />
<br />
== Merging RNN & 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 <math>S=A^TH</math> which has shape <math>z \times 3m</math> and is essentially a linear combination of the hidden states. The concatenated rows of S results in a vector in <math>\mathbb{R}^{3zm}</math>, 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 />
<ul><br />
<li> Use cross-entropy loss as the loss function </li><br />
<li> Perform dropout on random columns in matrix C in the CNN pipeline </li><br />
<li> Perform L2 regularization on all parameters </li><br />
<li> Use stochastic gradient descent with a learning rate of 0.001 </li><br />
</ul><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]]<br />
<br />
== Conclusion & 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 different aspects and stores it into a weight matrix. The Recurrent Neural Network learns each words contextual representation through the combination of the forward and backward context informations that are 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 analysis. In the future, one can explore the features that extracted from the model and use them to potentially learn new methods such as model space. [5]<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 />
== References ==<br />
----<br />
<br />
[1] 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 />
[2] N. Kalchbrenner, E. Grefenstette, and P. Blunsom, “A convolutional neural network for modelling sentences,”<br />
arXiv preprint arXiv:1404.2188, 2014.<br />
<br />
[3] 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 />
[4] 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 />
[5] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Group12_Figure1.png&diff=46126File:Group12 Figure1.png2020-11-23T20:55:58Z<p>Q58yu: </p>
<hr />
<div></div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=46122User:Cvmustat2020-11-23T20:49:33Z<p>Q58yu: /* Introduction */</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.[1] 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 />
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 embedding of words together, and it is able to capture both local and position invariant features of the text.[2] 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. [3] 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. In addition, 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.[4] 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 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. The 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. The architecture combines these two matrix representations to classify the text as well as offer the importance information of each word for the prediction which can help with the interpretation of 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.<br />
<br />
'''20 Newsgroups:''' a news categorization dataset, again using only 4 large classes from the dataset.<br />
<br />
'''Sogou News:''' a Chinese news categorization dataset, using the 4 largest classes from the dataset.<br />
<br />
'''Yahoo! Answers:''' a topic classification dataset, with 10 classes.<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, to obtain the following results:<br />
<br />
[[File:table of results.png|550px]]<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 />
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]]<br />
<br />
== CRNN Model Architecture ==<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 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: <math> \hat{y}_{t} </math> and <math> h_t </math>. For a time step <math> t </math>, <math> h_t </math> is fed back into the layer to compute <math> \hat{y}_{t+1} </math> and <math> h_{t+1} </math>. <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 memorizing 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 are 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 <math>h_{t-1} \in \mathbb{R}^m, x_t \in \mathbb{R}^d </math> be the inputs, and let <math>\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}</math> be trainable weight matrices. Then the following equations describe the update and reset gates:<br />
<br />
<math><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 />
</math><br />
<br />
Note that <math> \sigma, \text{tanh}, \circ </math> are all element-wise functions. The above equations do the following:<br />
<br />
<ol><br />
<li> <math>h_{t-1}</math> carries information from the previous iteration and <math>x_t</math> is the current input </li><br />
<li> the update gate <math>z_t</math> controls how much past information should be forwarded to the next hidden state </li><br />
<li> the rest gate <math>r_t</math> controls how much past information is forgotten or reset </li><br />
<li> new memory <math>\tilde{h}_t</math> contains the relevant past memory as instructed by <math>r_t</math> and current information from the input <math>x_t</math> </li><br />
<li> then <math>z_t</math> is used to control what is passed on from <math>h_{t-1}</math> and <math>(1-z_t)</math> controls the new memory that is passed on<br />
</ol><br />
<br />
We treat <math>h_0</math> and <math> h_{n+1} </math> as zero vectors in the method. Thus, each <math>h_t</math> can be computed as above to yield results for the bi-directional RNN. The resulting hidden states <math>\overrightarrow{h_t}</math> and <math>\overleftarrow{h_t}</math> contain contextual information around the <math> t</math>-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, <math>V^i </math>, we compute a new representation that aggregates meanings from the forward and backward hidden states more accurately as follows:<br />
<br />
<math> <br />
[\hat{h_t}]_i = tanh(\overrightarrow{h_t}V^i\overleftarrow{h_t} + b_i) <br />
</math><br />
<br />
Where <math>V^i \in \mathbb{R}^{m \times m} </math> is the learned tensor layer, and <math> b_i \in \mathbb{R} </math> is the bias.We repeat this <math> m </math> times with different <math>V^i </math> matrices and <math> b_i </math> vectors. Through the neural tensor layer, each element in <math> [\hat{h_t}]_i </math> can be viewed as a different type of intersection between the forward and backward hidden states. In the model, <math> [\hat{h_t}]_i </math> 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 />
<math><br />
\overleftrightarrow{h_t} = [\overrightarrow{h_t}^T,\overleftarrow{h_t}^T,\hat{h_t}]^T <br />
</math><br />
<br />
We calculate this vector for every word in the text and then stack them all into matrix <math> H </math> with shape <math>n</math>-by-<math>3m</math>.<br />
<br />
<math><br />
H = [\overleftrightarrow{h_1};...\overleftrightarrow{h_n}]<br />
</math><br />
<br />
This <math>H</math> 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 />
<ol><br />
<li> Given a sequence of words, each word is converted into a word vector using the word2vec algorithm which gives matrix X. <br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
<ul><br />
<li> 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 />
<li> Temporal dimension example: convolve words from 1 to K, then convolve words 2 to K+1, etc<br />
</li><br />
</ul><br />
<br />
<li> 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 />
</li><br />
<br />
<li> Each linear combination of the K-gram representations gives the relative word importance based on the aspect that the linear combination encodes.<br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
</ol><br />
<br />
== Merging RNN & 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 <math>S=A^TH</math> which has shape <math>z \times 3m</math> and is essentially a linear combination of the hidden states. The concatenated rows of S results in a vector in <math>\mathbb{R}^{3zm}</math>, 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 />
<ul><br />
<li> Use cross-entropy loss as the loss function </li><br />
<li> Perform dropout on random columns in matrix C in the CNN pipeline </li><br />
<li> Perform L2 regularization on all parameters </li><br />
<li> Use stochastic gradient descent with a learning rate of 0.001 </li><br />
</ul><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]]<br />
<br />
== Conclusion & 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 different aspects and stores it into a weight matrix. The Recurrent Neural Network learns each words contextual representation through the combination of the forward and backward context informations that are 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 analysis. In the future, one can explore the features that extracted from the model and use them to potentially learn new methods such as model space. [5]<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 />
== References ==<br />
----<br />
<br />
[1] 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 />
[2] N. Kalchbrenner, E. Grefenstette, and P. Blunsom, “A convolutional neural network for modelling sentences,”<br />
arXiv preprint arXiv:1404.2188, 2014.<br />
<br />
[3] 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 />
[4] 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 />
[5] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat&diff=46121User:Cvmustat2020-11-23T20:48:57Z<p>Q58yu: /* Introduction */</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.[1] 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 />
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 embedding of words together and is able to capture both local and position invariant features of the text.[2] 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. [3] 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. In addition, 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.[4] 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 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. The 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. The architecture combines these two matrix representations to classify the text as well as offer the importance information of each word for the prediction which can help with the interpretation of 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.<br />
<br />
'''20 Newsgroups:''' a news categorization dataset, again using only 4 large classes from the dataset.<br />
<br />
'''Sogou News:''' a Chinese news categorization dataset, using the 4 largest classes from the dataset.<br />
<br />
'''Yahoo! Answers:''' a topic classification dataset, with 10 classes.<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, to obtain the following results:<br />
<br />
[[File:table of results.png|550px]]<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 />
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]]<br />
<br />
== CRNN Model Architecture ==<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 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: <math> \hat{y}_{t} </math> and <math> h_t </math>. For a time step <math> t </math>, <math> h_t </math> is fed back into the layer to compute <math> \hat{y}_{t+1} </math> and <math> h_{t+1} </math>. <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 memorizing 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 are 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 <math>h_{t-1} \in \mathbb{R}^m, x_t \in \mathbb{R}^d </math> be the inputs, and let <math>\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}</math> be trainable weight matrices. Then the following equations describe the update and reset gates:<br />
<br />
<math><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 />
</math><br />
<br />
Note that <math> \sigma, \text{tanh}, \circ </math> are all element-wise functions. The above equations do the following:<br />
<br />
<ol><br />
<li> <math>h_{t-1}</math> carries information from the previous iteration and <math>x_t</math> is the current input </li><br />
<li> the update gate <math>z_t</math> controls how much past information should be forwarded to the next hidden state </li><br />
<li> the rest gate <math>r_t</math> controls how much past information is forgotten or reset </li><br />
<li> new memory <math>\tilde{h}_t</math> contains the relevant past memory as instructed by <math>r_t</math> and current information from the input <math>x_t</math> </li><br />
<li> then <math>z_t</math> is used to control what is passed on from <math>h_{t-1}</math> and <math>(1-z_t)</math> controls the new memory that is passed on<br />
</ol><br />
<br />
We treat <math>h_0</math> and <math> h_{n+1} </math> as zero vectors in the method. Thus, each <math>h_t</math> can be computed as above to yield results for the bi-directional RNN. The resulting hidden states <math>\overrightarrow{h_t}</math> and <math>\overleftarrow{h_t}</math> contain contextual information around the <math> t</math>-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, <math>V^i </math>, we compute a new representation that aggregates meanings from the forward and backward hidden states more accurately as follows:<br />
<br />
<math> <br />
[\hat{h_t}]_i = tanh(\overrightarrow{h_t}V^i\overleftarrow{h_t} + b_i) <br />
</math><br />
<br />
Where <math>V^i \in \mathbb{R}^{m \times m} </math> is the learned tensor layer, and <math> b_i \in \mathbb{R} </math> is the bias.We repeat this <math> m </math> times with different <math>V^i </math> matrices and <math> b_i </math> vectors. Through the neural tensor layer, each element in <math> [\hat{h_t}]_i </math> can be viewed as a different type of intersection between the forward and backward hidden states. In the model, <math> [\hat{h_t}]_i </math> 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 />
<math><br />
\overleftrightarrow{h_t} = [\overrightarrow{h_t}^T,\overleftarrow{h_t}^T,\hat{h_t}]^T <br />
</math><br />
<br />
We calculate this vector for every word in the text and then stack them all into matrix <math> H </math> with shape <math>n</math>-by-<math>3m</math>.<br />
<br />
<math><br />
H = [\overleftrightarrow{h_1};...\overleftrightarrow{h_n}]<br />
</math><br />
<br />
This <math>H</math> 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 />
<ol><br />
<li> Given a sequence of words, each word is converted into a word vector using the word2vec algorithm which gives matrix X. <br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
<ul><br />
<li> 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 />
<li> Temporal dimension example: convolve words from 1 to K, then convolve words 2 to K+1, etc<br />
</li><br />
</ul><br />
<br />
<li> 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 />
</li><br />
<br />
<li> Each linear combination of the K-gram representations gives the relative word importance based on the aspect that the linear combination encodes.<br />
</li><br />
<br />
<li> 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 />
</li><br />
<br />
</ol><br />
<br />
== Merging RNN & 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 <math>S=A^TH</math> which has shape <math>z \times 3m</math> and is essentially a linear combination of the hidden states. The concatenated rows of S results in a vector in <math>\mathbb{R}^{3zm}</math>, 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 />
<ul><br />
<li> Use cross-entropy loss as the loss function </li><br />
<li> Perform dropout on random columns in matrix C in the CNN pipeline </li><br />
<li> Perform L2 regularization on all parameters </li><br />
<li> Use stochastic gradient descent with a learning rate of 0.001 </li><br />
</ul><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]]<br />
<br />
== Conclusion & 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 different aspects and stores it into a weight matrix. The Recurrent Neural Network learns each words contextual representation through the combination of the forward and backward context informations that are 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 analysis. In the future, one can explore the features that extracted from the model and use them to potentially learn new methods such as model space. [5]<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 />
== References ==<br />
----<br />
<br />
[1] 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 />
[2] N. Kalchbrenner, E. Grefenstette, and P. Blunsom, “A convolutional neural network for modelling sentences,”<br />
arXiv preprint arXiv:1404.2188, 2014.<br />
<br />
[3] 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 />
[4] 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 />
[5] 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>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost&diff=46081IPBoost2020-11-23T17:36:11Z<p>Q58yu: /* Introduction */</p>
<hr />
<div>== Presented by == <br />
Casey De Vera, Solaiman Jawad<br />
<br />
== Introduction == <br />
Boosting is an important and a fairly standard technique in classification that combines several base learners (learners which have a “low accuracy”), into one boosted learner (learner with a “high accuracy”). Pioneered by the AdaBoost approach of Freund & Schapire, in recent decades there has been extensive work on boosting procedures and analyses of their limitations.<br />
<br />
In a nutshell, boosting procedures are (typically) iterative schemes that roughly work as follows:<br />
<br />
Let <math>T</math> represents the number of iteration and <math>t</math> represents the iterator. <br />
<br />
for <math> t= 1, \cdots, T </math> do the following:<br />
<br />
::1. Train a learner <math> \mu_t</math> from a given class of base learners on the data distribution <math> \mathcal D_t</math><br />
<br />
::2. Evaluate the performance of <math> \mu_t</math> by computing its loss.<br />
<br />
::3. Push weight of the data distribution <math> \mathcal D_t</math> towards the misclassified examples leading to <math> \mathcal D_{t+1}</math>, usually a relatively good model will have a higher weight on those data that misclassified.<br />
<br />
Finally, the learners are combined with some form of voting (e.g., soft or hard voting, averaging, thresholding).<br />
<br />
<br />
[[File:boosting.gif|200px|thumb|right]] A close inspection of most boosting procedures reveals that they solve an underlying convex optimization problem over a convex loss function by means of coordinate gradient descent. Boosting schemes of this type are often referred to as '''convex potential boosters'''. These procedures can achieve exceptional performance on many data sets if the data is correctly labeled. However, they can be defeated easily by a small amount of incorrect labels which can be quite difficult to fix. The reason being is that we try to solve misclassified examples by moving the weights around, which results in bad performance on unseen data (Shown by zoomed example to the right). In fact, in theory, provided the class of base learners is rich enough, a perfect strong learner can be constructed that has accuracy 1, however, clearly, such a learner might not necessarily generalize well. Boosted learners can generate some quite complicated decision boundaries, much more complicated than that of the base learners. Here is an example from Paul van der Laken’s blog / Extreme gradient boosting gif by Ryan Holbrook. Here data is generated online according to some process with optimal decision boundary represented by the dotted line and XGBoost was used to learn a classifier:<br />
<br />
<br />
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper, the non-convex boosting in classification using integer programming has been explored, and the real-world practicability of the approach while circumventing shortcomings of convex boosting approaches is also shown. The paper reports results that are comparable to or better than current state-of-the-art approaches.<br />
<br />
== Motivation ==<br />
<br />
In reality, we usually face unclean data and so-called label noise, where some percentage of the classification labels might be corrupted. We would also like to construct strong learners for such data. Noisy labels are an issue because when a model is trained with excessive amounts of noisy labels, the performance and accuracy deteriorates greatly. However, if we revisit the general boosting template from above, then we might suspect that we run into trouble as soon as a certain fraction of training examples is misclassified: in this case, these examples cannot be correctly classified and the procedure shifts more and more weight towards these bad examples. This eventually leads to a strong learner, that perfectly predicts the (flawed) training data; however, that does not generalize well anymore. This intuition has been formalized by [LS] who construct a “hard” training data distribution, where a small percentage of labels is randomly flipped. This label noise then leads to a significant reduction in performance of these boosted learners; see tables below. The more technical reason for this problem is actually the convexity of the loss function that is minimized by the boosting procedure. Clearly, one can use all types of “tricks” such as early stopping but at the end of the day, this is not solving the fundamental problem.<br />
<br />
== IPBoost: Boosting via Integer Programming ==<br />
<br />
<br />
===Integer Program Formulation===<br />
Let <math>(x_1,y_1),\cdots, (x_N,y_N) </math> be the training set with points <math>x_i \in \mathbb{R}^d</math> and two-class labels <math>y_i \in \{\pm 1\}</math> <br />
* class of base learners: <math> \Omega :=\{h_1, \cdots, h_L: \mathbb{R}^d \rightarrow \{\pm 1\}\} </math> and <math>\rho \ge 0</math> be given. <br />
* error function <math> \eta </math><br />
Our boosting model is captured by the integer programming problem. We can call this our primal problem: <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j=1}^L \eta_{ij}\lambda_k+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i=1,\cdots, N \\ <br />
&\sum_{j=1}^L \lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
For the error function <math>\eta</math>, three options were considered:<br />
<br />
(i) <math> \pm 1 </math> classification from learners<br />
$$ \eta_{ij} := 2\mathbb{I}[h_j(x_i) = y_i] - 1 = y_i \cdot h_j(x_i) $$<br />
(ii) class probabilities of learners<br />
$$ \eta_{ij} := 2\mathbb{P}[h_j(x_i) = y_i] - 1$$<br />
(iii) SAMME.R error function for learners<br />
$$ \frac{1}{2}y_i\log\left(\frac{\mathbb{P}[h_j(x_i) = 1]}{\mathbb{P}[h_j(x_i) = -1]}\right)$$<br />
<br />
===Solution of the IP using Column Generation===<br />
<br />
The goal of column generation is to provide an efficient way to solve the linear programming relaxation of the primal by allowing the <math>z_i </math> variables to assume fractional values. Moreover, columns, i.e., the base learners, <math> \mathcal L \subseteq [L]. </math> are left out because there are too many to handle efficiently and most of them will have their associated weight equal to zero in the optimal solution anyway. To generate columns, a <i>branch and bound</i> framework is used. Columns are generated within a<br />
branch-and-bound framework leading effectively to a branch-and-bound-and-price algorithm being used; this is significantly more involved compared to column generation in linear programming. To check the optimality of an LP solution, a subproblem, called the pricing problem, is solved to try to identify columns with a profitable reduced cost. If such columns are found, the LP is re-optimized. Branching occurs when no profitable columns are found, but the LP solution does not satisfy the integrality conditions. Branch and price apply column generation at every node of the branch and bound tree.<br />
<br />
The restricted master primal problem is <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j\in \mathcal L} \eta_{ij}\lambda_j+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i \in [N]\\ <br />
&\sum_{j\in \mathcal L}\lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
<br />
Its restricted dual problem is:<br />
<br />
$$ \begin{align*}\max \rho &\sum^{N}_{i=1}w_i + v - \sum^{N}_{i=1}u_i<br />
\\ s.t. &\sum_{i=1}^N \eta_{ij}w_k+ v \le 0 \ \ \ \forall j \in L \\ <br />
&(1+\rho)w_i - u_i \le 1 \ \ \ \forall i \in [N] \\ &w \ge 0, u \ge 0, v\ free\end{align*}$$<br />
<br />
Furthermore, there is a pricing problem used to determine, for every supposed optimal solution of the dual, whether the solution is actually optimal, or whether further constraints need to be added into the primal solution. With this pricing problem, we check whether the solution to the restricted dual is feasible. This pricing problem can be expressed as follows:<br />
<br />
$$ \sum_{i=1}^N \eta_{ij}w_k^* + v^* > 0 $$<br />
<br />
The optimal misclassification values are determined by a branch-and-price process that branches on the variables <math> z_i </math> and solves the intermediate LPs using column generation.<br />
<br />
===Algorithm===<br />
<div style="margin-left: 3em;"><br />
<math> D = \{(x_i, y_i) | i ∈ I\} ⊆ R^d × \{±1\} </math>, class of base learners <math>Ω </math>, margin <math> \rho </math> <br><br />
'''Output:''' Boosted learner <math> \sum_{j∈L^∗}h_jλ_j^* </math> with base learners <math> h_j </math> and weights <math> λ_j^* </math> <br><br />
<br />
<ol><br />
<br />
<li margin-left:30px> <math> T ← \{([0, 1]^N, \emptyset)\} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // set of local bounds and learners for open subproblems </li><br />
<li> <math> U ← \infty, L^∗ ← \emptyset </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Upper bound on optimal objective </li><br />
<li> '''while''' <math>\ T \neq \emptyset </math> '''do''' </li><br />
<li> &emsp; Choose and remove <math>(B,L) </math> from <math>T </math> </li><br />
<li> &emsp; '''repeat''' </li><br />
<li> &emsp; &emsp; Solve the primal IP using the local bounds on <math> z </math> in <math>B</math> with optimal dual solution <math> (w^∗, v^∗, u^∗) </math> </li><br />
<li> &emsp; &emsp; Find learner <math> h_j ∈ Ω </math> satisfying the pricing problem. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Solve pricing problem. </li><br />
<li> &emsp; '''until''' <math> h_j </math> is not found </li> <br />
<li> &emsp; Let <math> (\widetilde{λ} , \widetilde{z}) </math> be the final solution of the primal IP with base learners <math> \widetilde{L} = \{j | \widetilde{λ}_j > 0\} </math> </li><br />
<li> &emsp; '''if''' <math> \widetilde{z} ∈ \mathbb{Z}^N </math> and <math> \sum^{N}_{i=1}\widetilde{z}_i < U </math> '''then''' </li><br />
<li> &emsp; &emsp; <math> U ← \sum^{N}_{i=1}\widetilde{z}_i, L^∗ ← \widetilde{L}, λ^∗ ← \widetilde{\lambda} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Update best solution. </li><br />
<li> &emsp; '''else''' </li><br />
<li> &emsp; &emsp; Choose <math> i ∈ [N] </math> with <math> \widetilde{z}_i \notin Z </math> </li><br />
<li> &emsp; &emsp; Set <math> B_0 ← B ∩ \{z_i ≤ 0\}, B_1 ← B ∩ \{z_i ≥ 1\} </math> </li><br />
<li> &emsp; &emsp; Add <math> (B_0,\widetilde{L}), (B_1,\widetilde{L}) </math> to <math> T </math>. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Create new branching nodes. </li><br />
<li> &emsp; '''end''' if </li><br />
<li> '''end''' while </li><br />
<li> ''Optionally sparsify final solution <math>L^*</math>'' </li><br />
<br />
</ol><br />
</div><br />
<br />
===Sparsification===<br />
<br />
When building the boosting model, one of the challenges is to balance model accuracy and generalization. In order to control complexity, overfitting, and generalization of the model, typically some sparsity is applied, which is easier to interpret for some applications. There are two techniques commonly used. One is early stopping, another is regularization by adding a complexity term for the learners in the objective function. Previous approaches in the context of LP-based boosting have promoted sparsity by means of cutting planes. Sparsification can be handled in the approach introduced in this paper by solving a delayed integer program using additional cutting planes.<br />
<br />
== Results and Performance ==<br />
<br />
''All tests were run on identical Linux clusters with Intel Xeon Quad Core CPUs, with 3.50GHz, 10 MB cache, and 32 GB of main memory.''<br />
<br />
<br />
The following results reflect IPBoost's performance in hard instances. Note that by hard instances, we mean a binary classification problem with predefined labels. These examples are tailored to using the ±1 classification from learners. On every hard instance sample, IPBoost significantly outperforms both LPBoost and AdaBoost (although implementations depending on the libraries used have often caused results to differ slightly). For the considered instances the best value for the margin ρ was 0.05 for LPBoost and IPBoost; AdaBoost has no margin parameter. The accuracy reported is test accuracy recorded across various different walkthroughs of the algorithm, while <math>L </math> denotes the aggregate number of learners required to find the optimal learner, N is the number of points and <math> \gamma </math> refers to the noise level.<br />
<br />
[[File:ipboostres.png|center]]<br />
<br />
<br />
<br />
For the next table, the classification instances from LIBSVM data sets available at [https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/]. We report accuracies on the test set and train set, respectively. In each case, we report the averages of the accuracies over 10 runs with a different random seed and their standard deviations. We can see IPboost again outperforming LPBoost and AdaBoost significantly. Solving Integer Programming problems is no doubt more computationally expensive than traditional boosting methods like AdaBoost. The average run time of IPBoost (for ρ = 0.05) being 1367.78 seconds, as opposed to LPBoost's 164.35 seconds and AdaBoost's 3.59 seconds reflects exactly that. However, on the flip side, we gain much better stability in our results, as well as higher scores across the board for both training and test sets.<br />
<br />
[[file:svmlibres.png|center]]<br />
<br />
<br />
== Conclusion ==<br />
<br />
IP-boosting avoids the bad performance on well-known hard classes and improves upon LP-boosting and AdaBoost on the LIBSVM instances where even a few percent improvements is valuable. The major drawback is that the running time with the current implementation is much longer. Nevertheless, the algorithm can be improved in the future by solving the intermediate LPs only approximately and deriving tailored heuristics that generate decent primal solutions to save on time.<br />
<br />
The approach is suited very well to an offline setting in which training may take time and where even a small improvement is beneficial or when convex boosters have egregious behaviour. It can also be served as a tool to investigate the general performance of methods like this.<br />
<br />
The IPBoost algorithm added extra complexity into basic boosting models to gain slight accuracy gain while greatly increased the time spent. It is 381 times slower compared to an AdaBoost model on a small dataset which makes the actual usage of this model doubtable. If we are supplied with a larger dataset with millions of records this model would take too long to complete. The base classifier choice was XGBoost which is too complicated for a base classifier, maybe try some weaker learners such as tree stumps to compare the result with other models. In addition, this model might not be accurate compared to the model-ensembling technique where each model utilizes a different algorithm.<br />
<br />
I think IP Boost can be helpful in cases where a small improvement in accuracy is worth the additional computational effort involved. For example,there are applications in Finance where predicting the movement of stock prices slightly more accurately can help traders make millions more. In such cases, investing in expensive computing systems to implement such boosting techniques can perhaps be justified.<br />
<br />
== Critique ==<br />
<br />
In practise AdaBoost & LP Boost are quite robust to over fitting. In practise if you use simple weak learns stumps (1-level decision trees) then the algorithms are much less prone to over fitting. However the noise level in the data, particularly for AdaBoost is prone to overfitting on noisy datasets. To avoid this use regularised models (AdaBoostReg, LPBoost). Further, when in higher dimensional spaces, AdaBoost can suffer, since its just a linear combination of classifiers. You can use k-fold cross validation to set the stopping parameter to improve this.<br />
<br />
== References ==<br />
<br />
* Pfetsch, M. E., & Pokutta, S. (2020). IPBoost--Non-Convex Boosting via Integer Programming. arXiv preprint arXiv:2002.04679.<br />
<br />
* Freund, Y., & Schapire, R. E. (1995, March). A desicion-theoretic generalization of on-line learning and an application to boosting. In European conference on computational learning theory (pp. 23-37). Springer, Berlin, Heidelberg. pdf</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost&diff=46080IPBoost2020-11-23T17:32:46Z<p>Q58yu: /* Sparsification */</p>
<hr />
<div>== Presented by == <br />
Casey De Vera, Solaiman Jawad<br />
<br />
== Introduction == <br />
Boosting is an important and a fairly standard technique in classification that combines several base learners (learners which have a “low accuracy”), into one boosted learner (learner with a “high accuracy”). Pioneered by the AdaBoost approach of Freund & Schapire, in recent decades there has been extensive work on boosting procedures and analyses of their limitations.<br />
<br />
In a nutshell, boosting procedures are (typically) iterative schemes that roughly work as follows:<br />
<br />
Let <math>T</math> represents the number of iteration and <math>t</math> represents the iterator. <br />
<br />
for <math> t= 1, \cdots, T </math> do the following:<br />
<br />
::1. Train a learner <math> \mu_t</math> from a given class of base learners on the data distribution <math> \mathcal D_t</math><br />
<br />
::2. Evaluate the performance of <math> \mu_t</math> by computing its loss.<br />
<br />
::3. Push weight of the data distribution <math> \mathcal D_t</math> towards the misclassified examples leading to <math> \mathcal D_{t+1}</math>, usually a relatively good model will have a higher weight on those data that misclassified.<br />
<br />
Finally, the learners are combined with some form of voting (e.g., soft or hard voting, averaging, thresholding).<br />
<br />
<br />
[[File:boosting.gif|200px|thumb|right]] A close inspection of most boosting procedures reveals that they solve an underlying convex optimization problem over a convex loss function by means of coordinate gradient descent. Boosting schemes of this type are often referred to as '''convex potential boosters'''. These procedures can achieve exceptional performance on many data sets if the data is correctly labeled. However, they can be defeated easily by a small amount of incorrect labels which can be quite difficult to fix. The reason being is that we try to solve misclassified examples by moving the weights around, which results in bad performance on unseen data (Shown by zoomed example to the right). In fact, in theory, provided the class of base learners is rich enough, a perfect strong learner can be constructed that has accuracy 1, however, clearly, such a learner might not necessarily generalize well. Boosted learners can generate some quite complicated decision boundaries, much more complicated than that of the base learners. Here is an example from Paul van der Laken’s blog / Extreme gradient boosting gif by Ryan Holbrook. Here data is generated online according to some process with optimal decision boundary represented by the dotted line and XGBoost was used to learn a classifier:<br />
<br />
<br />
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper, we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumventing shortcomings of convex boosting approaches. The paper reports results that are comparable to or better than current state-of-the-art approaches.<br />
<br />
== Motivation ==<br />
<br />
In reality, we usually face unclean data and so-called label noise, where some percentage of the classification labels might be corrupted. We would also like to construct strong learners for such data. Noisy labels are an issue because when a model is trained with excessive amounts of noisy labels, the performance and accuracy deteriorates greatly. However, if we revisit the general boosting template from above, then we might suspect that we run into trouble as soon as a certain fraction of training examples is misclassified: in this case, these examples cannot be correctly classified and the procedure shifts more and more weight towards these bad examples. This eventually leads to a strong learner, that perfectly predicts the (flawed) training data; however, that does not generalize well anymore. This intuition has been formalized by [LS] who construct a “hard” training data distribution, where a small percentage of labels is randomly flipped. This label noise then leads to a significant reduction in performance of these boosted learners; see tables below. The more technical reason for this problem is actually the convexity of the loss function that is minimized by the boosting procedure. Clearly, one can use all types of “tricks” such as early stopping but at the end of the day, this is not solving the fundamental problem.<br />
<br />
== IPBoost: Boosting via Integer Programming ==<br />
<br />
<br />
===Integer Program Formulation===<br />
Let <math>(x_1,y_1),\cdots, (x_N,y_N) </math> be the training set with points <math>x_i \in \mathbb{R}^d</math> and two-class labels <math>y_i \in \{\pm 1\}</math> <br />
* class of base learners: <math> \Omega :=\{h_1, \cdots, h_L: \mathbb{R}^d \rightarrow \{\pm 1\}\} </math> and <math>\rho \ge 0</math> be given. <br />
* error function <math> \eta </math><br />
Our boosting model is captured by the integer programming problem. We can call this our primal problem: <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j=1}^L \eta_{ij}\lambda_k+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i=1,\cdots, N \\ <br />
&\sum_{j=1}^L \lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
For the error function <math>\eta</math>, three options were considered:<br />
<br />
(i) <math> \pm 1 </math> classification from learners<br />
$$ \eta_{ij} := 2\mathbb{I}[h_j(x_i) = y_i] - 1 = y_i \cdot h_j(x_i) $$<br />
(ii) class probabilities of learners<br />
$$ \eta_{ij} := 2\mathbb{P}[h_j(x_i) = y_i] - 1$$<br />
(iii) SAMME.R error function for learners<br />
$$ \frac{1}{2}y_i\log\left(\frac{\mathbb{P}[h_j(x_i) = 1]}{\mathbb{P}[h_j(x_i) = -1]}\right)$$<br />
<br />
===Solution of the IP using Column Generation===<br />
<br />
The goal of column generation is to provide an efficient way to solve the linear programming relaxation of the primal by allowing the <math>z_i </math> variables to assume fractional values. Moreover, columns, i.e., the base learners, <math> \mathcal L \subseteq [L]. </math> are left out because there are too many to handle efficiently and most of them will have their associated weight equal to zero in the optimal solution anyway. To generate columns, a <i>branch and bound</i> framework is used. Columns are generated within a<br />
branch-and-bound framework leading effectively to a branch-and-bound-and-price algorithm being used; this is significantly more involved compared to column generation in linear programming. To check the optimality of an LP solution, a subproblem, called the pricing problem, is solved to try to identify columns with a profitable reduced cost. If such columns are found, the LP is re-optimized. Branching occurs when no profitable columns are found, but the LP solution does not satisfy the integrality conditions. Branch and price apply column generation at every node of the branch and bound tree.<br />
<br />
The restricted master primal problem is <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j\in \mathcal L} \eta_{ij}\lambda_j+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i \in [N]\\ <br />
&\sum_{j\in \mathcal L}\lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
<br />
Its restricted dual problem is:<br />
<br />
$$ \begin{align*}\max \rho &\sum^{N}_{i=1}w_i + v - \sum^{N}_{i=1}u_i<br />
\\ s.t. &\sum_{i=1}^N \eta_{ij}w_k+ v \le 0 \ \ \ \forall j \in L \\ <br />
&(1+\rho)w_i - u_i \le 1 \ \ \ \forall i \in [N] \\ &w \ge 0, u \ge 0, v\ free\end{align*}$$<br />
<br />
Furthermore, there is a pricing problem used to determine, for every supposed optimal solution of the dual, whether the solution is actually optimal, or whether further constraints need to be added into the primal solution. With this pricing problem, we check whether the solution to the restricted dual is feasible. This pricing problem can be expressed as follows:<br />
<br />
$$ \sum_{i=1}^N \eta_{ij}w_k^* + v^* > 0 $$<br />
<br />
The optimal misclassification values are determined by a branch-and-price process that branches on the variables <math> z_i </math> and solves the intermediate LPs using column generation.<br />
<br />
===Algorithm===<br />
<div style="margin-left: 3em;"><br />
<math> D = \{(x_i, y_i) | i ∈ I\} ⊆ R^d × \{±1\} </math>, class of base learners <math>Ω </math>, margin <math> \rho </math> <br><br />
'''Output:''' Boosted learner <math> \sum_{j∈L^∗}h_jλ_j^* </math> with base learners <math> h_j </math> and weights <math> λ_j^* </math> <br><br />
<br />
<ol><br />
<br />
<li margin-left:30px> <math> T ← \{([0, 1]^N, \emptyset)\} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // set of local bounds and learners for open subproblems </li><br />
<li> <math> U ← \infty, L^∗ ← \emptyset </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Upper bound on optimal objective </li><br />
<li> '''while''' <math>\ T \neq \emptyset </math> '''do''' </li><br />
<li> &emsp; Choose and remove <math>(B,L) </math> from <math>T </math> </li><br />
<li> &emsp; '''repeat''' </li><br />
<li> &emsp; &emsp; Solve the primal IP using the local bounds on <math> z </math> in <math>B</math> with optimal dual solution <math> (w^∗, v^∗, u^∗) </math> </li><br />
<li> &emsp; &emsp; Find learner <math> h_j ∈ Ω </math> satisfying the pricing problem. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Solve pricing problem. </li><br />
<li> &emsp; '''until''' <math> h_j </math> is not found </li> <br />
<li> &emsp; Let <math> (\widetilde{λ} , \widetilde{z}) </math> be the final solution of the primal IP with base learners <math> \widetilde{L} = \{j | \widetilde{λ}_j > 0\} </math> </li><br />
<li> &emsp; '''if''' <math> \widetilde{z} ∈ \mathbb{Z}^N </math> and <math> \sum^{N}_{i=1}\widetilde{z}_i < U </math> '''then''' </li><br />
<li> &emsp; &emsp; <math> U ← \sum^{N}_{i=1}\widetilde{z}_i, L^∗ ← \widetilde{L}, λ^∗ ← \widetilde{\lambda} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Update best solution. </li><br />
<li> &emsp; '''else''' </li><br />
<li> &emsp; &emsp; Choose <math> i ∈ [N] </math> with <math> \widetilde{z}_i \notin Z </math> </li><br />
<li> &emsp; &emsp; Set <math> B_0 ← B ∩ \{z_i ≤ 0\}, B_1 ← B ∩ \{z_i ≥ 1\} </math> </li><br />
<li> &emsp; &emsp; Add <math> (B_0,\widetilde{L}), (B_1,\widetilde{L}) </math> to <math> T </math>. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Create new branching nodes. </li><br />
<li> &emsp; '''end''' if </li><br />
<li> '''end''' while </li><br />
<li> ''Optionally sparsify final solution <math>L^*</math>'' </li><br />
<br />
</ol><br />
</div><br />
<br />
===Sparsification===<br />
<br />
When building the boosting model, one of the challenges is to balance model accuracy and generalization. In order to control complexity, overfitting, and generalization of the model, typically some sparsity is applied, which is easier to interpret for some applications. There are two techniques commonly used. One is early stopping, another is regularization by adding a complexity term for the learners in the objective function. Previous approaches in the context of LP-based boosting have promoted sparsity by means of cutting planes. Sparsification can be handled in the approach introduced in this paper by solving a delayed integer program using additional cutting planes.<br />
<br />
== Results and Performance ==<br />
<br />
''All tests were run on identical Linux clusters with Intel Xeon Quad Core CPUs, with 3.50GHz, 10 MB cache, and 32 GB of main memory.''<br />
<br />
<br />
The following results reflect IPBoost's performance in hard instances. Note that by hard instances, we mean a binary classification problem with predefined labels. These examples are tailored to using the ±1 classification from learners. On every hard instance sample, IPBoost significantly outperforms both LPBoost and AdaBoost (although implementations depending on the libraries used have often caused results to differ slightly). For the considered instances the best value for the margin ρ was 0.05 for LPBoost and IPBoost; AdaBoost has no margin parameter. The accuracy reported is test accuracy recorded across various different walkthroughs of the algorithm, while <math>L </math> denotes the aggregate number of learners required to find the optimal learner, N is the number of points and <math> \gamma </math> refers to the noise level.<br />
<br />
[[File:ipboostres.png|center]]<br />
<br />
<br />
<br />
For the next table, the classification instances from LIBSVM data sets available at [https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/]. We report accuracies on the test set and train set, respectively. In each case, we report the averages of the accuracies over 10 runs with a different random seed and their standard deviations. We can see IPboost again outperforming LPBoost and AdaBoost significantly. Solving Integer Programming problems is no doubt more computationally expensive than traditional boosting methods like AdaBoost. The average run time of IPBoost (for ρ = 0.05) being 1367.78 seconds, as opposed to LPBoost's 164.35 seconds and AdaBoost's 3.59 seconds reflects exactly that. However, on the flip side, we gain much better stability in our results, as well as higher scores across the board for both training and test sets.<br />
<br />
[[file:svmlibres.png|center]]<br />
<br />
<br />
== Conclusion ==<br />
<br />
IP-boosting avoids the bad performance on well-known hard classes and improves upon LP-boosting and AdaBoost on the LIBSVM instances where even a few percent improvements is valuable. The major drawback is that the running time with the current implementation is much longer. Nevertheless, the algorithm can be improved in the future by solving the intermediate LPs only approximately and deriving tailored heuristics that generate decent primal solutions to save on time.<br />
<br />
The approach is suited very well to an offline setting in which training may take time and where even a small improvement is beneficial or when convex boosters have egregious behaviour. It can also be served as a tool to investigate the general performance of methods like this.<br />
<br />
The IPBoost algorithm added extra complexity into basic boosting models to gain slight accuracy gain while greatly increased the time spent. It is 381 times slower compared to an AdaBoost model on a small dataset which makes the actual usage of this model doubtable. If we are supplied with a larger dataset with millions of records this model would take too long to complete. The base classifier choice was XGBoost which is too complicated for a base classifier, maybe try some weaker learners such as tree stumps to compare the result with other models. In addition, this model might not be accurate compared to the model-ensembling technique where each model utilizes a different algorithm.<br />
<br />
I think IP Boost can be helpful in cases where a small improvement in accuracy is worth the additional computational effort involved. For example,there are applications in Finance where predicting the movement of stock prices slightly more accurately can help traders make millions more. In such cases, investing in expensive computing systems to implement such boosting techniques can perhaps be justified.<br />
<br />
== Critique ==<br />
<br />
In practise AdaBoost & LP Boost are quite robust to over fitting. In practise if you use simple weak learns stumps (1-level decision trees) then the algorithms are much less prone to over fitting. However the noise level in the data, particularly for AdaBoost is prone to overfitting on noisy datasets. To avoid this use regularised models (AdaBoostReg, LPBoost). Further, when in higher dimensional spaces, AdaBoost can suffer, since its just a linear combination of classifiers. You can use k-fold cross validation to set the stopping parameter to improve this.<br />
<br />
== References ==<br />
<br />
* Pfetsch, M. E., & Pokutta, S. (2020). IPBoost--Non-Convex Boosting via Integer Programming. arXiv preprint arXiv:2002.04679.<br />
<br />
* Freund, Y., & Schapire, R. E. (1995, March). A desicion-theoretic generalization of on-line learning and an application to boosting. In European conference on computational learning theory (pp. 23-37). Springer, Berlin, Heidelberg. pdf</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost&diff=46079IPBoost2020-11-23T17:31:53Z<p>Q58yu: /* Sparsification */</p>
<hr />
<div>== Presented by == <br />
Casey De Vera, Solaiman Jawad<br />
<br />
== Introduction == <br />
Boosting is an important and a fairly standard technique in classification that combines several base learners (learners which have a “low accuracy”), into one boosted learner (learner with a “high accuracy”). Pioneered by the AdaBoost approach of Freund & Schapire, in recent decades there has been extensive work on boosting procedures and analyses of their limitations.<br />
<br />
In a nutshell, boosting procedures are (typically) iterative schemes that roughly work as follows:<br />
<br />
Let <math>T</math> represents the number of iteration and <math>t</math> represents the iterator. <br />
<br />
for <math> t= 1, \cdots, T </math> do the following:<br />
<br />
::1. Train a learner <math> \mu_t</math> from a given class of base learners on the data distribution <math> \mathcal D_t</math><br />
<br />
::2. Evaluate the performance of <math> \mu_t</math> by computing its loss.<br />
<br />
::3. Push weight of the data distribution <math> \mathcal D_t</math> towards the misclassified examples leading to <math> \mathcal D_{t+1}</math>, usually a relatively good model will have a higher weight on those data that misclassified.<br />
<br />
Finally, the learners are combined with some form of voting (e.g., soft or hard voting, averaging, thresholding).<br />
<br />
<br />
[[File:boosting.gif|200px|thumb|right]] A close inspection of most boosting procedures reveals that they solve an underlying convex optimization problem over a convex loss function by means of coordinate gradient descent. Boosting schemes of this type are often referred to as '''convex potential boosters'''. These procedures can achieve exceptional performance on many data sets if the data is correctly labeled. However, they can be defeated easily by a small amount of incorrect labels which can be quite difficult to fix. The reason being is that we try to solve misclassified examples by moving the weights around, which results in bad performance on unseen data (Shown by zoomed example to the right). In fact, in theory, provided the class of base learners is rich enough, a perfect strong learner can be constructed that has accuracy 1, however, clearly, such a learner might not necessarily generalize well. Boosted learners can generate some quite complicated decision boundaries, much more complicated than that of the base learners. Here is an example from Paul van der Laken’s blog / Extreme gradient boosting gif by Ryan Holbrook. Here data is generated online according to some process with optimal decision boundary represented by the dotted line and XGBoost was used to learn a classifier:<br />
<br />
<br />
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper, we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumventing shortcomings of convex boosting approaches. The paper reports results that are comparable to or better than current state-of-the-art approaches.<br />
<br />
== Motivation ==<br />
<br />
In reality, we usually face unclean data and so-called label noise, where some percentage of the classification labels might be corrupted. We would also like to construct strong learners for such data. Noisy labels are an issue because when a model is trained with excessive amounts of noisy labels, the performance and accuracy deteriorates greatly. However, if we revisit the general boosting template from above, then we might suspect that we run into trouble as soon as a certain fraction of training examples is misclassified: in this case, these examples cannot be correctly classified and the procedure shifts more and more weight towards these bad examples. This eventually leads to a strong learner, that perfectly predicts the (flawed) training data; however, that does not generalize well anymore. This intuition has been formalized by [LS] who construct a “hard” training data distribution, where a small percentage of labels is randomly flipped. This label noise then leads to a significant reduction in performance of these boosted learners; see tables below. The more technical reason for this problem is actually the convexity of the loss function that is minimized by the boosting procedure. Clearly, one can use all types of “tricks” such as early stopping but at the end of the day, this is not solving the fundamental problem.<br />
<br />
== IPBoost: Boosting via Integer Programming ==<br />
<br />
<br />
===Integer Program Formulation===<br />
Let <math>(x_1,y_1),\cdots, (x_N,y_N) </math> be the training set with points <math>x_i \in \mathbb{R}^d</math> and two-class labels <math>y_i \in \{\pm 1\}</math> <br />
* class of base learners: <math> \Omega :=\{h_1, \cdots, h_L: \mathbb{R}^d \rightarrow \{\pm 1\}\} </math> and <math>\rho \ge 0</math> be given. <br />
* error function <math> \eta </math><br />
Our boosting model is captured by the integer programming problem. We can call this our primal problem: <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j=1}^L \eta_{ij}\lambda_k+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i=1,\cdots, N \\ <br />
&\sum_{j=1}^L \lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
For the error function <math>\eta</math>, three options were considered:<br />
<br />
(i) <math> \pm 1 </math> classification from learners<br />
$$ \eta_{ij} := 2\mathbb{I}[h_j(x_i) = y_i] - 1 = y_i \cdot h_j(x_i) $$<br />
(ii) class probabilities of learners<br />
$$ \eta_{ij} := 2\mathbb{P}[h_j(x_i) = y_i] - 1$$<br />
(iii) SAMME.R error function for learners<br />
$$ \frac{1}{2}y_i\log\left(\frac{\mathbb{P}[h_j(x_i) = 1]}{\mathbb{P}[h_j(x_i) = -1]}\right)$$<br />
<br />
===Solution of the IP using Column Generation===<br />
<br />
The goal of column generation is to provide an efficient way to solve the linear programming relaxation of the primal by allowing the <math>z_i </math> variables to assume fractional values. Moreover, columns, i.e., the base learners, <math> \mathcal L \subseteq [L]. </math> are left out because there are too many to handle efficiently and most of them will have their associated weight equal to zero in the optimal solution anyway. To generate columns, a <i>branch and bound</i> framework is used. Columns are generated within a<br />
branch-and-bound framework leading effectively to a branch-and-bound-and-price algorithm being used; this is significantly more involved compared to column generation in linear programming. To check the optimality of an LP solution, a subproblem, called the pricing problem, is solved to try to identify columns with a profitable reduced cost. If such columns are found, the LP is re-optimized. Branching occurs when no profitable columns are found, but the LP solution does not satisfy the integrality conditions. Branch and price apply column generation at every node of the branch and bound tree.<br />
<br />
The restricted master primal problem is <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j\in \mathcal L} \eta_{ij}\lambda_j+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i \in [N]\\ <br />
&\sum_{j\in \mathcal L}\lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
<br />
Its restricted dual problem is:<br />
<br />
$$ \begin{align*}\max \rho &\sum^{N}_{i=1}w_i + v - \sum^{N}_{i=1}u_i<br />
\\ s.t. &\sum_{i=1}^N \eta_{ij}w_k+ v \le 0 \ \ \ \forall j \in L \\ <br />
&(1+\rho)w_i - u_i \le 1 \ \ \ \forall i \in [N] \\ &w \ge 0, u \ge 0, v\ free\end{align*}$$<br />
<br />
Furthermore, there is a pricing problem used to determine, for every supposed optimal solution of the dual, whether the solution is actually optimal, or whether further constraints need to be added into the primal solution. With this pricing problem, we check whether the solution to the restricted dual is feasible. This pricing problem can be expressed as follows:<br />
<br />
$$ \sum_{i=1}^N \eta_{ij}w_k^* + v^* > 0 $$<br />
<br />
The optimal misclassification values are determined by a branch-and-price process that branches on the variables <math> z_i </math> and solves the intermediate LPs using column generation.<br />
<br />
===Algorithm===<br />
<div style="margin-left: 3em;"><br />
<math> D = \{(x_i, y_i) | i ∈ I\} ⊆ R^d × \{±1\} </math>, class of base learners <math>Ω </math>, margin <math> \rho </math> <br><br />
'''Output:''' Boosted learner <math> \sum_{j∈L^∗}h_jλ_j^* </math> with base learners <math> h_j </math> and weights <math> λ_j^* </math> <br><br />
<br />
<ol><br />
<br />
<li margin-left:30px> <math> T ← \{([0, 1]^N, \emptyset)\} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // set of local bounds and learners for open subproblems </li><br />
<li> <math> U ← \infty, L^∗ ← \emptyset </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Upper bound on optimal objective </li><br />
<li> '''while''' <math>\ T \neq \emptyset </math> '''do''' </li><br />
<li> &emsp; Choose and remove <math>(B,L) </math> from <math>T </math> </li><br />
<li> &emsp; '''repeat''' </li><br />
<li> &emsp; &emsp; Solve the primal IP using the local bounds on <math> z </math> in <math>B</math> with optimal dual solution <math> (w^∗, v^∗, u^∗) </math> </li><br />
<li> &emsp; &emsp; Find learner <math> h_j ∈ Ω </math> satisfying the pricing problem. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Solve pricing problem. </li><br />
<li> &emsp; '''until''' <math> h_j </math> is not found </li> <br />
<li> &emsp; Let <math> (\widetilde{λ} , \widetilde{z}) </math> be the final solution of the primal IP with base learners <math> \widetilde{L} = \{j | \widetilde{λ}_j > 0\} </math> </li><br />
<li> &emsp; '''if''' <math> \widetilde{z} ∈ \mathbb{Z}^N </math> and <math> \sum^{N}_{i=1}\widetilde{z}_i < U </math> '''then''' </li><br />
<li> &emsp; &emsp; <math> U ← \sum^{N}_{i=1}\widetilde{z}_i, L^∗ ← \widetilde{L}, λ^∗ ← \widetilde{\lambda} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Update best solution. </li><br />
<li> &emsp; '''else''' </li><br />
<li> &emsp; &emsp; Choose <math> i ∈ [N] </math> with <math> \widetilde{z}_i \notin Z </math> </li><br />
<li> &emsp; &emsp; Set <math> B_0 ← B ∩ \{z_i ≤ 0\}, B_1 ← B ∩ \{z_i ≥ 1\} </math> </li><br />
<li> &emsp; &emsp; Add <math> (B_0,\widetilde{L}), (B_1,\widetilde{L}) </math> to <math> T </math>. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Create new branching nodes. </li><br />
<li> &emsp; '''end''' if </li><br />
<li> '''end''' while </li><br />
<li> ''Optionally sparsify final solution <math>L^*</math>'' </li><br />
<br />
</ol><br />
</div><br />
<br />
===Sparsification===<br />
<br />
When building the boosting model, one of the challenges is to balance model accuracy and generalization. In order to control complexity, overfitting, and generalization of the model, typically some sparsity is enforced, which is easier to interpret for some applications. There are two techniques commonly applied. One is early stopping, another is regularization by adding a complexity term for the learners in the objective function. Previous approaches in the context of LP-based boosting have promoted sparsity by means of cutting planes. Sparsification can be handled in the approach introduced in this paper by solving a delayed integer program using additional cutting planes.<br />
<br />
== Results and Performance ==<br />
<br />
''All tests were run on identical Linux clusters with Intel Xeon Quad Core CPUs, with 3.50GHz, 10 MB cache, and 32 GB of main memory.''<br />
<br />
<br />
The following results reflect IPBoost's performance in hard instances. Note that by hard instances, we mean a binary classification problem with predefined labels. These examples are tailored to using the ±1 classification from learners. On every hard instance sample, IPBoost significantly outperforms both LPBoost and AdaBoost (although implementations depending on the libraries used have often caused results to differ slightly). For the considered instances the best value for the margin ρ was 0.05 for LPBoost and IPBoost; AdaBoost has no margin parameter. The accuracy reported is test accuracy recorded across various different walkthroughs of the algorithm, while <math>L </math> denotes the aggregate number of learners required to find the optimal learner, N is the number of points and <math> \gamma </math> refers to the noise level.<br />
<br />
[[File:ipboostres.png|center]]<br />
<br />
<br />
<br />
For the next table, the classification instances from LIBSVM data sets available at [https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/]. We report accuracies on the test set and train set, respectively. In each case, we report the averages of the accuracies over 10 runs with a different random seed and their standard deviations. We can see IPboost again outperforming LPBoost and AdaBoost significantly. Solving Integer Programming problems is no doubt more computationally expensive than traditional boosting methods like AdaBoost. The average run time of IPBoost (for ρ = 0.05) being 1367.78 seconds, as opposed to LPBoost's 164.35 seconds and AdaBoost's 3.59 seconds reflects exactly that. However, on the flip side, we gain much better stability in our results, as well as higher scores across the board for both training and test sets.<br />
<br />
[[file:svmlibres.png|center]]<br />
<br />
<br />
== Conclusion ==<br />
<br />
IP-boosting avoids the bad performance on well-known hard classes and improves upon LP-boosting and AdaBoost on the LIBSVM instances where even a few percent improvements is valuable. The major drawback is that the running time with the current implementation is much longer. Nevertheless, the algorithm can be improved in the future by solving the intermediate LPs only approximately and deriving tailored heuristics that generate decent primal solutions to save on time.<br />
<br />
The approach is suited very well to an offline setting in which training may take time and where even a small improvement is beneficial or when convex boosters have egregious behaviour. It can also be served as a tool to investigate the general performance of methods like this.<br />
<br />
The IPBoost algorithm added extra complexity into basic boosting models to gain slight accuracy gain while greatly increased the time spent. It is 381 times slower compared to an AdaBoost model on a small dataset which makes the actual usage of this model doubtable. If we are supplied with a larger dataset with millions of records this model would take too long to complete. The base classifier choice was XGBoost which is too complicated for a base classifier, maybe try some weaker learners such as tree stumps to compare the result with other models. In addition, this model might not be accurate compared to the model-ensembling technique where each model utilizes a different algorithm.<br />
<br />
I think IP Boost can be helpful in cases where a small improvement in accuracy is worth the additional computational effort involved. For example,there are applications in Finance where predicting the movement of stock prices slightly more accurately can help traders make millions more. In such cases, investing in expensive computing systems to implement such boosting techniques can perhaps be justified.<br />
<br />
== Critique ==<br />
<br />
In practise AdaBoost & LP Boost are quite robust to over fitting. In practise if you use simple weak learns stumps (1-level decision trees) then the algorithms are much less prone to over fitting. However the noise level in the data, particularly for AdaBoost is prone to overfitting on noisy datasets. To avoid this use regularised models (AdaBoostReg, LPBoost). Further, when in higher dimensional spaces, AdaBoost can suffer, since its just a linear combination of classifiers. You can use k-fold cross validation to set the stopping parameter to improve this.<br />
<br />
== References ==<br />
<br />
* Pfetsch, M. E., & Pokutta, S. (2020). IPBoost--Non-Convex Boosting via Integer Programming. arXiv preprint arXiv:2002.04679.<br />
<br />
* Freund, Y., & Schapire, R. E. (1995, March). A desicion-theoretic generalization of on-line learning and an application to boosting. In European conference on computational learning theory (pp. 23-37). Springer, Berlin, Heidelberg. pdf</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost&diff=46078IPBoost2020-11-23T17:25:02Z<p>Q58yu: /* Sparsification */</p>
<hr />
<div>== Presented by == <br />
Casey De Vera, Solaiman Jawad<br />
<br />
== Introduction == <br />
Boosting is an important and a fairly standard technique in classification that combines several base learners (learners which have a “low accuracy”), into one boosted learner (learner with a “high accuracy”). Pioneered by the AdaBoost approach of Freund & Schapire, in recent decades there has been extensive work on boosting procedures and analyses of their limitations.<br />
<br />
In a nutshell, boosting procedures are (typically) iterative schemes that roughly work as follows:<br />
<br />
Let <math>T</math> represents the number of iteration and <math>t</math> represents the iterator. <br />
<br />
for <math> t= 1, \cdots, T </math> do the following:<br />
<br />
::1. Train a learner <math> \mu_t</math> from a given class of base learners on the data distribution <math> \mathcal D_t</math><br />
<br />
::2. Evaluate the performance of <math> \mu_t</math> by computing its loss.<br />
<br />
::3. Push weight of the data distribution <math> \mathcal D_t</math> towards the misclassified examples leading to <math> \mathcal D_{t+1}</math>, usually a relatively good model will have a higher weight on those data that misclassified.<br />
<br />
Finally, the learners are combined with some form of voting (e.g., soft or hard voting, averaging, thresholding).<br />
<br />
<br />
[[File:boosting.gif|200px|thumb|right]] A close inspection of most boosting procedures reveals that they solve an underlying convex optimization problem over a convex loss function by means of coordinate gradient descent. Boosting schemes of this type are often referred to as '''convex potential boosters'''. These procedures can achieve exceptional performance on many data sets if the data is correctly labeled. However, they can be defeated easily by a small amount of incorrect labels which can be quite difficult to fix. The reason being is that we try to solve misclassified examples by moving the weights around, which results in bad performance on unseen data (Shown by zoomed example to the right). In fact, in theory, provided the class of base learners is rich enough, a perfect strong learner can be constructed that has accuracy 1, however, clearly, such a learner might not necessarily generalize well. Boosted learners can generate some quite complicated decision boundaries, much more complicated than that of the base learners. Here is an example from Paul van der Laken’s blog / Extreme gradient boosting gif by Ryan Holbrook. Here data is generated online according to some process with optimal decision boundary represented by the dotted line and XGBoost was used to learn a classifier:<br />
<br />
<br />
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper, we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumventing shortcomings of convex boosting approaches. The paper reports results that are comparable to or better than current state-of-the-art approaches.<br />
<br />
== Motivation ==<br />
<br />
In reality, we usually face unclean data and so-called label noise, where some percentage of the classification labels might be corrupted. We would also like to construct strong learners for such data. Noisy labels are an issue because when a model is trained with excessive amounts of noisy labels, the performance and accuracy deteriorates greatly. However, if we revisit the general boosting template from above, then we might suspect that we run into trouble as soon as a certain fraction of training examples is misclassified: in this case, these examples cannot be correctly classified and the procedure shifts more and more weight towards these bad examples. This eventually leads to a strong learner, that perfectly predicts the (flawed) training data; however, that does not generalize well anymore. This intuition has been formalized by [LS] who construct a “hard” training data distribution, where a small percentage of labels is randomly flipped. This label noise then leads to a significant reduction in performance of these boosted learners; see tables below. The more technical reason for this problem is actually the convexity of the loss function that is minimized by the boosting procedure. Clearly, one can use all types of “tricks” such as early stopping but at the end of the day, this is not solving the fundamental problem.<br />
<br />
== IPBoost: Boosting via Integer Programming ==<br />
<br />
<br />
===Integer Program Formulation===<br />
Let <math>(x_1,y_1),\cdots, (x_N,y_N) </math> be the training set with points <math>x_i \in \mathbb{R}^d</math> and two-class labels <math>y_i \in \{\pm 1\}</math> <br />
* class of base learners: <math> \Omega :=\{h_1, \cdots, h_L: \mathbb{R}^d \rightarrow \{\pm 1\}\} </math> and <math>\rho \ge 0</math> be given. <br />
* error function <math> \eta </math><br />
Our boosting model is captured by the integer programming problem. We can call this our primal problem: <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j=1}^L \eta_{ij}\lambda_k+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i=1,\cdots, N \\ <br />
&\sum_{j=1}^L \lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
For the error function <math>\eta</math>, three options were considered:<br />
<br />
(i) <math> \pm 1 </math> classification from learners<br />
$$ \eta_{ij} := 2\mathbb{I}[h_j(x_i) = y_i] - 1 = y_i \cdot h_j(x_i) $$<br />
(ii) class probabilities of learners<br />
$$ \eta_{ij} := 2\mathbb{P}[h_j(x_i) = y_i] - 1$$<br />
(iii) SAMME.R error function for learners<br />
$$ \frac{1}{2}y_i\log\left(\frac{\mathbb{P}[h_j(x_i) = 1]}{\mathbb{P}[h_j(x_i) = -1]}\right)$$<br />
<br />
===Solution of the IP using Column Generation===<br />
<br />
The goal of column generation is to provide an efficient way to solve the linear programming relaxation of the primal by allowing the <math>z_i </math> variables to assume fractional values. Moreover, columns, i.e., the base learners, <math> \mathcal L \subseteq [L]. </math> are left out because there are too many to handle efficiently and most of them will have their associated weight equal to zero in the optimal solution anyway. To generate columns, a <i>branch and bound</i> framework is used. Columns are generated within a<br />
branch-and-bound framework leading effectively to a branch-and-bound-and-price algorithm being used; this is significantly more involved compared to column generation in linear programming. To check the optimality of an LP solution, a subproblem, called the pricing problem, is solved to try to identify columns with a profitable reduced cost. If such columns are found, the LP is re-optimized. Branching occurs when no profitable columns are found, but the LP solution does not satisfy the integrality conditions. Branch and price apply column generation at every node of the branch and bound tree.<br />
<br />
The restricted master primal problem is <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j\in \mathcal L} \eta_{ij}\lambda_j+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i \in [N]\\ <br />
&\sum_{j\in \mathcal L}\lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
<br />
Its restricted dual problem is:<br />
<br />
$$ \begin{align*}\max \rho &\sum^{N}_{i=1}w_i + v - \sum^{N}_{i=1}u_i<br />
\\ s.t. &\sum_{i=1}^N \eta_{ij}w_k+ v \le 0 \ \ \ \forall j \in L \\ <br />
&(1+\rho)w_i - u_i \le 1 \ \ \ \forall i \in [N] \\ &w \ge 0, u \ge 0, v\ free\end{align*}$$<br />
<br />
Furthermore, there is a pricing problem used to determine, for every supposed optimal solution of the dual, whether the solution is actually optimal, or whether further constraints need to be added into the primal solution. With this pricing problem, we check whether the solution to the restricted dual is feasible. This pricing problem can be expressed as follows:<br />
<br />
$$ \sum_{i=1}^N \eta_{ij}w_k^* + v^* > 0 $$<br />
<br />
The optimal misclassification values are determined by a branch-and-price process that branches on the variables <math> z_i </math> and solves the intermediate LPs using column generation.<br />
<br />
===Algorithm===<br />
<div style="margin-left: 3em;"><br />
<math> D = \{(x_i, y_i) | i ∈ I\} ⊆ R^d × \{±1\} </math>, class of base learners <math>Ω </math>, margin <math> \rho </math> <br><br />
'''Output:''' Boosted learner <math> \sum_{j∈L^∗}h_jλ_j^* </math> with base learners <math> h_j </math> and weights <math> λ_j^* </math> <br><br />
<br />
<ol><br />
<br />
<li margin-left:30px> <math> T ← \{([0, 1]^N, \emptyset)\} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // set of local bounds and learners for open subproblems </li><br />
<li> <math> U ← \infty, L^∗ ← \emptyset </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Upper bound on optimal objective </li><br />
<li> '''while''' <math>\ T \neq \emptyset </math> '''do''' </li><br />
<li> &emsp; Choose and remove <math>(B,L) </math> from <math>T </math> </li><br />
<li> &emsp; '''repeat''' </li><br />
<li> &emsp; &emsp; Solve the primal IP using the local bounds on <math> z </math> in <math>B</math> with optimal dual solution <math> (w^∗, v^∗, u^∗) </math> </li><br />
<li> &emsp; &emsp; Find learner <math> h_j ∈ Ω </math> satisfying the pricing problem. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Solve pricing problem. </li><br />
<li> &emsp; '''until''' <math> h_j </math> is not found </li> <br />
<li> &emsp; Let <math> (\widetilde{λ} , \widetilde{z}) </math> be the final solution of the primal IP with base learners <math> \widetilde{L} = \{j | \widetilde{λ}_j > 0\} </math> </li><br />
<li> &emsp; '''if''' <math> \widetilde{z} ∈ \mathbb{Z}^N </math> and <math> \sum^{N}_{i=1}\widetilde{z}_i < U </math> '''then''' </li><br />
<li> &emsp; &emsp; <math> U ← \sum^{N}_{i=1}\widetilde{z}_i, L^∗ ← \widetilde{L}, λ^∗ ← \widetilde{\lambda} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Update best solution. </li><br />
<li> &emsp; '''else''' </li><br />
<li> &emsp; &emsp; Choose <math> i ∈ [N] </math> with <math> \widetilde{z}_i \notin Z </math> </li><br />
<li> &emsp; &emsp; Set <math> B_0 ← B ∩ \{z_i ≤ 0\}, B_1 ← B ∩ \{z_i ≥ 1\} </math> </li><br />
<li> &emsp; &emsp; Add <math> (B_0,\widetilde{L}), (B_1,\widetilde{L}) </math> to <math> T </math>. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Create new branching nodes. </li><br />
<li> &emsp; '''end''' if </li><br />
<li> '''end''' while </li><br />
<li> ''Optionally sparsify final solution <math>L^*</math>'' </li><br />
<br />
</ol><br />
</div><br />
<br />
===Sparsification===<br />
<br />
When building the boosting model, one of the challenges is to balance model accuracy and generalization. In order to control complexity, overfitting, and generalization of the model, typically some sparsity is enforced, which is easier to interpret for some applications. There are two techniques that can be applied. One is early stopping, another is regularization by adding a complexity term for the learners in the objective function. Previous approaches in the context of LP-based boosting have promoted sparsity by means of cutting planes. Sparsification can be handled in the approach introduced in this paper by solving a delayed integer program using additional cutting planes.<br />
<br />
== Results and Performance ==<br />
<br />
''All tests were run on identical Linux clusters with Intel Xeon Quad Core CPUs, with 3.50GHz, 10 MB cache, and 32 GB of main memory.''<br />
<br />
<br />
The following results reflect IPBoost's performance in hard instances. Note that by hard instances, we mean a binary classification problem with predefined labels. These examples are tailored to using the ±1 classification from learners. On every hard instance sample, IPBoost significantly outperforms both LPBoost and AdaBoost (although implementations depending on the libraries used have often caused results to differ slightly). For the considered instances the best value for the margin ρ was 0.05 for LPBoost and IPBoost; AdaBoost has no margin parameter. The accuracy reported is test accuracy recorded across various different walkthroughs of the algorithm, while <math>L </math> denotes the aggregate number of learners required to find the optimal learner, N is the number of points and <math> \gamma </math> refers to the noise level.<br />
<br />
[[File:ipboostres.png|center]]<br />
<br />
<br />
<br />
For the next table, the classification instances from LIBSVM data sets available at [https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/]. We report accuracies on the test set and train set, respectively. In each case, we report the averages of the accuracies over 10 runs with a different random seed and their standard deviations. We can see IPboost again outperforming LPBoost and AdaBoost significantly. Solving Integer Programming problems is no doubt more computationally expensive than traditional boosting methods like AdaBoost. The average run time of IPBoost (for ρ = 0.05) being 1367.78 seconds, as opposed to LPBoost's 164.35 seconds and AdaBoost's 3.59 seconds reflects exactly that. However, on the flip side, we gain much better stability in our results, as well as higher scores across the board for both training and test sets.<br />
<br />
[[file:svmlibres.png|center]]<br />
<br />
<br />
== Conclusion ==<br />
<br />
IP-boosting avoids the bad performance on well-known hard classes and improves upon LP-boosting and AdaBoost on the LIBSVM instances where even a few percent improvements is valuable. The major drawback is that the running time with the current implementation is much longer. Nevertheless, the algorithm can be improved in the future by solving the intermediate LPs only approximately and deriving tailored heuristics that generate decent primal solutions to save on time.<br />
<br />
The approach is suited very well to an offline setting in which training may take time and where even a small improvement is beneficial or when convex boosters have egregious behaviour. It can also be served as a tool to investigate the general performance of methods like this.<br />
<br />
The IPBoost algorithm added extra complexity into basic boosting models to gain slight accuracy gain while greatly increased the time spent. It is 381 times slower compared to an AdaBoost model on a small dataset which makes the actual usage of this model doubtable. If we are supplied with a larger dataset with millions of records this model would take too long to complete. The base classifier choice was XGBoost which is too complicated for a base classifier, maybe try some weaker learners such as tree stumps to compare the result with other models. In addition, this model might not be accurate compared to the model-ensembling technique where each model utilizes a different algorithm.<br />
<br />
I think IP Boost can be helpful in cases where a small improvement in accuracy is worth the additional computational effort involved. For example,there are applications in Finance where predicting the movement of stock prices slightly more accurately can help traders make millions more. In such cases, investing in expensive computing systems to implement such boosting techniques can perhaps be justified.<br />
<br />
== Critique ==<br />
<br />
In practise AdaBoost & LP Boost are quite robust to over fitting. In practise if you use simple weak learns stumps (1-level decision trees) then the algorithms are much less prone to over fitting. However the noise level in the data, particularly for AdaBoost is prone to overfitting on noisy datasets. To avoid this use regularised models (AdaBoostReg, LPBoost). Further, when in higher dimensional spaces, AdaBoost can suffer, since its just a linear combination of classifiers. You can use k-fold cross validation to set the stopping parameter to improve this.<br />
<br />
== References ==<br />
<br />
* Pfetsch, M. E., & Pokutta, S. (2020). IPBoost--Non-Convex Boosting via Integer Programming. arXiv preprint arXiv:2002.04679.<br />
<br />
* Freund, Y., & Schapire, R. E. (1995, March). A desicion-theoretic generalization of on-line learning and an application to boosting. In European conference on computational learning theory (pp. 23-37). Springer, Berlin, Heidelberg. pdf</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost&diff=46075IPBoost2020-11-23T17:12:28Z<p>Q58yu: /* IPBoost: Boosting via Integer Programming */</p>
<hr />
<div>== Presented by == <br />
Casey De Vera, Solaiman Jawad<br />
<br />
== Introduction == <br />
Boosting is an important and a fairly standard technique in classification that combines several base learners (learners which have a “low accuracy”), into one boosted learner (learner with a “high accuracy”). Pioneered by the AdaBoost approach of Freund & Schapire, in recent decades there has been extensive work on boosting procedures and analyses of their limitations.<br />
<br />
In a nutshell, boosting procedures are (typically) iterative schemes that roughly work as follows:<br />
<br />
Let <math>T</math> represents the number of iteration and <math>t</math> represents the iterator. <br />
<br />
for <math> t= 1, \cdots, T </math> do the following:<br />
<br />
::1. Train a learner <math> \mu_t</math> from a given class of base learners on the data distribution <math> \mathcal D_t</math><br />
<br />
::2. Evaluate the performance of <math> \mu_t</math> by computing its loss.<br />
<br />
::3. Push weight of the data distribution <math> \mathcal D_t</math> towards the misclassified examples leading to <math> \mathcal D_{t+1}</math>, usually a relatively good model will have a higher weight on those data that misclassified.<br />
<br />
Finally, the learners are combined with some form of voting (e.g., soft or hard voting, averaging, thresholding).<br />
<br />
<br />
[[File:boosting.gif|200px|thumb|right]] A close inspection of most boosting procedures reveals that they solve an underlying convex optimization problem over a convex loss function by means of coordinate gradient descent. Boosting schemes of this type are often referred to as '''convex potential boosters'''. These procedures can achieve exceptional performance on many data sets if the data is correctly labeled. However, they can be defeated easily by a small amount of incorrect labels which can be quite difficult to fix. The reason being is that we try to solve misclassified examples by moving the weights around, which results in bad performance on unseen data (Shown by zoomed example to the right). In fact, in theory, provided the class of base learners is rich enough, a perfect strong learner can be constructed that has accuracy 1, however, clearly, such a learner might not necessarily generalize well. Boosted learners can generate some quite complicated decision boundaries, much more complicated than that of the base learners. Here is an example from Paul van der Laken’s blog / Extreme gradient boosting gif by Ryan Holbrook. Here data is generated online according to some process with optimal decision boundary represented by the dotted line and XGBoost was used to learn a classifier:<br />
<br />
<br />
Recently non-convex optimization approaches for solving machine learning problems have gained significant attention. In this paper, we explore non-convex boosting in classification by means of integer programming and demonstrate real-world practicability of the approach while circumventing shortcomings of convex boosting approaches. The paper reports results that are comparable to or better than current state-of-the-art approaches.<br />
<br />
== Motivation ==<br />
<br />
In reality, we usually face unclean data and so-called label noise, where some percentage of the classification labels might be corrupted. We would also like to construct strong learners for such data. Noisy labels are an issue because when a model is trained with excessive amounts of noisy labels, the performance and accuracy deteriorates greatly. However, if we revisit the general boosting template from above, then we might suspect that we run into trouble as soon as a certain fraction of training examples is misclassified: in this case, these examples cannot be correctly classified and the procedure shifts more and more weight towards these bad examples. This eventually leads to a strong learner, that perfectly predicts the (flawed) training data; however, that does not generalize well anymore. This intuition has been formalized by [LS] who construct a “hard” training data distribution, where a small percentage of labels is randomly flipped. This label noise then leads to a significant reduction in performance of these boosted learners; see tables below. The more technical reason for this problem is actually the convexity of the loss function that is minimized by the boosting procedure. Clearly, one can use all types of “tricks” such as early stopping but at the end of the day, this is not solving the fundamental problem.<br />
<br />
== IPBoost: Boosting via Integer Programming ==<br />
<br />
<br />
===Integer Program Formulation===<br />
Let <math>(x_1,y_1),\cdots, (x_N,y_N) </math> be the training set with points <math>x_i \in \mathbb{R}^d</math> and two-class labels <math>y_i \in \{\pm 1\}</math> <br />
* class of base learners: <math> \Omega :=\{h_1, \cdots, h_L: \mathbb{R}^d \rightarrow \{\pm 1\}\} </math> and <math>\rho \ge 0</math> be given. <br />
* error function <math> \eta </math><br />
Our boosting model is captured by the integer programming problem. We can call this our primal problem: <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j=1}^L \eta_{ij}\lambda_k+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i=1,\cdots, N \\ <br />
&\sum_{j=1}^L \lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
For the error function <math>\eta</math>, three options were considered:<br />
<br />
(i) <math> \pm 1 </math> classification from learners<br />
$$ \eta_{ij} := 2\mathbb{I}[h_j(x_i) = y_i] - 1 = y_i \cdot h_j(x_i) $$<br />
(ii) class probabilities of learners<br />
$$ \eta_{ij} := 2\mathbb{P}[h_j(x_i) = y_i] - 1$$<br />
(iii) SAMME.R error function for learners<br />
$$ \frac{1}{2}y_i\log\left(\frac{\mathbb{P}[h_j(x_i) = 1]}{\mathbb{P}[h_j(x_i) = -1]}\right)$$<br />
<br />
===Solution of the IP using Column Generation===<br />
<br />
The goal of column generation is to provide an efficient way to solve the linear programming relaxation of the primal by allowing the <math>z_i </math> variables to assume fractional values. Moreover, columns, i.e., the base learners, <math> \mathcal L \subseteq [L]. </math> are left out because there are too many to handle efficiently and most of them will have their associated weight equal to zero in the optimal solution anyway. To generate columns, a <i>branch and bound</i> framework is used. Columns are generated within a<br />
branch-and-bound framework leading effectively to a branch-and-bound-and-price algorithm being used; this is significantly more involved compared to column generation in linear programming. To check the optimality of an LP solution, a subproblem, called the pricing problem, is solved to try to identify columns with a profitable reduced cost. If such columns are found, the LP is re-optimized. Branching occurs when no profitable columns are found, but the LP solution does not satisfy the integrality conditions. Branch and price apply column generation at every node of the branch and bound tree.<br />
<br />
The restricted master primal problem is <br />
<br />
$$ \begin{align*} \min &\sum_{i=1}^N z_i \\ s.t. &\sum_{j\in \mathcal L} \eta_{ij}\lambda_j+(1+\rho)z_i \ge \rho \ \ \ <br />
\forall i \in [N]\\ <br />
&\sum_{j\in \mathcal L}\lambda_j=1, \lambda \ge 0,\\ &z\in \{0,1\}^N. \end{align*}$$<br />
<br />
<br />
Its restricted dual problem is:<br />
<br />
$$ \begin{align*}\max \rho &\sum^{N}_{i=1}w_i + v - \sum^{N}_{i=1}u_i<br />
\\ s.t. &\sum_{i=1}^N \eta_{ij}w_k+ v \le 0 \ \ \ \forall j \in L \\ <br />
&(1+\rho)w_i - u_i \le 1 \ \ \ \forall i \in [N] \\ &w \ge 0, u \ge 0, v\ free\end{align*}$$<br />
<br />
Furthermore, there is a pricing problem used to determine, for every supposed optimal solution of the dual, whether the solution is actually optimal, or whether further constraints need to be added into the primal solution. With this pricing problem, we check whether the solution to the restricted dual is feasible. This pricing problem can be expressed as follows:<br />
<br />
$$ \sum_{i=1}^N \eta_{ij}w_k^* + v^* > 0 $$<br />
<br />
The optimal misclassification values are determined by a branch-and-price process that branches on the variables <math> z_i </math> and solves the intermediate LPs using column generation.<br />
<br />
===Algorithm===<br />
<div style="margin-left: 3em;"><br />
<math> D = \{(x_i, y_i) | i ∈ I\} ⊆ R^d × \{±1\} </math>, class of base learners <math>Ω </math>, margin <math> \rho </math> <br><br />
'''Output:''' Boosted learner <math> \sum_{j∈L^∗}h_jλ_j^* </math> with base learners <math> h_j </math> and weights <math> λ_j^* </math> <br><br />
<br />
<ol><br />
<br />
<li margin-left:30px> <math> T ← \{([0, 1]^N, \emptyset)\} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // set of local bounds and learners for open subproblems </li><br />
<li> <math> U ← \infty, L^∗ ← \emptyset </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Upper bound on optimal objective </li><br />
<li> '''while''' <math>\ T \neq \emptyset </math> '''do''' </li><br />
<li> &emsp; Choose and remove <math>(B,L) </math> from <math>T </math> </li><br />
<li> &emsp; '''repeat''' </li><br />
<li> &emsp; &emsp; Solve the primal IP using the local bounds on <math> z </math> in <math>B</math> with optimal dual solution <math> (w^∗, v^∗, u^∗) </math> </li><br />
<li> &emsp; &emsp; Find learner <math> h_j ∈ Ω </math> satisfying the pricing problem. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Solve pricing problem. </li><br />
<li> &emsp; '''until''' <math> h_j </math> is not found </li> <br />
<li> &emsp; Let <math> (\widetilde{λ} , \widetilde{z}) </math> be the final solution of the primal IP with base learners <math> \widetilde{L} = \{j | \widetilde{λ}_j > 0\} </math> </li><br />
<li> &emsp; '''if''' <math> \widetilde{z} ∈ \mathbb{Z}^N </math> and <math> \sum^{N}_{i=1}\widetilde{z}_i < U </math> '''then''' </li><br />
<li> &emsp; &emsp; <math> U ← \sum^{N}_{i=1}\widetilde{z}_i, L^∗ ← \widetilde{L}, λ^∗ ← \widetilde{\lambda} </math> &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Update best solution. </li><br />
<li> &emsp; '''else''' </li><br />
<li> &emsp; &emsp; Choose <math> i ∈ [N] </math> with <math> \widetilde{z}_i \notin Z </math> </li><br />
<li> &emsp; &emsp; Set <math> B_0 ← B ∩ \{z_i ≤ 0\}, B_1 ← B ∩ \{z_i ≥ 1\} </math> </li><br />
<li> &emsp; &emsp; Add <math> (B_0,\widetilde{L}), (B_1,\widetilde{L}) </math> to <math> T </math>. &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; // Create new branching nodes. </li><br />
<li> &emsp; '''end''' if </li><br />
<li> '''end''' while </li><br />
<li> ''Optionally sparsify final solution <math>L^*</math>'' </li><br />
<br />
</ol><br />
</div><br />
<br />
===Sparsification===<br />
<br />
== Results and Performance ==<br />
<br />
''All tests were run on identical Linux clusters with Intel Xeon Quad Core CPUs, with 3.50GHz, 10 MB cache, and 32 GB of main memory.''<br />
<br />
<br />
The following results reflect IPBoost's performance in hard instances. Note that by hard instances, we mean a binary classification problem with predefined labels. These examples are tailored to using the ±1 classification from learners. On every hard instance sample, IPBoost significantly outperforms both LPBoost and AdaBoost (although implementations depending on the libraries used have often caused results to differ slightly). For the considered instances the best value for the margin ρ was 0.05 for LPBoost and IPBoost; AdaBoost has no margin parameter. The accuracy reported is test accuracy recorded across various different walkthroughs of the algorithm, while <math>L </math> denotes the aggregate number of learners required to find the optimal learner, N is the number of points and <math> \gamma </math> refers to the noise level.<br />
<br />
[[File:ipboostres.png|center]]<br />
<br />
<br />
<br />
For the next table, the classification instances from LIBSVM data sets available at [https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets/]. We report accuracies on the test set and train set, respectively. In each case, we report the averages of the accuracies over 10 runs with a different random seed and their standard deviations. We can see IPboost again outperforming LPBoost and AdaBoost significantly. Solving Integer Programming problems is no doubt more computationally expensive than traditional boosting methods like AdaBoost. The average run time of IPBoost (for ρ = 0.05) being 1367.78 seconds, as opposed to LPBoost's 164.35 seconds and AdaBoost's 3.59 seconds reflects exactly that. However, on the flip side, we gain much better stability in our results, as well as higher scores across the board for both training and test sets.<br />
<br />
[[file:svmlibres.png|center]]<br />
<br />
<br />
== Conclusion ==<br />
<br />
IP-boosting avoids the bad performance on well-known hard classes and improves upon LP-boosting and AdaBoost on the LIBSVM instances where even a few percent improvements is valuable. The major drawback is that the running time with the current implementation is much longer. Nevertheless, the algorithm can be improved in the future by solving the intermediate LPs only approximately and deriving tailored heuristics that generate decent primal solutions to save on time.<br />
<br />
The approach is suited very well to an offline setting in which training may take time and where even a small improvement is beneficial or when convex boosters have egregious behaviour. It can also be served as a tool to investigate the general performance of methods like this.<br />
<br />
The IPBoost algorithm added extra complexity into basic boosting models to gain slight accuracy gain while greatly increased the time spent. It is 381 times slower compared to an AdaBoost model on a small dataset which makes the actual usage of this model doubtable. If we are supplied with a larger dataset with millions of records this model would take too long to complete. The base classifier choice was XGBoost which is too complicated for a base classifier, maybe try some weaker learners such as tree stumps to compare the result with other models. In addition, this model might not be accurate compared to the model-ensembling technique where each model utilizes a different algorithm.<br />
<br />
I think IP Boost can be helpful in cases where a small improvement in accuracy is worth the additional computational effort involved. For example,there are applications in Finance where predicting the movement of stock prices slightly more accurately can help traders make millions more. In such cases, investing in expensive computing systems to implement such boosting techniques can perhaps be justified.<br />
<br />
== Critique ==<br />
<br />
In practise AdaBoost & LP Boost are quite robust to over fitting. In practise if you use simple weak learns stumps (1-level decision trees) then the algorithms are much less prone to over fitting. However the noise level in the data, particularly for AdaBoost is prone to overfitting on noisy datasets. To avoid this use regularised models (AdaBoostReg, LPBoost). Further, when in higher dimensional spaces, AdaBoost can suffer, since its just a linear combination of classifiers. You can use k-fold cross validation to set the stopping parameter to improve this.<br />
<br />
== References ==<br />
<br />
* Pfetsch, M. E., & Pokutta, S. (2020). IPBoost--Non-Convex Boosting via Integer Programming. arXiv preprint arXiv:2002.04679.<br />
<br />
* Freund, Y., & Schapire, R. E. (1995, March). A desicion-theoretic generalization of on-line learning and an application to boosting. In European conference on computational learning theory (pp. 23-37). Springer, Berlin, Heidelberg. pdf</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes&diff=45648Influenza Forecasting Framework based on Gaussian Processes2020-11-22T04:19:26Z<p>Q58yu: /* Related Work */</p>
<hr />
<div><br />
== Abstract ==<br />
<br />
This paper presents a novel framework for seasonal epidemic forecasting using Gaussian process regression. Compared with other state-of-the-art models, the new novel framework introduced in this paper shows accurate retrospective forecasts through training a subset of the CDC influenza-like-illness (ILI) dataset using the official CDC scoring rule (log-score).<br />
<br />
== Background ==<br />
<br />
Each year, the seasonal influenza epidemic affects public health at a massive scale, resulting in 38 million cases, 400 000 hospitalizations, and 22 000 deaths in the United States in 2019-2020 alone [1]. Given this, reliable forecasts of future influenza development are invaluable, because they allow for improved public health policies and informed resource development and allocation. Many statistical methods have been developed to use data from the CDC and other real-time data sources, such as Google Trends to forecast influenza activities.<br />
<br />
Given the process of data collection and surveillance lag, accurate statistics for influenza warning systems are often delayed by some margin of time, making early prediction imperative. However, there are challenges in long-term epidemic forecasting. First, the temporal dependency is hard to capture with short-term input data. Without manually added seasonal trends, most statistical models fail to provide high accuracy. Second, the influence from other locations has not been exhaustively explored with limited data input. Spatio-temporal effects would therefore require adequate data sources to achieve good performance.<br />
<br />
== Related Work ==<br />
<br />
Given the value of epidemic forecasts, the CDC regularly publishes ILI data and has funded a seasonal ILI forecasting challenge. This challenge has to lead to four states of the art models in the field; MSS, a physical susceptible-infected-recovered model with assumed linear noise [4]; SARIMA, a framework based on seasonal auto-regressive moving average models [2]; and LinEns, an ensemble of three linear regression models.<br />
<br />
One disadvantage for forecasting is the publication of the CDC official ILI data is usually 1-3 weeks delayed. Therefore, several attempts use indirect web-based data to gain timelier estimates of the CDC’s ILI, which is also known as nowcasting. The forecasting framework introduced in this paper is able to use those nowcasting approaches to receive a more timely data stream.<br />
<br />
== Motivation ==<br />
<br />
It has been shown that LinEns forecasts outperform the other frameworks on the ILI data-set. However, this framework assumes a deterministic relationship between the epidemic week and its case count, which does not reflect the stochastic nature of the trend. Therefore, it is natural to ask whether a similar framework that assumes a stochastic relationship between these variables would provide better performance. This motivated the development of the proposed Gaussian process regression framework and the subsequent performance comparison to the benchmark models.<br />
<br />
== Gaussian Process Regression ==<br />
<br />
A Gaussian process is specified with a mean function and a kernel function. Besides, the mean and the variance function of the Gaussian process is defined by:<br />
\[\mu(x) = k(x, X)^T(K_n+\sigma^2I)^{-1}Y\]<br />
\[\sigma(x) = k^{**}(x,x)-k(x,X)^T(K_n+\sigma^2I)^{-1}k(x,X)\]<br />
where <math>K_n</math> is the covariance matrix and for the kernel, it is being specified that it will use the Gaussian kernel.<br />
<br />
Consider the following set up: let <math>X = [\mathbf{x}_1,\ldots,\mathbf{x}_n]</math> <math>(d\times n)</math> be your training data, <math>\mathbf{y} = [y_1,y_2,\ldots,y_n]^T</math> be your noisy observations where <math>y_i = f(\mathbf{x}_i) + \epsilon_i</math>, <math>(\epsilon_i:i = 1,\ldots,n)</math> i.i.d. <math>\sim \mathcal{N}(0,{\sigma}^2)</math>, and <math>f</math> is the trend we are trying to model (by <math>\hat{f}</math>). Let <math>\mathbf{x}^*</math> <math>(d\times 1)</math> be your test data point, and <math>\hat{y} = \hat{f}(\mathbf{x}^*)</math> be your predicted outcome.<br />
<br />
<br />
Instead of assuming a deterministic form of <math>f</math>, and thus of <math>\mathbf{y}</math> and <math>\hat{y}</math> (as classical linear regression would, for example), Gaussian process regression assumes <math>f</math> is stochastic. More precisely, <math>\mathbf{y}</math> and <math>\hat{y}</math> are assumed to have a joint prior distribution. Indeed, we have <br />
<br />
$$<br />
(\mathbf{y},\hat{y}) \sim \mathcal{N}(0,\Sigma(X,\mathbf{x}^*))<br />
$$<br />
<br />
where <math>\Sigma(X,\mathbf{x}^*)</math> is a matrix of covariances dependent on some kernel function <math>k</math>. In this paper, the kernel function is assumed to be Gaussian and takes the form <br />
<br />
$$<br />
k(\mathbf{x}_i,\mathbf{x}_j) = \sigma^2\exp(-\frac{1}{2}(\mathbf{x}_i-\mathbf{x}_j)^T\Sigma(\mathbf{x}_i-\mathbf{x}_j)).<br />
$$<br />
<br />
It is important to note that this gives a joint prior distribution of '''functions''' ('''Fig. 1''' left, grey curves). <br />
<br />
By restricting this distribution to contain only those functions ('''Fig. 1''' right, grey curves) that agree with the observed data points <math>\mathbf{x}</math> ('''Fig. 1''' right, solid black) we obtain the posterior distribution for <math>\hat{y}</math> which has the form<br />
<br />
$$<br />
p(\hat{y} | \mathbf{x}^*, X, \mathbf{y}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}),\sigma(\mathbf{x}^*,X))<br />
$$<br />
<br />
<br />
<div style="text-align:center;"> [[File:GPRegression.png|500px]] </div><br />
<br />
<div align="center">'''Figure 1. Gaussian process regression''': Select the functions from your joint prior distribution (left, grey curves) with mean <math>0</math> (left, bold line) that agree with the observed data points (right, black bullets). These form your posterior distribution (right, grey curves) with mean <math>\mu(\mathbf{x})</math> (right, bold line). Red triangle helps compare the two images (location marker) [3]. </div><br />
<br />
== Data-set ==<br />
<br />
Let <math>d_j^i</math> denote the number of epidemic cases recorded in week <math>j</math> of season <math>i</math>, and let <math>j^*</math> and <math>i^*</math> denote the current week and season, respectively. The ILI data-set contains <math>d_j^i</math> for all previous weeks and seasons, up to the current season with a 1-3 week publishing delay. Note that a season refers to the time of year when the epidemic is prevalent (e.g. an influenza season lasts 30 weeks and contains the last 10 weeks of year k, and the first 20 weeks of year k+1). The goal is to predict <math>\hat{y}_T = \hat{f}_T(x^*) = d^{i^*}_{j* + T}</math> where <math>T, \;(T = 1,\ldots,K)</math> is the target week (how many weeks into the future that you want to predict).<br />
<br />
To do this, a design matrix <math>X</math> is constructed where each element <math>X_{ji} = d_j^i</math> corresponds to the number of cases in week (row) j of season (column) i. The training outcomes <math>y_{i,T}, i = 1,\ldots,n</math> correspond to the number of cases that were observed in target week <math>T,\; (T = 1,\ldots,K)</math> of season <math>i, (i = 1,\ldots,n)</math>.<br />
<br />
== Proposed Framework ==<br />
<br />
To compute <math>\hat{y}</math>, the following algorithm is executed. <br />
<br />
<ol><br />
<br />
<li> Let <math>J \subseteq \{j^*-4 \leq j \leq j^*\}</math> (subset of possible weeks).<br />
<br />
<li> Assemble the Training Set <math>\{X_J, \mathbf{y}_{T,J}\}</math> <br />
<br />
<li> Train the Gaussian process<br />
<br />
<li> Calculate the '''distribution''' of <math>\hat{y}_{T,J}</math> using <math>p(\hat{y}_{T,J} | \mathbf{x}^*, X_J, \mathbf{y}_{T,J}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}_{T,J}),\sigma(\mathbf{x}^*,X_J))</math><br />
<br />
<li> Set <math>\hat{y}_{T,J} =\mu(x^*,X_J,\mathbf{y}_{T,J})</math><br />
<br />
<li> Repeat steps 2-5 for all sets of weeks <math>J</math><br />
<br />
<li> Determine the best 3 performing sets J (on the 2010/11 and 2011/12 validation sets)<br />
<br />
<li> Calculate the ensemble forecast by averaging the 3 best performing predictive distribution densities i.e. <math>\hat{y}_T = \frac{1}{3}\sum_{k=1}^3 \hat{y}_{T,J_{best}}</math><br />
<br />
</ol><br />
<br />
== Results ==<br />
<br />
To demonstrate the accuracy of their results, retrospective forecasting was done on the ILI data-set. In other words, the Gaussian process model was trained to assume a previous season (2012/13) was the current season. In this fashion, the forecast could be compared to the already observed true outcome. <br />
<br />
To produce a forecast for the entire 2012/13 season, 30 Gaussian processes were trained (each influenza season has 30 test points <math>\mathbf{x^*}</math>) and a curve connecting the predicted outputs <math>y_T = \hat{f}(\mathbf{x^*)}</math> was plotted ('''Fig.2''', blue line). As shown in '''Fig.2''', this forecast (blue line) was reliable for both 1 (left) and 3 (right) week targets, given that the 95% prediction interval ('''Fig.2''', purple shaded) contained the true values ('''Fig.2''', red x's) 95% of the time.<br />
<br />
<div style="text-align:center;"> [[File:ResultsOne.png|600px]] </div><br />
<br />
<div align="center">'''Figure 2. Retrospective forecasts and their uncertainty''': One week retrospective influenza forecasting for two targets (T = 1, 3). Red x’s are the true observed values, and blue lines and purple shaded areas represent point forecasts and 95% prediction intervals, respectively. </div><br />
<br />
<br />
Moreover, as shown in '''Fig.3''', the novel Gaussian process regression framework outperformed all state-of-the-art models, included LinEns, for four different targets <math>(T = 1,\ldots, 4)</math>, when compared using the official CDC scoring criterion ''log-score''. Log-score describes the logarithmic probability of the forecast being within an interval around the true value. <br />
<br />
<div style="text-align:center;"> [[File:ComparisonNew.png|600px]] </div><br />
<br />
<div align="center">'''Figure 3. Average log-score gain of proposed framework''': Each bar shows the mean seasonal log-score gain of the proposed framework vs. the given state-of-the-art model, and each panel corresponds to a different target week <math> T = 1,...4 </math>. </div><br />
<br />
== Conclusion ==<br />
<br />
This paper presented a novel framework for forecasting seasonal epidemics using Gaussian process regression that outperformed multiple state-of-the-art forecasting methods on the CDC's ILI data-set. Hence, this work may play a key role in future influenza forecasting and as result, the improvement of public health policies and resource allocation.<br />
<br />
== Critique ==<br />
<br />
The proposed framework provides a computationally efficient method to forecast any seasonal epidemic count data that is easily extendable to multiple target types. In particular, one can compute key parameters such as the peak infection incidence <math>\left(\hat{y} = \text{max}_{0 \leq j \leq 52} d^i_j \right)</math>, the timing of the peak infection incidence <math>\left(\hat{y} = \text{argmax}_{0 \leq j \leq 52} d^i_j\right)</math> and the final epidemic size of a season <math>\left(\hat{y} = \sum_{j=1}^{52} d^i_j\right)</math>. However, given it is not a physical model, it cannot provide insights on parameters describing the disease spread. Moreover, the framework requires training data and hence, is not applicable for non-seasonal epidemics.<br />
<br />
This paper provides a state of the art approach for forecasting epidemics. It would have been interesting to see other types of kernels being used, such as a periodic kernel <math>k(x, x') = \sigma^2 \exp\left({-\frac{2 \sin^2 (\pi|x-x'|)/p}{l^2}}\right) </math>, as intuitively epidemics are known to have waves within seasons. This may have resulted in better-calibrated uncertainty estimates as well.<br />
<br />
It is mentioned that the the framework might not be good for non-seasonal epidemics because it requires training data, given that the COVID-19 pandemic comes in multiple waves and we have enough data from the first wave and second wave, we might be able to use this framework to predict the third wave and possibly the fourth one as well. It'd be interesting to see this forecasting framework being trained using the data from the first and second wave of COVID-19.<br />
<br />
== References ==<br />
<br />
[1] Estimated Influenza Illnesses, Medical visits, Hospitalizations, and Deaths in the United States - 2019–2020 Influenza Season. (2020). Retrieved November 16, 2020, from https://www.cdc.gov/flu/about/burden/2019-2020.html<br />
<br />
[2] Ray, E. L., Sakrejda, K., Lauer, S. A., Johansson, M. A.,and Reich, N. G. (2017).Infectious disease prediction with kernel conditional densityestimation.Statistics in Medicine, 36(30):4908–4929.<br />
<br />
[3] Schulz, E., Speekenbrink, M., and Krause, A. (2017).A tutorial on gaussian process regression with a focus onexploration-exploitation scenarios.bioRxiv.<br />
<br />
[4] Zimmer, C., Leuba, S. I., Cohen, T., and Yaesoubi, R.(2019).Accurate quantification of uncertainty in epidemicparameter estimates and predictions using stochasticcompartmental models.Statistical Methods in Medical Research,28(12):3591–3608.PMID: 30428780.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes&diff=45645Influenza Forecasting Framework based on Gaussian Processes2020-11-22T03:55:38Z<p>Q58yu: /* Abstract */</p>
<hr />
<div><br />
== Abstract ==<br />
<br />
This paper presents a novel framework for seasonal epidemic forecasting using Gaussian process regression. Compared with other state-of-the-art models, the new novel framework introduced in this paper shows accurate retrospective forecasts through training a subset of the CDC influenza-like-illness (ILI) dataset using the official CDC scoring rule (log-score).<br />
<br />
== Background ==<br />
<br />
Each year, the seasonal influenza epidemic affects public health at a massive scale, resulting in 38 million cases, 400 000 hospitalizations, and 22 000 deaths in the United States in 2019-2020 alone [1]. Given this, reliable forecasts of future influenza development are invaluable, because they allow for improved public health policies and informed resource development and allocation. Many statistical methods have been developed to use data from the CDC and other real-time data sources, such as Google Trends to forecast influenza activities.<br />
<br />
Given the process of data collection and surveillance lag, accurate statistics for influenza warning systems are often delayed by some margin of time, making early prediction imperative. However, there are challenges in long-term epidemic forecasting. First, the temporal dependency is hard to capture with short-term input data. Without manually added seasonal trends, most statistical models fail to provide high accuracy. Second, the influence from other locations has not been exhaustively explored with limited data input. Spatio-temporal effects would therefore require adequate data sources to achieve good performance.<br />
<br />
== Related Work ==<br />
<br />
Given the value of epidemic forecasts, the CDC regularly publishes ILI data and has funded a seasonal ILI forecasting challenge. This challenge has to lead to four states of the art models in the field; MSS, a physical susceptible-infected-recovered model with assumed linear noise [4]; SARIMA, a framework based on seasonal auto-regressive moving average models [2]; and LinEns, an ensemble of three linear regression models.<br />
<br />
== Motivation ==<br />
<br />
It has been shown that LinEns forecasts outperform the other frameworks on the ILI data-set. However, this framework assumes a deterministic relationship between the epidemic week and its case count, which does not reflect the stochastic nature of the trend. Therefore, it is natural to ask whether a similar framework that assumes a stochastic relationship between these variables would provide better performance. This motivated the development of the proposed Gaussian process regression framework and the subsequent performance comparison to the benchmark models.<br />
<br />
== Gaussian Process Regression ==<br />
<br />
A Gaussian process is specified with a mean function and a kernel function. Besides, the mean and the variance function of the Gaussian process is defined by:<br />
\[\mu(x) = k(x, X)^T(K_n+\sigma^2I)^{-1}Y\]<br />
\[\sigma(x) = k^{**}(x,x)-k(x,X)^T(K_n+\sigma^2I)^{-1}k(x,X)\]<br />
where <math>K_n</math> is the covariance matrix and for the kernel, it is being specified that it will use the Gaussian kernel.<br />
<br />
Consider the following set up: let <math>X = [\mathbf{x}_1,\ldots,\mathbf{x}_n]</math> <math>(d\times n)</math> be your training data, <math>\mathbf{y} = [y_1,y_2,\ldots,y_n]^T</math> be your noisy observations where <math>y_i = f(\mathbf{x}_i) + \epsilon_i</math>, <math>(\epsilon_i:i = 1,\ldots,n)</math> i.i.d. <math>\sim \mathcal{N}(0,{\sigma}^2)</math>, and <math>f</math> is the trend we are trying to model (by <math>\hat{f}</math>). Let <math>\mathbf{x}^*</math> <math>(d\times 1)</math> be your test data point, and <math>\hat{y} = \hat{f}(\mathbf{x}^*)</math> be your predicted outcome.<br />
<br />
<br />
Instead of assuming a deterministic form of <math>f</math>, and thus of <math>\mathbf{y}</math> and <math>\hat{y}</math> (as classical linear regression would, for example), Gaussian process regression assumes <math>f</math> is stochastic. More precisely, <math>\mathbf{y}</math> and <math>\hat{y}</math> are assumed to have a joint prior distribution. Indeed, we have <br />
<br />
$$<br />
(\mathbf{y},\hat{y}) \sim \mathcal{N}(0,\Sigma(X,\mathbf{x}^*))<br />
$$<br />
<br />
where <math>\Sigma(X,\mathbf{x}^*)</math> is a matrix of covariances dependent on some kernel function <math>k</math>. In this paper, the kernel function is assumed to be Gaussian and takes the form <br />
<br />
$$<br />
k(\mathbf{x}_i,\mathbf{x}_j) = \sigma^2\exp(-\frac{1}{2}(\mathbf{x}_i-\mathbf{x}_j)^T\Sigma(\mathbf{x}_i-\mathbf{x}_j)).<br />
$$<br />
<br />
It is important to note that this gives a joint prior distribution of '''functions''' ('''Fig. 1''' left, grey curves). <br />
<br />
By restricting this distribution to contain only those functions ('''Fig. 1''' right, grey curves) that agree with the observed data points <math>\mathbf{x}</math> ('''Fig. 1''' right, solid black) we obtain the posterior distribution for <math>\hat{y}</math> which has the form<br />
<br />
$$<br />
p(\hat{y} | \mathbf{x}^*, X, \mathbf{y}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}),\sigma(\mathbf{x}^*,X))<br />
$$<br />
<br />
<br />
<div style="text-align:center;"> [[File:GPRegression.png|500px]] </div><br />
<br />
<div align="center">'''Figure 1. Gaussian process regression''': Select the functions from your joint prior distribution (left, grey curves) with mean <math>0</math> (left, bold line) that agree with the observed data points (right, black bullets). These form your posterior distribution (right, grey curves) with mean <math>\mu(\mathbf{x})</math> (right, bold line). Red triangle helps compare the two images (location marker) [3]. </div><br />
<br />
== Data-set ==<br />
<br />
Let <math>d_j^i</math> denote the number of epidemic cases recorded in week <math>j</math> of season <math>i</math>, and let <math>j^*</math> and <math>i^*</math> denote the current week and season, respectively. The ILI data-set contains <math>d_j^i</math> for all previous weeks and seasons, up to the current season with a 1-3 week publishing delay. Note that a season refers to the time of year when the epidemic is prevalent (e.g. an influenza season lasts 30 weeks and contains the last 10 weeks of year k, and the first 20 weeks of year k+1). The goal is to predict <math>\hat{y}_T = \hat{f}_T(x^*) = d^{i^*}_{j* + T}</math> where <math>T, \;(T = 1,\ldots,K)</math> is the target week (how many weeks into the future that you want to predict).<br />
<br />
To do this, a design matrix <math>X</math> is constructed where each element <math>X_{ji} = d_j^i</math> corresponds to the number of cases in week (row) j of season (column) i. The training outcomes <math>y_{i,T}, i = 1,\ldots,n</math> correspond to the number of cases that were observed in target week <math>T,\; (T = 1,\ldots,K)</math> of season <math>i, (i = 1,\ldots,n)</math>.<br />
<br />
== Proposed Framework ==<br />
<br />
To compute <math>\hat{y}</math>, the following algorithm is executed. <br />
<br />
<ol><br />
<br />
<li> Let <math>J \subseteq \{j^*-4 \leq j \leq j^*\}</math> (subset of possible weeks).<br />
<br />
<li> Assemble the Training Set <math>\{X_J, \mathbf{y}_{T,J}\}</math> <br />
<br />
<li> Train the Gaussian process<br />
<br />
<li> Calculate the '''distribution''' of <math>\hat{y}_{T,J}</math> using <math>p(\hat{y}_{T,J} | \mathbf{x}^*, X_J, \mathbf{y}_{T,J}) \sim \mathcal{N}(\mu(\mathbf{x}^*,X,\mathbf{y}_{T,J}),\sigma(\mathbf{x}^*,X_J))</math><br />
<br />
<li> Set <math>\hat{y}_{T,J} =\mu(x^*,X_J,\mathbf{y}_{T,J})</math><br />
<br />
<li> Repeat steps 2-5 for all sets of weeks <math>J</math><br />
<br />
<li> Determine the best 3 performing sets J (on the 2010/11 and 2011/12 validation sets)<br />
<br />
<li> Calculate the ensemble forecast by averaging the 3 best performing predictive distribution densities i.e. <math>\hat{y}_T = \frac{1}{3}\sum_{k=1}^3 \hat{y}_{T,J_{best}}</math><br />
<br />
</ol><br />
<br />
== Results ==<br />
<br />
To demonstrate the accuracy of their results, retrospective forecasting was done on the ILI data-set. In other words, the Gaussian process model was trained to assume a previous season (2012/13) was the current season. In this fashion, the forecast could be compared to the already observed true outcome. <br />
<br />
To produce a forecast for the entire 2012/13 season, 30 Gaussian processes were trained (each influenza season has 30 test points <math>\mathbf{x^*}</math>) and a curve connecting the predicted outputs <math>y_T = \hat{f}(\mathbf{x^*)}</math> was plotted ('''Fig.2''', blue line). As shown in '''Fig.2''', this forecast (blue line) was reliable for both 1 (left) and 3 (right) week targets, given that the 95% prediction interval ('''Fig.2''', purple shaded) contained the true values ('''Fig.2''', red x's) 95% of the time.<br />
<br />
<div style="text-align:center;"> [[File:ResultsOne.png|600px]] </div><br />
<br />
<div align="center">'''Figure 2. Retrospective forecasts and their uncertainty''': One week retrospective influenza forecasting for two targets (T = 1, 3). Red x’s are the true observed values, and blue lines and purple shaded areas represent point forecasts and 95% prediction intervals, respectively. </div><br />
<br />
<br />
Moreover, as shown in '''Fig.3''', the novel Gaussian process regression framework outperformed all state-of-the-art models, included LinEns, for four different targets <math>(T = 1,\ldots, 4)</math>, when compared using the official CDC scoring criterion ''log-score''. Log-score describes the logarithmic probability of the forecast being within an interval around the true value. <br />
<br />
<div style="text-align:center;"> [[File:ComparisonNew.png|600px]] </div><br />
<br />
<div align="center">'''Figure 3. Average log-score gain of proposed framework''': Each bar shows the mean seasonal log-score gain of the proposed framework vs. the given state-of-the-art model, and each panel corresponds to a different target week <math> T = 1,...4 </math>. </div><br />
<br />
== Conclusion ==<br />
<br />
This paper presented a novel framework for forecasting seasonal epidemics using Gaussian process regression that outperformed multiple state-of-the-art forecasting methods on the CDC's ILI data-set. Hence, this work may play a key role in future influenza forecasting and as result, the improvement of public health policies and resource allocation.<br />
<br />
== Critique ==<br />
<br />
The proposed framework provides a computationally efficient method to forecast any seasonal epidemic count data that is easily extendable to multiple target types. In particular, one can compute key parameters such as the peak infection incidence <math>\left(\hat{y} = \text{max}_{0 \leq j \leq 52} d^i_j \right)</math>, the timing of the peak infection incidence <math>\left(\hat{y} = \text{argmax}_{0 \leq j \leq 52} d^i_j\right)</math> and the final epidemic size of a season <math>\left(\hat{y} = \sum_{j=1}^{52} d^i_j\right)</math>. However, given it is not a physical model, it cannot provide insights on parameters describing the disease spread. Moreover, the framework requires training data and hence, is not applicable for non-seasonal epidemics.<br />
<br />
This paper provides a state of the art approach for forecasting epidemics. It would have been interesting to see other types of kernels being used, such as a periodic kernel <math>k(x, x') = \sigma^2 \exp\left({-\frac{2 \sin^2 (\pi|x-x'|)/p}{l^2}}\right) </math>, as intuitively epidemics are known to have waves within seasons. This may have resulted in better-calibrated uncertainty estimates as well.<br />
<br />
It is mentioned that the the framework might not be good for non-seasonal epidemics because it requires training data, given that the COVID-19 pandemic comes in multiple waves and we have enough data from the first wave and second wave, we might be able to use this framework to predict the third wave and possibly the fourth one as well. It'd be interesting to see this forecasting framework being trained using the data from the first and second wave of COVID-19.<br />
<br />
== References ==<br />
<br />
[1] Estimated Influenza Illnesses, Medical visits, Hospitalizations, and Deaths in the United States - 2019–2020 Influenza Season. (2020). Retrieved November 16, 2020, from https://www.cdc.gov/flu/about/burden/2019-2020.html<br />
<br />
[2] Ray, E. L., Sakrejda, K., Lauer, S. A., Johansson, M. A.,and Reich, N. G. (2017).Infectious disease prediction with kernel conditional densityestimation.Statistics in Medicine, 36(30):4908–4929.<br />
<br />
[3] Schulz, E., Speekenbrink, M., and Krause, A. (2017).A tutorial on gaussian process regression with a focus onexploration-exploitation scenarios.bioRxiv.<br />
<br />
[4] Zimmer, C., Leuba, S. I., Cohen, T., and Yaesoubi, R.(2019).Accurate quantification of uncertainty in epidemicparameter estimates and predictions using stochasticcompartmental models.Statistical Methods in Medical Research,28(12):3591–3608.PMID: 30428780.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Summary_for_survey_of_neural_networked-based_cancer_prediction_models_from_microarray_data&diff=45643Summary for survey of neural networked-based cancer prediction models from microarray data2020-11-22T03:38:13Z<p>Q58yu: /* Neural network-based cancer prediction models */</p>
<hr />
<div>== Presented by == <br />
Rao Fu, Siqi Li, Yuqin Fang, Zeping Zhou<br />
<br />
== Introduction == <br />
Microarray technology is widely used in analyzing genetic diseases as it can help researchers detect genetic information rapidly. In the study of cancer, the researchers use this technology to compare normal and abnormal cancerous tissues so that they can gain a better understanding about the pathology of cancer. However, what could affect the accuracy and computation time of this cancer model is the high dimensionality of the gene expressions. To cope with this problem, we need to use the feature selection method or feature creation method. The former (feature selection methods), reduce the dimensionality of your data-set by selecting only a subset of the key discerning features to use as input to your model. In contrast, the latter (feature creation methods), create an entirely new set of lower dimensional features, meant to represent your original (higher-dimensional) features. <br />
One of the most powerful methods in machine learning is neural networks. In this paper, 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''' <br><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 for example 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 desired output is what we called 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 numbers of neurons to review the neural network-based cancer prediction models for learning the gene expression features.<br />
<br />
'''Cancer prediction models'''<br><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 ROC curve. It reflects the sensitivity of the response to the same signal stimulus under different criteria. To test its validity, we need to consider it with the confidence interval. Usually, a model is a good one when its ROC is greater than 0.7. Another way to measure the performance of a model is to use CI, which explains the concordance probability of the predicted and observed survival. The closer its value to 0.7, the better the model is. The third measurement method is using the Brier score. A brier score 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.<br />
<br />
== Neural network-based cancer prediction models ==<br />
By performing an extensive search relevant to neural network-based cancer prediction using Google scholar and other electronic databases namely PubMed and Scopus with keywords such as “Neural Networks AND Cancer Prediction” and “gene expression clustering”, the chosen papers covered cancer classification, discovery, survivability prediction and the statistical analysis models. The following figure 1 shows a graph representing the number of citations including filtering, predictive and clustering for chosen papers. [[File:f1.png]]<br />
<br />
'''Datasets and preprocessing''' <br><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 of techniques used in processing dataset including removing the genes that have zero expression across all samples, Normalization, filtering with p value > <math>10^{-05}</math> to remove some unwanted technical variation and <math>\log_2</math> transformations. Statistical methods, neural network, 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 datasets 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 overcame 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 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 />
[[File:Datasets and preprocessing.png]]<br />
<br />
'''Neural network architecture''' <br><br />
Most recent studies reveal that filtering, predicting methods and cluster methods are used in cancer prediction. For filtering, the resulted features are used with statistical methods or machine learning classification and cluster tools such as decision trees, K Nearest Neighbor and Self Organizing Maps(SOM) as figure 2 indicates.[[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. For our categorization into filtering, predicting and clustering methods was based on the overall rule that a neural network performs in the cancer prediction method. 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 an 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''' <br><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 algorithm 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 to a new test set with unknown labels.<br />
<br />
'''Neural network filters for cancer prediction''' <br><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 different number of hidden layers, different activation functions (e.g. sigmoid function, exponential linear unit function), and different optimization algorithms (e.g. stochastic gradient decent 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''' <br><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 C’k 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 on 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 classifier are better than those of SVM, logistic regression, naïve Bayes, classification trees and KNN.<br />
<br />
'''Neural network clustering methods in cancer prediction''' <br><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 backpropagation mechanism, is one of the traditional model-based techniques to be applied on 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. To solve the high dimensionality problem, there are two methods: clustering ensembles by running a single clustering algorithm for 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 gene-to-cluster assignment into consideration.<br />
<br />
Also, the paper provides 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 more than 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 binary cases, the network architecture has only one or two output neurons that diagnose a given sample as cancerous or non-cancerous, while 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 and 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 ensembling 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. <br><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 "observations".<br><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. <br><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.<br><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.<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. 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.<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 algorithm 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 />
==Reference==<br />
Daoud, M., & Mayo, M. (2019). A survey of neural network-based cancer prediction models from microarray data. Artificial Intelligence in Medicine, 97, 204–214.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Summary_for_survey_of_neural_networked-based_cancer_prediction_models_from_microarray_data&diff=45638Summary for survey of neural networked-based cancer prediction models from microarray data2020-11-22T03:18:28Z<p>Q58yu: /* Discussion */</p>
<hr />
<div>== Presented by == <br />
Rao Fu, Siqi Li, Yuqin Fang, Zeping Zhou<br />
<br />
== Introduction == <br />
Microarray technology is widely used in analyzing genetic diseases as it can help researchers detect genetic information rapidly. In the study of cancer, the researchers use this technology to compare normal and abnormal cancerous tissues so that they can gain a better understanding about the pathology of cancer. However, what could affect the accuracy and computation time of this cancer model is the high dimensionality of the gene expressions. To cope with this problem, we need to use the feature selection method or feature creation method. The former (feature selection methods), reduce the dimensionality of your data-set by selecting only a subset of the key discerning features to use as input to your model. In contrast, the latter (feature creation methods), create an entirely new set of lower dimensional features, meant to represent your original (higher-dimensional) features. <br />
One of the most powerful methods in machine learning is neural networks. In this paper, 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''' <br><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 for example 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 desired output is what we called 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 numbers of neurons to review the neural network-based cancer prediction models for learning the gene expression features.<br />
<br />
'''Cancer prediction models'''<br><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 ROC curve. It reflects the sensitivity of the response to the same signal stimulus under different criteria. To test its validity, we need to consider it with the confidence interval. Usually, a model is a good one when its ROC is greater than 0.7. Another way to measure the performance of a model is to use CI, which explains the concordance probability of the predicted and observed survival. The closer its value to 0.7, the better the model is. The third measurement method is using the Brier score. A brier score 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.<br />
<br />
== Neural network-based cancer prediction models ==<br />
By performing an extensive search relevant to neural network-based cancer prediction using Google scholar and other electronic databases namely PubMed and Scopus with keywords such as “Neural Networks AND Cancer Prediction” and “gene expression clustering”, the chosen papers covered cancer classification, discovery, survivability prediction and the statistical analysis models. The following figure 1 shows a graph representing the number of citations including filtering, predictive and clustering for chosen papers. [[File:f1.png]]<br />
<br />
'''Datasets and preprocessing''' <br><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 of techniques used in processing dataset including removing the genes that have zero expression across all samples, Normalization, filtering with p value > 10^-05 to remove some unwanted technical variation and log2 transformations. Statistical methods, neural network, 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 datasets 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 overcame 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 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 />
[[File:Datasets and preprocessing.png]]<br />
<br />
'''Neural network architecture''' <br><br />
Most recent studies reveal that filtering, predicting methods and cluster methods are used in cancer prediction. For filtering, the resulted features are used with statistical methods or machine learning classification and cluster tools such as decision trees, K Nearest Neighbor and Self Organizing Maps(SOM) as figure 2 indicates.[[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. For our categorization into filtering, predicting and clustering methods was based on the overall rule that a neural network performs in the cancer prediction method. 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 an 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''' <br><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 algorithm 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 to a new test set with unknown labels.<br />
<br />
'''Neural network filters for cancer prediction''' <br><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 different number of hidden layers, different activation functions (e.g. sigmoid function, exponential linear unit function), and different optimization algorithms (e.g. stochastic gradient decent optimization, Adam optimizer).<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''' <br><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 C’k 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 on 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 classifier are better than those of SVM, logistic regression, naïve Bayes, classification trees and KNN.<br />
<br />
'''Neural network clustering methods in cancer prediction''' <br><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 backpropagation mechanism, is one of the traditional model-based techniques to be applied on 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. To solve the high dimensionality problem, there are two methods: clustering ensembles by running a single clustering algorithm for 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 gene-to-cluster assignment into consideration.<br />
<br />
Also, the paper provides 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 more than 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 binary cases, the network architecture has only one or two output neurons that diagnose a given sample as cancerous or non-cancerous, while 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 and 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 ensembling 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. <br><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 "observations".<br><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. <br><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.<br><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.<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. 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.<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 algorithm 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 />
==Reference==<br />
Daoud, M., & Mayo, M. (2019). A survey of neural network-based cancer prediction models from microarray data. Artificial Intelligence in Medicine, 97, 204–214.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=what_game_are_we_playing&diff=45599what game are we playing2020-11-21T21:48:27Z<p>Q58yu: /* One-Card Poker */</p>
<hr />
<div>== Authors == <br />
Yuxin Wang, Evan Peters, Yifan Mou, Sangeeth Kalaichanthiran <br />
<br />
== Introduction ==<br />
Recently, there have been many different studies of methods using AI to solve large-scale, zero-sum, extensive form problems. However, most of these works operate under the assumption that the parameters of the game are known, and the objective is just finding the optimal strategy for the game. This scenario is unrealistic since most of the time parameters of the game are unknown. This paper proposes a framework for finding an optimal solution using a primal-dual Newton Method and then using back-propagation to analytically compute the gradients of all the relevant game parameters.<br />
<br />
The approach to solving this problem is to consider ''quantal response equilibrium'' (QRE), which is a generalization of Nash equilibrium (NE) where the agents can make suboptimal decisions. It is shown that the solution to the QRE is a differentiable function of the payoff matrix. Consequently, back-propagation can be used to analytically solve for the payoff matrix (or other game parameters). This strategy has many future application areas as it allows for game-solving (both extensive and normal form) to be integrated as a module in a deep neural network.<br />
<br />
An example of architecture is presented below:<br />
<br />
[[File:Framework.png ]]<br />
<br />
Payoff matrix <math> P </math> is parameterized by a domain-dependent low dimensional vector <math> \phi </math>, which <math> \phi </math> depends on a differentiable function <math> M_1(x) </math>. Furthermore, <math> P </math> is applied to QRE to get the equilibrium strategies <math> (u^∗, v^∗) </math>. Lastly, loss function is calculated after applying through any differentiable <math> M_2(u^∗, v^∗) </math>.<br />
<br />
The effectiveness of this model is demonstrated using the games “Rock, Paper, Scissors”, one-card poker, and a security defense game.<br />
<br />
== Learning and Quantal Response in Normal Form Games ==<br />
<br />
The game-solving module provides all elements required in differentiable learning, which maps contextual features to payoff matrices, and computes equilibrium strategies under a set of contextual features. This paper will learn zero-sum games and start with normal form games since they have game solver and learning approach capturing much of intuition and basic methodology.<br />
<br />
=== Zero-Sum Normal Form Games ===<br />
<br />
In two-player zero-sum games there is a '''payoff matrix''' <math>P</math> that describes the rewards for two players employing specific strategies u and v respectively. The optimal strategy mixture may be found with a classic min-max formulation:<br />
$$\min_u \max_v \ u^T P v \\ subject \ to \ 1^T u =1, u \ge 0 \\ 1^T v =1, v \ge 0. \ $$<br />
<br />
Here, we consider the case where <math>P</math> is not known a priori. The solution <math> (u^*, v_0) </math> to this optimization and the solution <math> (u_0,v^*) </math> to the corresponding problem with inverse player order form the Nash equilibrium <math>(u^*,v^*) </math>. At this equilibrium, the players do not have anything to gain by changing their strategy, so this point is a stable state of the system. When the payoff matrix P is not known, we observe samples of actions <math> a^{(i)}, i =1,...,N </math> from one or both players, which depends on some external content <math> x </math>, sampled from the equilibrium strategies <math>(u^*,v^*) </math>, to recover the true underlying payoff matrix P or a function form P(x) depending on the current context.<br />
<br />
=== Quantal Response Equilibria ===<br />
<br />
However, NE is poorly suited because NEs are overly strict, discontinuous with respect to P, and may not be unique. To address these issues, model the players' actions with the '''quantal response equilibria''' (QRE), where noise is added to the payoff matric. Specifically, consider the ''logit'' equilibrium for zero-sum games that obeys the fixed point:<br />
$$<br />
u^* _i = \frac {exp(-Pv)_i}{\sum_{q \in [n]} exp (-Pv)_q}, \ v^* _j= \frac {exp(P^T u)_j}{\sum_{q \in [m]} exp (P^T u)_q} .\qquad \ (1)<br />
$$<br />
For a fixed opponent strategy, the logit equilibrium corresponding to a strategy is strictly convex, and thus the regularized best response is unique.<br />
<br />
=== End-to-End Learning ===<br />
<br />
Then to integrate zero-sum solver, [1] introduced a method to solve the QRE and to differentiate through its solution.<br />
<br />
'''QRE solver''':<br />
To find the fixed point in (1), it is equivalent to solve the regularized min-max game:<br />
$$<br />
\min_{u \in \mathbb{R}^n} \max_{v \in \mathbb{R}^m} \ u^T P v -H(v) + H(u) \\<br />
\text{subject to } 1^T u =1, \ 1^T v =1, <br />
$$<br />
where H(y) is the Gibbs entropy <math> \sum_i y_i log y_i</math>.<br />
Entropy regularization guarantees the non-negative condition and makes the equilibrium continuous with respect to P, which means players are encouraged to play more randomly, and all actions have non-zero probability. Moreover, this problem has a unique saddle point corresponding to <math> (u^*, v^*) </math>.<br />
<br />
Using a primal-dual Newton Method to solve the QRE for two-player zero-sum games, the KKT conditions for the problem are:<br />
$$ <br />
Pv + \log(u) + 1 +\mu 1 = 0 \\<br />
P^T v -\log(v) -1 +\nu 1 = 0 \\<br />
1^T u = 1, \ 1^T v = 1, <br />
$$<br />
where <math> (\mu, \nu) </math> are Lagrange multipliers for the equality constraints on u, v respectively. Then applying Newton's method gives the the update rule:<br />
$$<br />
Q \begin{bmatrix} \Delta u \\ \Delta v \\ \Delta \mu \\ \Delta \nu \\ \end{bmatrix} = - \begin{bmatrix} P v + \log u + 1 + \mu 1 \\ P^T u - \log v - 1 + \nu 1 \\ 1^T u - 1 \\ 1^T v - 1 \\ \end{bmatrix}, \qquad (2)<br />
$$<br />
where Q is the Hessian of the Lagrangian, given by <br />
$$ <br />
Q = \begin{bmatrix} <br />
diag(\frac{1}{u}) & P & 1 & 0 \\ <br />
P^T & -diag(\frac{1}{v}) & 0 & 1\\<br />
1^T & 0 & 0 & 0 \\<br />
0 & 1^T & 0 & 0 \\<br />
\end{bmatrix}. <br />
$$<br />
<br />
'''Differentiating Through QRE Solutions''':<br />
The QRE solver provides a method to compute the necessary Jacobian-vector products. Specifically, we compute the gradient of the loss given the solution <math> (u^*,v^*) </math> to the QRE, and some loss function <math> L(u^*,v^*) </math>: <br />
<br />
1. Take differentials of the KKT conditions: <br />
<math><br />
Q \begin{bmatrix} <br />
du & dv & d\mu & d\nu \\ <br />
\end{bmatrix} ^T = \begin{bmatrix} <br />
-dPv & -dP^Tu & 0 & 0 \\ <br />
\end{bmatrix}^T. \ <br />
</math><br />
<br />
2. For small changes du, dv, <br />
<math><br />
dL = \begin{bmatrix} <br />
v^TdP^T & u^TdP & 0 & 0 \\ <br />
\end{bmatrix} Q^{-1} \begin{bmatrix} <br />
-\nabla_u L & -\nabla_v L & 0 & 0 \\ <br />
\end{bmatrix}^T.<br />
</math><br />
<br />
3. Apply this to P, and take limits as dP is small:<br />
<math><br />
\nabla_P L = y_u v^T + u y_v^T, \qquad (3)<br />
</math> where <br />
<math><br />
\begin{bmatrix} <br />
y_u & y_v & y_{\mu} & y_{\nu}\\ <br />
\end{bmatrix}=Q^{-1}\begin{bmatrix} <br />
-\nabla_u L & -\nabla_v L & 0 & 0 \\ <br />
\end{bmatrix}^T.<br />
</math><br />
<br />
Hence, the forward pass is given by using the expression in (2) to solve for the logit equilibrium given P, and the backward pass is given by using <math> \nabla_u L </math> and <math> \nabla_v L </math> to obtain <math> \nabla_P L </math> using (3). There does not always exist a unique P which generates <math> u^*, v^* </math> under the logit QRE, and we cannot expect to recover P when under-constrained.<br />
<br />
== Learning Extensive form games ==<br />
<br />
The normal form representation for games where players have many choices quickly becomes intractable. For example, consider a chess game: One the first turn, player 1 has 20 possible moves and then player 2 has 20 possible responses. If in the following number of turns each player is estimated to have ~30 possible moves and if a typical game is 40 moves per player, the total number of strategies is roughly <math>10^{120} </math> per player (this is known as the Shannon number for game-tree complexity of chess) and so the payoff matrix for a typical game of chess must therefore have <math> O(10^{240}) </math> entries.<br />
<br />
Instead, it is much more useful to represent the game graphically as an "'''Extensive form game'''" (EFG). We'll also need to consider types of games where there is '''imperfect information''' - players do not necessarily have access to the full state of the game. An example of this is one-card poker: (1) Each player draws a single card from a 13-card deck (ignore suits) (2) Player 1 decides whether to bet/hold (3) Player 2 decides whether to call/raise (4) Player 1 must either call/fold if Player 2 raised. From this description, player 1 has <math> 2^{13} </math> possible first moves (all combinations of (card, raise/hold)) and has <math> 2^{13} </math> possible second moves (whenever player 1 gets a second move) for a total of <math> 2^{26} </math> possible strategies. In addition, Player 1 never knows what cards player 2 has and vice versa. So instead of representing the game with a huge payoff matrix we can instead represent it as a simple decision tree (for a ''single'' drawn card of player 1):<br />
<br />
<br />
<center> [[File:1cardpoker.PNG]] </center><br />
<br />
where player 1 is represented by "1", a node that has two branches corresponding to the allowed moves of player 1. However there must also be a notion of information available to either player: While this tree might correspond to say, player 1 holding a "9", it contains no information on what card player 2 is holding (and is much simpler because of this). This leads to the definition of an '''information set''': the set of all nodes belonging to a single player for which the other player cannot distinguish which node has been reached. The information set may therefore be treated as a node itself, for which actions stemming from the node must be chosen in ignorance to what the other player did immediately before arriving at the node. In the poker example, the full game tree consists of a much more complex version of the tree shown above (containing repetitions of the given tree for every possible combination of cards dealt) and the and an example of an information set for player 1 is the set of all of nodes owned by player 2 that immediately follow player 1's decision to hold. In other words, if player 1 holds there are 13 possible nodes describing the responses of player 2 (raise/hold for player 2 having card = ace, 1, ... King) and all 13 of these nodes are indistinguishable to player 1, and so form an information set for player 1.<br />
<br />
The following is a review of important concepts for extensive form games first formalized in [2]. Let <math> \mathcal{I}_i </math> be the set of all information sets for player i, and for each <math> t \in \mathcal{I}_i </math> let <math> \sigma_t </math> be the actions taken by player i to arrive at <math> t </math> and <math> C_t </math> be the actions that player i can take from <math> u </math>. Then the set of all possible sequences that can be taken by player i is given by<br />
<br />
$$<br />
S_i = \{\emptyset \} \cup \{ \sigma_t c | u\in \mathcal{I}_i, c \in C_t \}<br />
$$<br />
<br />
So for the one-card poker we would have <math>S_1 = \{\emptyset, \text{raise}, \text{hold}, \text{hold-call}, \text{hold-fold\} }</math>. From the possible sequences follows two important concepts:<br />
<ol><br />
<li>The EFG '''payoff matrix''' <math> P </math> is size <math>|S_1| \times |S_2| </math> (this is all possible actions available to either player), is populated with rewards from each leaf of the tree (or "zero" for each <math> (s_1, s_2) </math> that is an invalid pair), and the expected payoff for realization plans <math> (u, v) </math> is given by <math> u^T P v </math> </li><br />
<li> A '''realization plan''' <math> u \in \mathbb{R}^{|S_1|} </math> for player 1 (<math> v \in \mathbb{R}^{|S_2|} </math> for player 2 ) will describe probabilities for players to carry out each possible sequence, and each realization plan must be constrained by (i) compatibility of sequences (e.g. "raise" is not compatible with "hold-call") and (ii) information sets available to the player. These constraints are linear:<br />
<br />
$$<br />
Eu = e \\<br />
Fv = f<br />
$$<br />
<br />
where <math> e = f = (1, 0, ..., 0)^T </math> and <math> E, F</math> contain entries in <math> {-1, 0, 1} </math> describing compatibility and information sets. </li><br />
<br />
</ol> <br />
<br />
<br />
The paper's main contribution is to develop a minmax problem for extensive form games:<br />
<br />
<br />
$$<br />
\min_u \max_v u^T P v + \sum_{t\in \mathcal{I}_1} \sum_{c \in C_t} u_c \log \frac{u_c}{u_{p_t}} - \sum_{t\in \mathcal{I}_2} \sum_{c \in C_t} v_c \log \frac{v_c}{v_{p_t}}<br />
$$<br />
<br />
where <math> p_t </math> is the action immediately preceding information set <math> t </math>. Intuitively, each sum resembles a cross entropy over the distribution of probabilities in the realization plan comparing each probability to proceed from an information set to the probability to arrive at that information set. Importantly, these entropies are strictly convex or concave (for player 1 and player 2 respectively) [3] so that the minmax problem will have a unique solution and ''the objective function is continuous and continuously differntiable'' - this means there is a way to optimize the function. As noted in Theorem 1 of [1], the solution to this problem is equivalently a solution for the QRE of the game in reduced normal form.<br />
<br />
Having decided on a cost function, the method of Lagrange multipliers my be used to construct the Lagrangian that encodes the known constraints (<math> Eu = e \,, Fv = f </math>, and <math> u, v \geq 0</math>), and then optimize the Lagrangian using Newton's method (identically to the previous section). Accounting for the constraints, the Lagrangian becomes <br />
<br />
<br />
$$<br />
\mathcal{L} = g(u, v) + \sum_i \mu_i(Eu - e)_i + \sum_i \nu_i (Fv - f)_i<br />
$$<br />
<br />
where <math>g</math> is the argument from the minmax statement above and <math>u, v \geq 0</math> become KKT conditions. The general update rule for Newton's method may be written in terms of the derivatives of <math> \mathcal{L} </math> with respect to primal variables <math>u, v </math> and dual variables <math> \mu, \nu</math>, yielding:<br />
<br />
$$<br />
\nabla_{u,v,\mu,\nu}^2 \mathcal{L} \cdot (\Delta u, \Delta v, \Delta \mu, \Delta \nu)^T= - \nabla_{u,v,\mu,\nu} \mathcal{L}<br />
$$<br />
where <math>\nabla_{u,v,\mu,\nu}^2 \mathcal{L} </math> is the Hessian of the Lagrangian and <math>\nabla_{u,v,\mu,\nu} \mathcal{L} </math> is simply a column vector of the KKT stationarity conditions. Combined with the previous section, this completes the goal of the paper: To construct a differentiable problem for learning normal form and extensive form games.<br />
<br />
== Experiments ==<br />
<br />
The authors demonstrated learning on extensive form games in the presence of ''side information'', with ''partial observations'' using three experiments. In all cases, the goal was to maximize the likelihood of realizing an observed sequence from the player, assuming they act in accordance to the QRE.<br />
<br />
=== Rock, Paper, Scissors ===<br />
<br />
Rock, Paper, Scissors is a 2-player zero-sum game. For this game, the best strategy to reach a Nash equilibrium and a Quantal response equilibrium is to uniformly play each hand with equal odds.<br />
The first experiment was to learn a non-symmetric variant of Rock, Paper, Scissors with ''incomplete information'' with the following payoff matrix:<br />
<br />
{| class="wikitable" style="float:center; margin-left:1em; text-align:center;"<br />
|+ align="bottom"|''Payoff matrix of modified Rock-Paper-Scissors''<br />
! <br />
! ''Rock''<br />
! ''Paper''<br />
! ''Scissors''<br />
|-<br />
! ''Rock''<br />
| '''''0'''''<br />
| <math>-b_1</math><br />
| <math>b_2</math><br />
|-<br />
! ''Paper''<br />
| <math>b_1</math><br />
| '''''0'''''<br />
| <math>-b_3</math><br />
|-<br />
! ''Scissors''<br />
| <math>-b_2</math><br />
| <math>b_3</math><br />
| '''''0'''''<br />
|}<br />
<br />
where each of the <math> b </math> ’s are linear function of some features <math> x \in \mathbb{R}^{2} </math> (i.e., <math> b_y = x^Tw_y </math>, <math> y \in </math> {<math>1,2,3</math>} , where <math> w_y </math> are to be learned by the algorithm). Using many trials of random rewards the technique produced the following results for optimal strategies[1]: <br />
<br />
[[File:RPS Results.png|500px ]]<br />
<br />
From the graphs above, we can tell 1) both parameters learned and predicted strategies improve with larger dataset; and 2) with a reasonably sized dataset, >1000 here, convergence is stable and is fairly quick.<br />
<br />
=== One-Card Poker ===<br />
<br />
Next they investigated extensive form games using the one-Card Poker (with ''imperfect information'') introduced in the previous section. In the experimental setup, they used a deck stacked non-uniformly (meaning repeat cards were allowed). Their goal was to learn this distribution of cards from observations of many rounds of the play. Different from the distribution of cards dealt, the method built in the paper is more suited to learn the player’s perceived or believed distribution of cards. It may even be a function of contextual features such as demographics of players. Three experiments were run with <math> n=4 </math>. Each experiment comprised 5 runs of training, with same weights but different training sets. Let <math> d \in \mathbb{R}^{n}, d \ge 0, \sum_{i} d_i = 1 </math> be the weights of the cards. The probability that the players are dealt cards <math> (i,j) </math> is <math> \frac{d_i d_j}{1-d_i} </math>. This distribution is asymmetric between players. Matrix <math> P, E, F </math> for the case <math> n=4 </math> are presented in [1]. With training for 2500 epochs, the mean squared error of learned parameters (card weights, <math> u, v </math> ) are averaged over all runs of and are presented as following [1]: <br />
<br />
<br />
[[File:One-card_Poker_Results.png|500px ]]<br />
<br />
=== Security Resource Allocation Game ===<br />
<br />
<br />
From Security Resource Allocation Game, they demonstrated the ability to learn from ''imperfect observations''. The defender possesses <math> k </math> indistinguishable and indivisible defensive resources which he splits among <math> n </math> targets, { <math> T_1, ……, T_n </math>}. The attacker chooses one target. If the attack succeeds, the attacker gets <math> R_i </math> reward and defender gets <math> -R_i </math>, otherwise zero payoff for both. If there are n defenders guarding <math> T_i </math>, probability of successful attack on <math> T_i </math> is <math> \frac{1}{2^n} </math>. The expected payoff matrix when <math> n = 2, k = 3 </math>, where the attackers are the row players is:<br />
<br />
{| class="wikitable" style="float:center; margin-left:1em; text-align:center;"<br />
|+ align="bottom"|''Payoff matrix when <math> n = 2, k = 3 </math>''<br />
! {#<math>D_1</math>,#<math>D_2</math>}<br />
! {0, 3}<br />
! {1, 2}<br />
! {2, 1}<br />
! {3, 0}<br />
|-<br />
! <math>T_1</math><br />
| <math>-R_1</math><br />
| <math>-\frac{1}{2}R_1</math><br />
| <math>-\frac{1}{4}R_1</math><br />
| <math>-\frac{1}{8}R_1</math><br />
|-<br />
! <math>T_2</math><br />
| <math>-\frac{1}{8}R_2</math><br />
| <math>-\frac{1}{4}R_2</math><br />
| <math>-\frac{1}{2}R_2</math><br />
| <math>-R_2</math><br />
|} <br />
<br />
<br />
For a multi-stage game the attacker can launch <math> t </math> attacks, one in each stage while defender can only stick with stage 1. The attacker may change target if the attack in stage 1 is failed. Three experiments are run with <math> n = 2, k = 5 </math> for games with single attack and double attack, i.e, <math> t = 1 </math> and <math> t = 2 </math>. The results of simulated experiments are shown below [1]:<br />
<br />
[[File:Security Game Results.png|500px ]]<br />
<br />
<br />
They learned <math> R_i </math> only based on observations of the defender’s actions and could still recover the game setting by only observing the defender’s actions. Same as expectation, the larger dataset size improves the learned parameters. Two outliers are 1) Security Game, the green plot for when <math> t = 2 </math>; and 2) RPS, when comparing between training sizes of 2000 and 5000.<br />
<br />
== Conclusion ==<br />
Unsurprisingly, the results of this study show that in general the quality of learned parameters improved as the number of observations increased. The network presented in this paper demonstrated improvement over existing methodology. <br />
<br />
This paper presents an end-to-end framework for implementing a game solver, for both extensive and normal form, as a module in a deep neural network for zero-sum games. This method, unlike many previous works in this area, does not require the parameters of the game to be known to the agent prior to the start of the game. The two-part method analytically computes both the optimal solution and the parameters of the game. Future work involves taking advantage of the KKT matrix structure to increase computation speed, and extensions to the area of learning general-sum games.<br />
<br />
== Critiques ==<br />
The proposed method appears to suffer from two flaws. Firstly, the assumption that players behave in accordance to the QRE severely limits the space of player strategies, and is known to exhibit pathological behaviour even in one-player settings. Second, the solvers are computationally inefficient and are unable to scale.<br />
<br />
== References ==<br />
<br />
[1] Ling, C. K., Fang, F., & Kolter, J. Z. (2018). What game are we playing? end-to-end learning in normal and extensive form games. arXiv preprint arXiv:1805.02777.<br />
<br />
[2] B. von Stengel. Efficient computation of behavior strategies.Games and Economics Behavior,14(0050):220–246, 1996.<br />
<br />
[3] Boyd, S., Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=what_game_are_we_playing&diff=45597what game are we playing2020-11-21T21:33:04Z<p>Q58yu: /* Rock, Paper, Scissors */</p>
<hr />
<div>== Authors == <br />
Yuxin Wang, Evan Peters, Yifan Mou, Sangeeth Kalaichanthiran <br />
<br />
== Introduction ==<br />
Recently, there have been many different studies of methods using AI to solve large-scale, zero-sum, extensive form problems. However, most of these works operate under the assumption that the parameters of the game are known, and the objective is just finding the optimal strategy for the game. This scenario is unrealistic since most of the time parameters of the game are unknown. This paper proposes a framework for finding an optimal solution using a primal-dual Newton Method and then using back-propagation to analytically compute the gradients of all the relevant game parameters.<br />
<br />
The approach to solving this problem is to consider ''quantal response equilibrium'' (QRE), which is a generalization of Nash equilibrium (NE) where the agents can make suboptimal decisions. It is shown that the solution to the QRE is a differentiable function of the payoff matrix. Consequently, back-propagation can be used to analytically solve for the payoff matrix (or other game parameters). This strategy has many future application areas as it allows for game-solving (both extensive and normal form) to be integrated as a module in a deep neural network.<br />
<br />
An example of architecture is presented below:<br />
<br />
[[File:Framework.png ]]<br />
<br />
Payoff matrix <math> P </math> is parameterized by a domain-dependent low dimensional vector <math> \phi </math>, which <math> \phi </math> depends on a differentiable function <math> M_1(x) </math>. Furthermore, <math> P </math> is applied to QRE to get the equilibrium strategies <math> (u^∗, v^∗) </math>. Lastly, loss function is calculated after applying through any differentiable <math> M_2(u^∗, v^∗) </math>.<br />
<br />
The effectiveness of this model is demonstrated using the games “Rock, Paper, Scissors”, one-card poker, and a security defense game.<br />
<br />
== Learning and Quantal Response in Normal Form Games ==<br />
<br />
The game-solving module provides all elements required in differentiable learning, which maps contextual features to payoff matrices, and computes equilibrium strategies under a set of contextual features. This paper will learn zero-sum games and start with normal form games since they have game solver and learning approach capturing much of intuition and basic methodology.<br />
<br />
=== Zero-Sum Normal Form Games ===<br />
<br />
In two-player zero-sum games there is a '''payoff matrix''' <math>P</math> that describes the rewards for two players employing specific strategies u and v respectively. The optimal strategy mixture may be found with a classic min-max formulation:<br />
$$\min_u \max_v \ u^T P v \\ subject \ to \ 1^T u =1, u \ge 0 \\ 1^T v =1, v \ge 0. \ $$<br />
<br />
Here, we consider the case where <math>P</math> is not known a priori. The solution <math> (u^*, v_0) </math> to this optimization and the solution <math> (u_0,v^*) </math> to the corresponding problem with inverse player order form the Nash equilibrium <math>(u^*,v^*) </math>. At this equilibrium, the players do not have anything to gain by changing their strategy, so this point is a stable state of the system. When the payoff matrix P is not known, we observe samples of actions <math> a^{(i)}, i =1,...,N </math> from one or both players, which depends on some external content <math> x </math>, sampled from the equilibrium strategies <math>(u^*,v^*) </math>, to recover the true underlying payoff matrix P or a function form P(x) depending on the current context.<br />
<br />
=== Quantal Response Equilibria ===<br />
<br />
However, NE is poorly suited because NEs are overly strict, discontinuous with respect to P, and may not be unique. To address these issues, model the players' actions with the '''quantal response equilibria''' (QRE), where noise is added to the payoff matric. Specifically, consider the ''logit'' equilibrium for zero-sum games that obeys the fixed point:<br />
$$<br />
u^* _i = \frac {exp(-Pv)_i}{\sum_{q \in [n]} exp (-Pv)_q}, \ v^* _j= \frac {exp(P^T u)_j}{\sum_{q \in [m]} exp (P^T u)_q} .\qquad \ (1)<br />
$$<br />
For a fixed opponent strategy, the logit equilibrium corresponding to a strategy is strictly convex, and thus the regularized best response is unique.<br />
<br />
=== End-to-End Learning ===<br />
<br />
Then to integrate zero-sum solver, [1] introduced a method to solve the QRE and to differentiate through its solution.<br />
<br />
'''QRE solver''':<br />
To find the fixed point in (1), it is equivalent to solve the regularized min-max game:<br />
$$<br />
\min_{u \in \mathbb{R}^n} \max_{v \in \mathbb{R}^m} \ u^T P v -H(v) + H(u) \\<br />
\text{subject to } 1^T u =1, \ 1^T v =1, <br />
$$<br />
where H(y) is the Gibbs entropy <math> \sum_i y_i log y_i</math>.<br />
Entropy regularization guarantees the non-negative condition and makes the equilibrium continuous with respect to P, which means players are encouraged to play more randomly, and all actions have non-zero probability. Moreover, this problem has a unique saddle point corresponding to <math> (u^*, v^*) </math>.<br />
<br />
Using a primal-dual Newton Method to solve the QRE for two-player zero-sum games, the KKT conditions for the problem are:<br />
$$ <br />
Pv + \log(u) + 1 +\mu 1 = 0 \\<br />
P^T v -\log(v) -1 +\nu 1 = 0 \\<br />
1^T u = 1, \ 1^T v = 1, <br />
$$<br />
where <math> (\mu, \nu) </math> are Lagrange multipliers for the equality constraints on u, v respectively. Then applying Newton's method gives the the update rule:<br />
$$<br />
Q \begin{bmatrix} \Delta u \\ \Delta v \\ \Delta \mu \\ \Delta \nu \\ \end{bmatrix} = - \begin{bmatrix} P v + \log u + 1 + \mu 1 \\ P^T u - \log v - 1 + \nu 1 \\ 1^T u - 1 \\ 1^T v - 1 \\ \end{bmatrix}, \qquad (2)<br />
$$<br />
where Q is the Hessian of the Lagrangian, given by <br />
$$ <br />
Q = \begin{bmatrix} <br />
diag(\frac{1}{u}) & P & 1 & 0 \\ <br />
P^T & -diag(\frac{1}{v}) & 0 & 1\\<br />
1^T & 0 & 0 & 0 \\<br />
0 & 1^T & 0 & 0 \\<br />
\end{bmatrix}. <br />
$$<br />
<br />
'''Differentiating Through QRE Solutions''':<br />
The QRE solver provides a method to compute the necessary Jacobian-vector products. Specifically, we compute the gradient of the loss given the solution <math> (u^*,v^*) </math> to the QRE, and some loss function <math> L(u^*,v^*) </math>: <br />
<br />
1. Take differentials of the KKT conditions: <br />
<math><br />
Q \begin{bmatrix} <br />
du & dv & d\mu & d\nu \\ <br />
\end{bmatrix} ^T = \begin{bmatrix} <br />
-dPv & -dP^Tu & 0 & 0 \\ <br />
\end{bmatrix}^T. \ <br />
</math><br />
<br />
2. For small changes du, dv, <br />
<math><br />
dL = \begin{bmatrix} <br />
v^TdP^T & u^TdP & 0 & 0 \\ <br />
\end{bmatrix} Q^{-1} \begin{bmatrix} <br />
-\nabla_u L & -\nabla_v L & 0 & 0 \\ <br />
\end{bmatrix}^T.<br />
</math><br />
<br />
3. Apply this to P, and take limits as dP is small:<br />
<math><br />
\nabla_P L = y_u v^T + u y_v^T, \qquad (3)<br />
</math> where <br />
<math><br />
\begin{bmatrix} <br />
y_u & y_v & y_{\mu} & y_{\nu}\\ <br />
\end{bmatrix}=Q^{-1}\begin{bmatrix} <br />
-\nabla_u L & -\nabla_v L & 0 & 0 \\ <br />
\end{bmatrix}^T.<br />
</math><br />
<br />
Hence, the forward pass is given by using the expression in (2) to solve for the logit equilibrium given P, and the backward pass is given by using <math> \nabla_u L </math> and <math> \nabla_v L </math> to obtain <math> \nabla_P L </math> using (3). There does not always exist a unique P which generates <math> u^*, v^* </math> under the logit QRE, and we cannot expect to recover P when under-constrained.<br />
<br />
== Learning Extensive form games ==<br />
<br />
The normal form representation for games where players have many choices quickly becomes intractable. For example, consider a chess game: One the first turn, player 1 has 20 possible moves and then player 2 has 20 possible responses. If in the following number of turns each player is estimated to have ~30 possible moves and if a typical game is 40 moves per player, the total number of strategies is roughly <math>10^{120} </math> per player (this is known as the Shannon number for game-tree complexity of chess) and so the payoff matrix for a typical game of chess must therefore have <math> O(10^{240}) </math> entries.<br />
<br />
Instead, it is much more useful to represent the game graphically as an "'''Extensive form game'''" (EFG). We'll also need to consider types of games where there is '''imperfect information''' - players do not necessarily have access to the full state of the game. An example of this is one-card poker: (1) Each player draws a single card from a 13-card deck (ignore suits) (2) Player 1 decides whether to bet/hold (3) Player 2 decides whether to call/raise (4) Player 1 must either call/fold if Player 2 raised. From this description, player 1 has <math> 2^{13} </math> possible first moves (all combinations of (card, raise/hold)) and has <math> 2^{13} </math> possible second moves (whenever player 1 gets a second move) for a total of <math> 2^{26} </math> possible strategies. In addition, Player 1 never knows what cards player 2 has and vice versa. So instead of representing the game with a huge payoff matrix we can instead represent it as a simple decision tree (for a ''single'' drawn card of player 1):<br />
<br />
<br />
<center> [[File:1cardpoker.PNG]] </center><br />
<br />
where player 1 is represented by "1", a node that has two branches corresponding to the allowed moves of player 1. However there must also be a notion of information available to either player: While this tree might correspond to say, player 1 holding a "9", it contains no information on what card player 2 is holding (and is much simpler because of this). This leads to the definition of an '''information set''': the set of all nodes belonging to a single player for which the other player cannot distinguish which node has been reached. The information set may therefore be treated as a node itself, for which actions stemming from the node must be chosen in ignorance to what the other player did immediately before arriving at the node. In the poker example, the full game tree consists of a much more complex version of the tree shown above (containing repetitions of the given tree for every possible combination of cards dealt) and the and an example of an information set for player 1 is the set of all of nodes owned by player 2 that immediately follow player 1's decision to hold. In other words, if player 1 holds there are 13 possible nodes describing the responses of player 2 (raise/hold for player 2 having card = ace, 1, ... King) and all 13 of these nodes are indistinguishable to player 1, and so form an information set for player 1.<br />
<br />
The following is a review of important concepts for extensive form games first formalized in [2]. Let <math> \mathcal{I}_i </math> be the set of all information sets for player i, and for each <math> t \in \mathcal{I}_i </math> let <math> \sigma_t </math> be the actions taken by player i to arrive at <math> t </math> and <math> C_t </math> be the actions that player i can take from <math> u </math>. Then the set of all possible sequences that can be taken by player i is given by<br />
<br />
$$<br />
S_i = \{\emptyset \} \cup \{ \sigma_t c | u\in \mathcal{I}_i, c \in C_t \}<br />
$$<br />
<br />
So for the one-card poker we would have <math>S_1 = \{\emptyset, \text{raise}, \text{hold}, \text{hold-call}, \text{hold-fold\} }</math>. From the possible sequences follows two important concepts:<br />
<ol><br />
<li>The EFG '''payoff matrix''' <math> P </math> is size <math>|S_1| \times |S_2| </math> (this is all possible actions available to either player), is populated with rewards from each leaf of the tree (or "zero" for each <math> (s_1, s_2) </math> that is an invalid pair), and the expected payoff for realization plans <math> (u, v) </math> is given by <math> u^T P v </math> </li><br />
<li> A '''realization plan''' <math> u \in \mathbb{R}^{|S_1|} </math> for player 1 (<math> v \in \mathbb{R}^{|S_2|} </math> for player 2 ) will describe probabilities for players to carry out each possible sequence, and each realization plan must be constrained by (i) compatibility of sequences (e.g. "raise" is not compatible with "hold-call") and (ii) information sets available to the player. These constraints are linear:<br />
<br />
$$<br />
Eu = e \\<br />
Fv = f<br />
$$<br />
<br />
where <math> e = f = (1, 0, ..., 0)^T </math> and <math> E, F</math> contain entries in <math> {-1, 0, 1} </math> describing compatibility and information sets. </li><br />
<br />
</ol> <br />
<br />
<br />
The paper's main contribution is to develop a minmax problem for extensive form games:<br />
<br />
<br />
$$<br />
\min_u \max_v u^T P v + \sum_{t\in \mathcal{I}_1} \sum_{c \in C_t} u_c \log \frac{u_c}{u_{p_t}} - \sum_{t\in \mathcal{I}_2} \sum_{c \in C_t} v_c \log \frac{v_c}{v_{p_t}}<br />
$$<br />
<br />
where <math> p_t </math> is the action immediately preceding information set <math> t </math>. Intuitively, each sum resembles a cross entropy over the distribution of probabilities in the realization plan comparing each probability to proceed from an information set to the probability to arrive at that information set. Importantly, these entropies are strictly convex or concave (for player 1 and player 2 respectively) [3] so that the minmax problem will have a unique solution and ''the objective function is continuous and continuously differntiable'' - this means there is a way to optimize the function. As noted in Theorem 1 of [1], the solution to this problem is equivalently a solution for the QRE of the game in reduced normal form.<br />
<br />
Having decided on a cost function, the method of Lagrange multipliers my be used to construct the Lagrangian that encodes the known constraints (<math> Eu = e \,, Fv = f </math>, and <math> u, v \geq 0</math>), and then optimize the Lagrangian using Newton's method (identically to the previous section). Accounting for the constraints, the Lagrangian becomes <br />
<br />
<br />
$$<br />
\mathcal{L} = g(u, v) + \sum_i \mu_i(Eu - e)_i + \sum_i \nu_i (Fv - f)_i<br />
$$<br />
<br />
where <math>g</math> is the argument from the minmax statement above and <math>u, v \geq 0</math> become KKT conditions. The general update rule for Newton's method may be written in terms of the derivatives of <math> \mathcal{L} </math> with respect to primal variables <math>u, v </math> and dual variables <math> \mu, \nu</math>, yielding:<br />
<br />
$$<br />
\nabla_{u,v,\mu,\nu}^2 \mathcal{L} \cdot (\Delta u, \Delta v, \Delta \mu, \Delta \nu)^T= - \nabla_{u,v,\mu,\nu} \mathcal{L}<br />
$$<br />
where <math>\nabla_{u,v,\mu,\nu}^2 \mathcal{L} </math> is the Hessian of the Lagrangian and <math>\nabla_{u,v,\mu,\nu} \mathcal{L} </math> is simply a column vector of the KKT stationarity conditions. Combined with the previous section, this completes the goal of the paper: To construct a differentiable problem for learning normal form and extensive form games.<br />
<br />
== Experiments ==<br />
<br />
The authors demonstrated learning on extensive form games in the presence of ''side information'', with ''partial observations'' using three experiments. In all cases, the goal was to maximize the likelihood of realizing an observed sequence from the player, assuming they act in accordance to the QRE.<br />
<br />
=== Rock, Paper, Scissors ===<br />
<br />
Rock, Paper, Scissors is a 2-player zero-sum game. For this game, the best strategy to reach a Nash equilibrium and a Quantal response equilibrium is to uniformly play each hand with equal odds.<br />
The first experiment was to learn a non-symmetric variant of Rock, Paper, Scissors with ''incomplete information'' with the following payoff matrix:<br />
<br />
{| class="wikitable" style="float:center; margin-left:1em; text-align:center;"<br />
|+ align="bottom"|''Payoff matrix of modified Rock-Paper-Scissors''<br />
! <br />
! ''Rock''<br />
! ''Paper''<br />
! ''Scissors''<br />
|-<br />
! ''Rock''<br />
| '''''0'''''<br />
| <math>-b_1</math><br />
| <math>b_2</math><br />
|-<br />
! ''Paper''<br />
| <math>b_1</math><br />
| '''''0'''''<br />
| <math>-b_3</math><br />
|-<br />
! ''Scissors''<br />
| <math>-b_2</math><br />
| <math>b_3</math><br />
| '''''0'''''<br />
|}<br />
<br />
where each of the <math> b </math> ’s are linear function of some features <math> x \in \mathbb{R}^{2} </math> (i.e., <math> b_y = x^Tw_y </math>, <math> y \in </math> {<math>1,2,3</math>} , where <math> w_y </math> are to be learned by the algorithm). Using many trials of random rewards the technique produced the following results for optimal strategies[1]: <br />
<br />
[[File:RPS Results.png|500px ]]<br />
<br />
From the graphs above, we can tell 1) both parameters learned and predicted strategies improve with larger dataset; and 2) with a reasonably sized dataset, >1000 here, convergence is stable and is fairly quick.<br />
<br />
=== One-Card Poker ===<br />
<br />
Next they investigated extensive form games using the one-Card Poker (with ''imperfect information'') introduced in the previous section. In the experimental setup, they used a deck stacked non-uniformly (meaning repeat cards were allowed). Their goal was to learn this distribution of cards from observations of many rounds of the play. In this case, they needed to know the player’s perceived or believed distribution of cards may be different from the distribution of cards dealt. Three experiments were run with <math> n=4 </math>. Each experiment comprised 5 runs of training, with same weights but different training sets. Let <math> d \in \mathbb{R}^{n}, d \ge 0, \sum_{i} d_i = 1 </math> be the weights of the cards. The probability that the players are dealt cards <math> (i,j) </math> is <math> \frac{d_i d_j}{1-d_i} </math>. This distribution is asymmetric between players. Matrix <math> P, E, F </math> for the case <math> n=4 </math> are presented in [1]. With training for 2500 epochs, the mean squared error of learned parameters (card weights, <math> u, v </math> ) are averaged over all runs of and are presented as following [1]: <br />
<br />
<br />
[[File:One-card_Poker_Results.png|500px ]]<br />
<br />
=== Security Resource Allocation Game ===<br />
<br />
<br />
From Security Resource Allocation Game, they demonstrated the ability to learn from ''imperfect observations''. The defender possesses <math> k </math> indistinguishable and indivisible defensive resources which he splits among <math> n </math> targets, { <math> T_1, ……, T_n </math>}. The attacker chooses one target. If the attack succeeds, the attacker gets <math> R_i </math> reward and defender gets <math> -R_i </math>, otherwise zero payoff for both. If there are n defenders guarding <math> T_i </math>, probability of successful attack on <math> T_i </math> is <math> \frac{1}{2^n} </math>. The expected payoff matrix when <math> n = 2, k = 3 </math>, where the attackers are the row players is:<br />
<br />
{| class="wikitable" style="float:center; margin-left:1em; text-align:center;"<br />
|+ align="bottom"|''Payoff matrix when <math> n = 2, k = 3 </math>''<br />
! {#<math>D_1</math>,#<math>D_2</math>}<br />
! {0, 3}<br />
! {1, 2}<br />
! {2, 1}<br />
! {3, 0}<br />
|-<br />
! <math>T_1</math><br />
| <math>-R_1</math><br />
| <math>-\frac{1}{2}R_1</math><br />
| <math>-\frac{1}{4}R_1</math><br />
| <math>-\frac{1}{8}R_1</math><br />
|-<br />
! <math>T_2</math><br />
| <math>-\frac{1}{8}R_2</math><br />
| <math>-\frac{1}{4}R_2</math><br />
| <math>-\frac{1}{2}R_2</math><br />
| <math>-R_2</math><br />
|} <br />
<br />
<br />
For a multi-stage game the attacker can launch <math> t </math> attacks, one in each stage while defender can only stick with stage 1. The attacker may change target if the attack in stage 1 is failed. Three experiments are run with <math> n = 2, k = 5 </math> for games with single attack and double attack, i.e, <math> t = 1 </math> and <math> t = 2 </math>. The results of simulated experiments are shown below [1]:<br />
<br />
[[File:Security Game Results.png|500px ]]<br />
<br />
<br />
They learned <math> R_i </math> only based on observations of the defender’s actions and could still recover the game setting by only observing the defender’s actions. Same as expectation, the larger dataset size improves the learned parameters. Two outliers are 1) Security Game, the green plot for when <math> t = 2 </math>; and 2) RPS, when comparing between training sizes of 2000 and 5000.<br />
<br />
== Conclusion ==<br />
Unsurprisingly, the results of this study show that in general the quality of learned parameters improved as the number of observations increased. The network presented in this paper demonstrated improvement over existing methodology. <br />
<br />
This paper presents an end-to-end framework for implementing a game solver, for both extensive and normal form, as a module in a deep neural network for zero-sum games. This method, unlike many previous works in this area, does not require the parameters of the game to be known to the agent prior to the start of the game. The two-part method analytically computes both the optimal solution and the parameters of the game. Future work involves taking advantage of the KKT matrix structure to increase computation speed, and extensions to the area of learning general-sum games.<br />
<br />
== Critiques ==<br />
The proposed method appears to suffer from two flaws. Firstly, the assumption that players behave in accordance to the QRE severely limits the space of player strategies, and is known to exhibit pathological behaviour even in one-player settings. Second, the solvers are computationally inefficient and are unable to scale.<br />
<br />
== References ==<br />
<br />
[1] Ling, C. K., Fang, F., & Kolter, J. Z. (2018). What game are we playing? end-to-end learning in normal and extensive form games. arXiv preprint arXiv:1805.02777.<br />
<br />
[2] B. von Stengel. Efficient computation of behavior strategies.Games and Economics Behavior,14(0050):220–246, 1996.<br />
<br />
[3] Boyd, S., Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Gtompkin&diff=45591User:Gtompkin2020-11-21T20:56:57Z<p>Q58yu: /* Experimental Results */</p>
<hr />
<div>== Presented by == <br />
Grace Tompkins, Tatiana Krikella, Swaleh Hussain<br />
<br />
== Introduction ==<br />
<br />
One of the fundamental challenges in machine learning and data science is dealing with missing and incomplete data. This paper proposes theoretically justified methodology for using incomplete data in neural networks, eliminating the need for direct completion of the data by imputation or other commonly used methods in existing literature. The authors propose identifying missing data points with a parametric density and then training it together with the rest of the network's parameters. The neuron's response at the first hidden layer is generalized by taking its expected value to process this probabilistic representation. This process is essentially calculating the average activation of the neuron over imputations drawn from the missing data's density. The proposed approach is advantageous as it has the ability to train neural networks using incomplete observations from datasets, which are ubiquitous in practice. This approach also requires minimal adjustments and modifications to existing architectures. Theoretical results of this study show that this process does not lead to a loss of information, while experimental results showed the practical uses of this methodology on several different types of networks.<br />
<br />
== Related Work ==<br />
<br />
Currently, dealing with incomplete inputs in machine learning requires filling absent attributes based on complete, observed data. Two commonly used methods are mean imputation and k-NN imputation. Other methods for dealing with missing data involve training separate neural networks, extreme learning machines, and <math>k</math>-nearest neighbours. Probabilistic models of incomplete data can also be built depending on the mechanism missingness (i.e. whether the data is Missing At Random (MAR), Missing Completely At Random (MCAR), or Missing Not At Random (MNAR)), which can be fed into a particular learning model. Further, the decision function can also be trained using available/visible inputs alone. Previous work using neural networks for missing data includes a paper by Bengio and Gringras [1] where the authors used recurrent neural networks with feedback into the input units to fill absent attributes solely to minimize the learning criterion. Goodfellow et. al. [2] also used neural networks by introducing a multi-prediction deep Boltzmann machine which could perform classification on data with missingness in the inputs.<br />
<br />
== Layer for Processing Missing Data ==<br />
<br />
In this approach, the adaptation of a given neural network to incomplete data relies on two steps: the estimation of the missing data and the generalization of the neuron's activation. <br />
<br />
Let <math>(x,J)</math> represent a missing data point, where <math>x \in \mathbb{R}^D </math>, and <math>J \subset \{1,...,D\} </math> is a set of attributes with missing data. <math>(x,J)</math> therefore represents an "incomplete" data point for which <math>|J|</math>-many entries are unknown - examples of this could be a list of daily temperature readings over a week where temperature was not recorded on the third day (<math>x\in \mathbb{R}^7, J= \{3\}</math>), an audio transcript that goes silent for certain timespans, or images that are partially masked out (as discussed in the examples).<br />
<br />
For each missing point <math>(x,J)</math>, define an affine subspace consisting of all points which coincide with <math>x</math> on known coordinates <math>J'=\{1,…,N\}/J</math>: <br />
<br />
<center><math>S=Aff[x,J]=span(e_J) </math></center> <br />
where <math>e_J=[e_j]_{j\in J}</math> and <math>e_j</math> is the <math> j^{th}</math> canonical vector in <math>\mathbb{R}^D </math>.<br />
<br />
Assume that the missing data points come from the D-dimensional probability distribution, <math>F</math>. In their approach, the authors assume that the data points follow a mixture of Gaussians (GMM) with diagonal covariance matrices. By choosing diagonal covariance matrices, the number of model parameters is reduced. To model the missing points <math>(x,J)</math>, the density <math>F</math> is restricted to the affine subspace <math>S</math>. Thus, possible values of <math>(x,J)</math> are modelled using the conditional density <math>F_S: S \to \mathbb{R} </math>, <br />
<br />
<center><math>F_S(x) = \begin{cases}<br />
\frac{1}{\int_{S} F(s) \,ds}F(x) & \text{if $x \in S$,} \\<br />
0 & \text{otherwise.}<br />
\end{cases} </math></center><br />
<br />
To process the missing data by a neural network, the authors propose that only the first hidden layer needs modification. Specifically, they generalize the activation functions of all the neurons in the first hidden layer of the network to process the probability density functions representing the missing data points. For the conditional density function <math>F_S</math>, the authors define the generalized activation of a neuron <math>n: \mathbb{R}^D \to \mathbb{R}</math> on <math>F_S </math> as: <br />
<br />
<center><math>n(F_S)=E[n(x)|x \sim F_S]=\int n(x)F_S(x) \,dx</math>,</center> <br />
provided that the expectation exists. <br />
<br />
The following two theorems describe how to apply the above generalizations to both the ReLU and the RBF neurons, respectively. <br />
<br />
'''Theorem 3.1''' Let <math>F = \sum_i{p_iN(m_i, \Sigma_i)}</math> be the mixture of (possibly degenerate) Gaussians. Given weights <math>w=(w_1, ..., w_D) \in \mathbb{R}^D,</math><math> b \in \mathbb{R} </math>, we have<br />
<br />
<center><math>\text{ReLU}_{w,b}(F)=\sum_i{p_iNR\big(\frac{w^{\top}m_i+b}{\sqrt{w^{\top}\Sigma_iw}}}\big)</math></center> <br />
<br />
where <math>NR(x)=\text{ReLU}[N(x,1)]</math> and <math>\text{ReLU}_{w,b}(x)=\text{max}(w^{\top}+b, 0)</math>, <math>w \in \mathbb{R}^D </math> and <math> b \in \mathbb{R}</math> is the bias.<br />
<br />
'''Theorem 3.2''' Let <math>F = \sum_i{p_iN(m_i, \Sigma_i)}</math> be the mixture of (possibly degenerate) Gaussians and let the RBF unit be parametrized by <math>N(c, \Gamma) </math>. We have: <br />
<br />
<center><math>\text{RBF}_{c, \Gamma}(F) = \sum_{i=1}^k{p_iN(m_i-c, \Gamma+\Sigma_i)}(0)</math>.</center> <br />
<br />
In the case where the data set contains no missing values, the generalized neurons reduce to classical ones, since the distribution <math>F</math> is only used to estimate possible values at missing attributes. However, if one wishes to use an incomplete data set in the testing stage, then an incomplete data set must be used to train the model.<br />
<br />
<math> </math><br />
<br />
== Theoretical Analysis ==<br />
<br />
The main theoretical results, which are summarized below, show that using generalized neuron's activation at the first layer does not lead to the loss of information. <br />
<br />
Let the generalized response of a neuron <math>n: \mathbb{R}^D \rightarrow \mathbb{R}</math> evaluated on a probability measure <math>\mu</math> which is given by <br />
<center><math>n(\mu) := \int n(x)d\mu(x)</math></center>.<br />
<br />
Theorem 4.1 shows that a neural network with generalized ReLU units is able to identify any two probability measures. The proof presented by the authors uses the Universal Approximation Property (UAP), and is summarized as follows. <br />
<br />
<br />
'''Theorem 4.1.''' Let <math>\mu</math>, <math>v</math> be probabilistic measures satisfying <math>\int ||x|| d \mu(x) < \infty</math>. If <br />
<center><math>ReLU_{w,b}(\mu) = ReLU_{w,b}(\nu) \text{ for } w \in \mathbb{R}^D, b \in \mathbb{R}</math></center> then <math>\nu = \mu.</math><br />
<br />
''Sketch of Proof'' Let <math>w \in \mathbb{R}^D</math> be fixed and define the set <center><math>F_w = \{p: \mathbb{R} \rightarrow \mathbb{R}: \int p(w^Tx)d\mu(x) = \int p(w^Tx)d\nu(x)\}.</math></center> The first step of the proof involves showing that <math>F_w</math> contains all continuous and bounded functions. The authors show this by showing that a piecewise continuous function that is affine linear on specific intervals, <math>Q</math>, is in the set <math>F_w</math>. This involves re-writing <math>Q</math> as a sum of tent-like piecewise linear functions, <math>T</math> and showing that <math>T \in F_w</math> (since it is sufficient to only show <math>T \in F_w</math>). <br />
<br />
Next, the authors show that an arbitrary bounded continuous function <math>G</math> is in <math>F_w</math> by the Lebesgue dominated convergence theorem. <br />
<br />
Then, as <math>cos(\cdot), sin(\cdot) \in F_w</math>, the function <center><math>exp(ir) = cos(r) + i sin(r) \in F_w</math></center> and we have the equality <center><math>\int exp(iw^Tx)d\mu(x) = \int exp(iw^Tx)d\nu(x).</math></center> Since <math>w</math> was arbitrarily chosen, we can conclude that <math>\mu = \nu</math> <br />
as the characteristic functions of the two measures coincide. <br />
<br />
<br />
More general results can be obtained making stronger assumptions on the probability measures, for example, if a given family of neurons satisfies UAP, then their generalization can identify any probability measure with compact support.<br />
<br />
== Experimental Results ==<br />
The model was applied to three types of algorithms: an Autoencoder (AE), a multilayer perceptron, and a radial basis function network.<br />
<br />
'''Autoencoder'''<br />
<br />
Corrupted images were restored as a part of this experiment. Grayscale handwritten digits were obtained from the MNIST database. A 13 by 13 (169 pixels) square was removed from each 28 by 28 (784 pixels) image. The location of the square was uniformly sampled for each image. The autoencoder used included 5 hidden layers. The first layer used ReLU activation functions while the subsequent layers utilized sigmoids. The loss function was computed using pixels from outside the mask. <br />
<br />
Popular imputation techniques were compared against the conducted experiment:<br />
<br />
''k-nn:'' Replaced missing features with the mean of respective features calculated using K nearest training samples. Here, K=5. <br />
<br />
''mean:'' Replaced missing features with the mean of respective features calculated using all incomplete training samples.<br />
<br />
''dropout:'' Dropped input neutrons with missing values. <br />
<br />
Moreover, a context encoder (CE) was trained by replacing missing features with their means. Unlike mean imputation, the complete data was used in the training phase. The method under study performed better than the imputation methods inside and outside the mask. Additionally, the method under study outperformed CE based on the whole area and area outside the mask. <br />
<br />
The mean square error of reconstruction is used to test each method. The errors calculated over the whole area, inside and outside the mask are shown in Table 1, which indicates the method introduced in this paper is the most competitive.<br />
<br />
[[File:Group3_Table1.png |center]]<br />
<div align="center">Table 1: Mean square error of reconstruction on MNIST incomplete images scaled to [0, 1]</div><br />
<br />
'''Multilayer Perceptron'''<br />
<br />
A multilayer perceptron with 3 ReLU hidden layers was applied to a multi-class classification problem on the Epileptic Seizure Recognition (ESR) data set taken from [3]. Each 178-dimensional vector (out of 11500 samples) is the EEG recording of a given person for 1 second, categorized into one of 5 classes. To generate missing attributes, 25%, 50%, 75%, and 90% of observations were randomly removed. The aforementioned imputation methods were used in addition to Multiple Imputation by Chained Equation (mice) and a mixture of Gaussians (gmm). The former utilizes the conditional distribution of data by Markov chain Monte Carlo techniques to draw imputations. The latter replaces missing features with values sampled from GMM estimated from incomplete data using the EM algorithm. <br />
<br />
Double 5-fold cross-validation was used to report classification results. The model under study outperformed classical imputation methods, which give reasonable results only for a low number of missing values. The method under study performs nearly as well as CE, even though CE had access to complete training data. <br />
<br />
'''Radial Basis Function Network'''<br />
<br />
RBFN can be considered as a minimal architecture implementing our model, which contains only one hidden layer. A cross-entropy function was applied to a softmax in the output layer. Two-class data sets retrieved from the UCI repository [4] with internally missing attributes were used. Since the classification is binary, two additional SVM kernel models which work directly with incomplete data without performing any imputations were included in the experiment:<br />
<br />
''geom:'' The objective function is based on the geometric interpretation of the margin and aims to maximize the margin of each sample in its own subspace [5].<br />
<br />
''karma:'' This algorithm iteratively tunes kernel classifier under low-rank assumptions [6].<br />
<br />
The above SVM methods were combined with RBF kernel function. The number of RBF units was selected in the inner cross-validation from the range {25, 50, 75, 100}. Initial centers of RBFNs were randomly selected from training data while variances were samples from N(0,1) distribution. For SVM methods, the margin parameter <math>C</math> and kernel radius <math>\gamma</math> were selected from <math>\{2^k :k=−5,−3,...,9\}</math> for both parameters. For karma, additional parameter <math>\gamma_{karma}</math> was selected from the set <math>\{1, 2\}</math>.<br />
<br />
The model under study outperformed imputation techniques in almost all cases. It partially confirms that the use of raw incomplete data in neural networks is a usually better approach than filling missing attributes before the learning process. Moreover, it obtained more accurate results than modified kernel methods, which directly work on incomplete data. The performance of the model was once again comparable to, and in some cases better than CE, which had access to the complete data.<br />
<br />
== Conclusion ==<br />
<br />
The results with these experiments along with the theoretical results conclude that this novel approach for dealing with missing data through a modification of a neural network is beneficial and outperforms many existing methods. This approach, which utilizes representing missing data with a probability density function, allows a neural network to determine a more generalized and accurate response of the neuron.<br />
<br />
== Critiques ==<br />
<br />
- A simulation study where the mechanism of missingness is known will be interesting to examine. Doing this will allow us to see when the proposed method is better than existing methods, and under what conditions.<br />
<br />
- This method of imputing incomplete data has many limitations: in most cases when we have a missing data point we are facing a relatively small amount of data that does not require training of a neural network. For a large dataset, missing records does not seem to be very crucial because obtaining data will be relatively easier, and using an empirical way of imputing data such as a majority vote will be sufficient.<br />
<br />
- An interesting application of this problem is in NLP. In NLP, especially Question Answering, there is a problem where a query is given and an answer must be retrieved, but the knowledge base is incomplete. There is therefore a requirement for the model to be able to infer information from the existing knowledge base in order to answer the question. Although this problem is a little more contrived than the one mentioned here, it is nevertheless similar in nature because it requires the ability to probabilistically determine some value which can then be used as a response.<br />
<br />
- The experiments in this paper evaluate this method against low amounts of missing data. It would be interesting to see the properties of this imputation when a majority of the data is missing, and see if this method can outperform dropout training in this setting (dropout is known to be surprisingly robust even at high drop levels).<br />
<br />
- This problem can possibly be applied to face recognition where given a blurry image of a person's face, the neural network can make the image clearer such that the face of the person would be visible for humans to see and also possible for the software to identify who the person is.<br />
<br />
== References ==<br />
[1] Yoshua Bengio and Francois Gingras. Recurrent neural networks for missing or asynchronous<br />
data. In Advances in neural information processing systems, pages 395–401, 1996.<br />
<br />
[2] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep learning. MIT press, 2016.<br />
<br />
[3] Ralph G Andrzejak, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Peter David, and Christian E Elger. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Physical Review E, 64(6):061907, 2001.<br />
<br />
[4] Arthur Asuncion and David J. Newman. UCI Machine Learning Repository, 2007.<br />
<br />
[5] Gal Chechik, Geremy Heitz, Gal Elidan, Pieter Abbeel, and Daphne Koller. Max-margin classification of data with absent features. Journal of Machine Learning Research, 9:1–21, 2008.<br />
<br />
[6] Elad Hazan, Roi Livni, and Yishay Mansour. Classification with low rank and missing data. In Proceedings of The 32nd International Conference on Machine Learning, pages 257–266, 2015.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=File:Group3_Table1.png&diff=45590File:Group3 Table1.png2020-11-21T20:54:57Z<p>Q58yu: </p>
<hr />
<div></div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Gtompkin&diff=45589User:Gtompkin2020-11-21T20:54:23Z<p>Q58yu: /* Experimental Results */</p>
<hr />
<div>== Presented by == <br />
Grace Tompkins, Tatiana Krikella, Swaleh Hussain<br />
<br />
== Introduction ==<br />
<br />
One of the fundamental challenges in machine learning and data science is dealing with missing and incomplete data. This paper proposes theoretically justified methodology for using incomplete data in neural networks, eliminating the need for direct completion of the data by imputation or other commonly used methods in existing literature. The authors propose identifying missing data points with a parametric density and then training it together with the rest of the network's parameters. The neuron's response at the first hidden layer is generalized by taking its expected value to process this probabilistic representation. This process is essentially calculating the average activation of the neuron over imputations drawn from the missing data's density. The proposed approach is advantageous as it has the ability to train neural networks using incomplete observations from datasets, which are ubiquitous in practice. This approach also requires minimal adjustments and modifications to existing architectures. Theoretical results of this study show that this process does not lead to a loss of information, while experimental results showed the practical uses of this methodology on several different types of networks.<br />
<br />
== Related Work ==<br />
<br />
Currently, dealing with incomplete inputs in machine learning requires filling absent attributes based on complete, observed data. Two commonly used methods are mean imputation and k-NN imputation. Other methods for dealing with missing data involve training separate neural networks, extreme learning machines, and <math>k</math>-nearest neighbours. Probabilistic models of incomplete data can also be built depending on the mechanism missingness (i.e. whether the data is Missing At Random (MAR), Missing Completely At Random (MCAR), or Missing Not At Random (MNAR)), which can be fed into a particular learning model. Further, the decision function can also be trained using available/visible inputs alone. Previous work using neural networks for missing data includes a paper by Bengio and Gringras [1] where the authors used recurrent neural networks with feedback into the input units to fill absent attributes solely to minimize the learning criterion. Goodfellow et. al. [2] also used neural networks by introducing a multi-prediction deep Boltzmann machine which could perform classification on data with missingness in the inputs.<br />
<br />
== Layer for Processing Missing Data ==<br />
<br />
In this approach, the adaptation of a given neural network to incomplete data relies on two steps: the estimation of the missing data and the generalization of the neuron's activation. <br />
<br />
Let <math>(x,J)</math> represent a missing data point, where <math>x \in \mathbb{R}^D </math>, and <math>J \subset \{1,...,D\} </math> is a set of attributes with missing data. <math>(x,J)</math> therefore represents an "incomplete" data point for which <math>|J|</math>-many entries are unknown - examples of this could be a list of daily temperature readings over a week where temperature was not recorded on the third day (<math>x\in \mathbb{R}^7, J= \{3\}</math>), an audio transcript that goes silent for certain timespans, or images that are partially masked out (as discussed in the examples).<br />
<br />
For each missing point <math>(x,J)</math>, define an affine subspace consisting of all points which coincide with <math>x</math> on known coordinates <math>J'=\{1,…,N\}/J</math>: <br />
<br />
<center><math>S=Aff[x,J]=span(e_J) </math></center> <br />
where <math>e_J=[e_j]_{j\in J}</math> and <math>e_j</math> is the <math> j^{th}</math> canonical vector in <math>\mathbb{R}^D </math>.<br />
<br />
Assume that the missing data points come from the D-dimensional probability distribution, <math>F</math>. In their approach, the authors assume that the data points follow a mixture of Gaussians (GMM) with diagonal covariance matrices. By choosing diagonal covariance matrices, the number of model parameters is reduced. To model the missing points <math>(x,J)</math>, the density <math>F</math> is restricted to the affine subspace <math>S</math>. Thus, possible values of <math>(x,J)</math> are modelled using the conditional density <math>F_S: S \to \mathbb{R} </math>, <br />
<br />
<center><math>F_S(x) = \begin{cases}<br />
\frac{1}{\int_{S} F(s) \,ds}F(x) & \text{if $x \in S$,} \\<br />
0 & \text{otherwise.}<br />
\end{cases} </math></center><br />
<br />
To process the missing data by a neural network, the authors propose that only the first hidden layer needs modification. Specifically, they generalize the activation functions of all the neurons in the first hidden layer of the network to process the probability density functions representing the missing data points. For the conditional density function <math>F_S</math>, the authors define the generalized activation of a neuron <math>n: \mathbb{R}^D \to \mathbb{R}</math> on <math>F_S </math> as: <br />
<br />
<center><math>n(F_S)=E[n(x)|x \sim F_S]=\int n(x)F_S(x) \,dx</math>,</center> <br />
provided that the expectation exists. <br />
<br />
The following two theorems describe how to apply the above generalizations to both the ReLU and the RBF neurons, respectively. <br />
<br />
'''Theorem 3.1''' Let <math>F = \sum_i{p_iN(m_i, \Sigma_i)}</math> be the mixture of (possibly degenerate) Gaussians. Given weights <math>w=(w_1, ..., w_D) \in \mathbb{R}^D,</math><math> b \in \mathbb{R} </math>, we have<br />
<br />
<center><math>\text{ReLU}_{w,b}(F)=\sum_i{p_iNR\big(\frac{w^{\top}m_i+b}{\sqrt{w^{\top}\Sigma_iw}}}\big)</math></center> <br />
<br />
where <math>NR(x)=\text{ReLU}[N(x,1)]</math> and <math>\text{ReLU}_{w,b}(x)=\text{max}(w^{\top}+b, 0)</math>, <math>w \in \mathbb{R}^D </math> and <math> b \in \mathbb{R}</math> is the bias.<br />
<br />
'''Theorem 3.2''' Let <math>F = \sum_i{p_iN(m_i, \Sigma_i)}</math> be the mixture of (possibly degenerate) Gaussians and let the RBF unit be parametrized by <math>N(c, \Gamma) </math>. We have: <br />
<br />
<center><math>\text{RBF}_{c, \Gamma}(F) = \sum_{i=1}^k{p_iN(m_i-c, \Gamma+\Sigma_i)}(0)</math>.</center> <br />
<br />
In the case where the data set contains no missing values, the generalized neurons reduce to classical ones, since the distribution <math>F</math> is only used to estimate possible values at missing attributes. However, if one wishes to use an incomplete data set in the testing stage, then an incomplete data set must be used to train the model.<br />
<br />
<math> </math><br />
<br />
== Theoretical Analysis ==<br />
<br />
The main theoretical results, which are summarized below, show that using generalized neuron's activation at the first layer does not lead to the loss of information. <br />
<br />
Let the generalized response of a neuron <math>n: \mathbb{R}^D \rightarrow \mathbb{R}</math> evaluated on a probability measure <math>\mu</math> which is given by <br />
<center><math>n(\mu) := \int n(x)d\mu(x)</math></center>.<br />
<br />
Theorem 4.1 shows that a neural network with generalized ReLU units is able to identify any two probability measures. The proof presented by the authors uses the Universal Approximation Property (UAP), and is summarized as follows. <br />
<br />
<br />
'''Theorem 4.1.''' Let <math>\mu</math>, <math>v</math> be probabilistic measures satisfying <math>\int ||x|| d \mu(x) < \infty</math>. If <br />
<center><math>ReLU_{w,b}(\mu) = ReLU_{w,b}(\nu) \text{ for } w \in \mathbb{R}^D, b \in \mathbb{R}</math></center> then <math>\nu = \mu.</math><br />
<br />
''Sketch of Proof'' Let <math>w \in \mathbb{R}^D</math> be fixed and define the set <center><math>F_w = \{p: \mathbb{R} \rightarrow \mathbb{R}: \int p(w^Tx)d\mu(x) = \int p(w^Tx)d\nu(x)\}.</math></center> The first step of the proof involves showing that <math>F_w</math> contains all continuous and bounded functions. The authors show this by showing that a piecewise continuous function that is affine linear on specific intervals, <math>Q</math>, is in the set <math>F_w</math>. This involves re-writing <math>Q</math> as a sum of tent-like piecewise linear functions, <math>T</math> and showing that <math>T \in F_w</math> (since it is sufficient to only show <math>T \in F_w</math>). <br />
<br />
Next, the authors show that an arbitrary bounded continuous function <math>G</math> is in <math>F_w</math> by the Lebesgue dominated convergence theorem. <br />
<br />
Then, as <math>cos(\cdot), sin(\cdot) \in F_w</math>, the function <center><math>exp(ir) = cos(r) + i sin(r) \in F_w</math></center> and we have the equality <center><math>\int exp(iw^Tx)d\mu(x) = \int exp(iw^Tx)d\nu(x).</math></center> Since <math>w</math> was arbitrarily chosen, we can conclude that <math>\mu = \nu</math> <br />
as the characteristic functions of the two measures coincide. <br />
<br />
<br />
More general results can be obtained making stronger assumptions on the probability measures, for example, if a given family of neurons satisfies UAP, then their generalization can identify any probability measure with compact support.<br />
<br />
== Experimental Results ==<br />
The model was applied to three types of algorithms: an Autoencoder (AE), a multilayer perceptron, and a radial basis function network.<br />
<br />
'''Autoencoder'''<br />
<br />
Corrupted images were restored as a part of this experiment. Grayscale handwritten digits were obtained from the MNIST database. A 13 by 13 (169 pixels) square was removed from each 28 by 28 (784 pixels) image. The location of the square was uniformly sampled for each image. The autoencoder used included 5 hidden layers. The first layer used ReLU activation functions while the subsequent layers utilized sigmoids. The loss function was computed using pixels from outside the mask. <br />
<br />
Popular imputation techniques were compared against the conducted experiment:<br />
<br />
''k-nn:'' Replaced missing features with the mean of respective features calculated using K nearest training samples. Here, K=5. <br />
<br />
''mean:'' Replaced missing features with the mean of respective features calculated using all incomplete training samples.<br />
<br />
''dropout:'' Dropped input neutrons with missing values. <br />
<br />
Moreover, a context encoder (CE) was trained by replacing missing features with their means. Unlike mean imputation, the complete data was used in the training phase. The method under study performed better than the imputation methods inside and outside the mask. Additionally, the method under study outperformed CE based on the whole area and area outside the mask. <br />
<br />
The mean square error of reconstruction is used to test each method. The errors calculated over the whole area, inside and outside the mask are shown in Table 1, which indicates the method introduced in this paper is the most competitive.<br />
<br />
<br />
'''Multilayer Perceptron'''<br />
<br />
A multilayer perceptron with 3 ReLU hidden layers was applied to a multi-class classification problem on the Epileptic Seizure Recognition (ESR) data set taken from [3]. Each 178-dimensional vector (out of 11500 samples) is the EEG recording of a given person for 1 second, categorized into one of 5 classes. To generate missing attributes, 25%, 50%, 75%, and 90% of observations were randomly removed. The aforementioned imputation methods were used in addition to Multiple Imputation by Chained Equation (mice) and a mixture of Gaussians (gmm). The former utilizes the conditional distribution of data by Markov chain Monte Carlo techniques to draw imputations. The latter replaces missing features with values sampled from GMM estimated from incomplete data using the EM algorithm. <br />
<br />
Double 5-fold cross-validation was used to report classification results. The model under study outperformed classical imputation methods, which give reasonable results only for a low number of missing values. The method under study performs nearly as well as CE, even though CE had access to complete training data. <br />
<br />
'''Radial Basis Function Network'''<br />
<br />
RBFN can be considered as a minimal architecture implementing our model, which contains only one hidden layer. A cross-entropy function was applied to a softmax in the output layer. Two-class data sets retrieved from the UCI repository [4] with internally missing attributes were used. Since the classification is binary, two additional SVM kernel models which work directly with incomplete data without performing any imputations were included in the experiment:<br />
<br />
''geom:'' The objective function is based on the geometric interpretation of the margin and aims to maximize the margin of each sample in its own subspace [5].<br />
<br />
''karma:'' This algorithm iteratively tunes kernel classifier under low-rank assumptions [6].<br />
<br />
The above SVM methods were combined with RBF kernel function. The number of RBF units was selected in the inner cross-validation from the range {25, 50, 75, 100}. Initial centers of RBFNs were randomly selected from training data while variances were samples from N(0,1) distribution. For SVM methods, the margin parameter <math>C</math> and kernel radius <math>\gamma</math> were selected from <math>\{2^k :k=−5,−3,...,9\}</math> for both parameters. For karma, additional parameter <math>\gamma_{karma}</math> was selected from the set <math>\{1, 2\}</math>.<br />
<br />
The model under study outperformed imputation techniques in almost all cases. It partially confirms that the use of raw incomplete data in neural networks is a usually better approach than filling missing attributes before the learning process. Moreover, it obtained more accurate results than modified kernel methods, which directly work on incomplete data. The performance of the model was once again comparable to, and in some cases better than CE, which had access to the complete data.<br />
<br />
== Conclusion ==<br />
<br />
The results with these experiments along with the theoretical results conclude that this novel approach for dealing with missing data through a modification of a neural network is beneficial and outperforms many existing methods. This approach, which utilizes representing missing data with a probability density function, allows a neural network to determine a more generalized and accurate response of the neuron.<br />
<br />
== Critiques ==<br />
<br />
- A simulation study where the mechanism of missingness is known will be interesting to examine. Doing this will allow us to see when the proposed method is better than existing methods, and under what conditions.<br />
<br />
- This method of imputing incomplete data has many limitations: in most cases when we have a missing data point we are facing a relatively small amount of data that does not require training of a neural network. For a large dataset, missing records does not seem to be very crucial because obtaining data will be relatively easier, and using an empirical way of imputing data such as a majority vote will be sufficient.<br />
<br />
- An interesting application of this problem is in NLP. In NLP, especially Question Answering, there is a problem where a query is given and an answer must be retrieved, but the knowledge base is incomplete. There is therefore a requirement for the model to be able to infer information from the existing knowledge base in order to answer the question. Although this problem is a little more contrived than the one mentioned here, it is nevertheless similar in nature because it requires the ability to probabilistically determine some value which can then be used as a response.<br />
<br />
- The experiments in this paper evaluate this method against low amounts of missing data. It would be interesting to see the properties of this imputation when a majority of the data is missing, and see if this method can outperform dropout training in this setting (dropout is known to be surprisingly robust even at high drop levels).<br />
<br />
- This problem can possibly be applied to face recognition where given a blurry image of a person's face, the neural network can make the image clearer such that the face of the person would be visible for humans to see and also possible for the software to identify who the person is.<br />
<br />
== References ==<br />
[1] Yoshua Bengio and Francois Gingras. Recurrent neural networks for missing or asynchronous<br />
data. In Advances in neural information processing systems, pages 395–401, 1996.<br />
<br />
[2] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep learning. MIT press, 2016.<br />
<br />
[3] Ralph G Andrzejak, Klaus Lehnertz, Florian Mormann, Christoph Rieke, Peter David, and Christian E Elger. Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state. Physical Review E, 64(6):061907, 2001.<br />
<br />
[4] Arthur Asuncion and David J. Newman. UCI Machine Learning Repository, 2007.<br />
<br />
[5] Gal Chechik, Geremy Heitz, Gal Elidan, Pieter Abbeel, and Daphne Koller. Max-margin classification of data with absent features. Journal of Machine Learning Research, 9:1–21, 2008.<br />
<br />
[6] Elad Hazan, Roi Livni, and Yishay Mansour. Classification with low rank and missing data. In Proceedings of The 32nd International Conference on Machine Learning, pages 257–266, 2015.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Bsharman&diff=45576User:Bsharman2020-11-21T20:26:10Z<p>Q58yu: </p>
<hr />
<div>'''Risk prediction in life insurance industry using supervised learning algorithms'''<br />
<br />
'''Presented By'''<br />
<br />
Bharat Sharman, Dylan Li, Leonie Lu, Mingdao Li<br />
<br />
'''Introduction'''<br />
<br />
----<br />
<br />
Risk assessment lies at the core of the Life Insurance Industry. It is extremely important for companies to assess the risk of an application accurately to ensure that those submitted by actual low risk applicants are accepted, whereas applications submitted by high risk applicants are either rejected or placed aside for further review. The types of risks include but are not limited to, a person's smoking status, and family history (such as history of heart disease). If this is not the case, individuals with an extremely high risk profile might be issued policies and when they pass away and the company will face large losses due to high insurance payouts. Such a situation is called ‘Adverse Selection’, where individuals who are most likely to be issued a payout are in fact given a policy and those who are not as likely are not, thus causing the company to suffer losses as a result.<br />
<br />
Traditionally, the process of Underwriting (deciding whether or not to insure the life of an individual) has been done using Actuarial calculations. Actuaries group customers according to their estimated levels of risk determined from historical data. (Cummins J, 2013) However, these conventional techniques are time-consuming and it is not uncommon to take a month to issue a policy. They are expensive as a lot of manual processes need to be executed and a lot of data needs to be imported for the purpose of calculation. <br />
<br />
Predictive Analysis has emerged as a useful technique to streamline the underwriting process to reduce the time of Policy issuance and to improve the accuracy of risk prediction. In life insurance, this approach is widely used in mortality rates modeling to help underwriters make decisions and improve the profitability of the business. In this paper, the authors use data from Prudential Life Insurance company and investigate the most appropriate data extraction method and the most appropriate algorithm to assess risk. <br />
<br />
'''Literature Review'''<br />
<br />
----<br />
<br />
<br />
Before a Life Insurance company issues a policy, it must execute a series of underwriting related tasks (Mishr, 2016). These tasks involve gathering extensive information about the applicant. The insurer has to analyze the employment, medical, family and insurance histories of the applicant and factor all of them into a complicated series of calculations to determine the risk rating of the applicant. On basis of this risk rating, premiums are calculated (Prince, 2016).<br />
<br />
In a competitive marketplace, customers need policies to be issued quickly and long wait times can lead to them switch to other providers (Chen 2016). In addition, the costs of doing the data gathering and analysis can be expensive. The insurance company bears the expenses of the medical examinations and if a policy lapses, then the insurer has to bear the losses of all these costs (J Carson, 2017). If the underwriting process uses Predictive Analytics, then the costs and time associated with many of these processes can be reduced via streamlining. <br />
<br />
'''Methods and Techniques'''<br />
<br />
----<br />
<br />
<br />
In Figure 1, the process flow of the analytics approach has been depicted. These stages will now be described in the following sections.<br />
<br />
[[File:Data_Analytics_Process_Flow.PNG]]<br />
<br />
'''Description of the Dataset'''<br />
<br />
----<br />
<br />
<br />
The data is obtained from the Kaggle competition hosted by the Prudential Life Insurance company. It has 59381 applications with 128 attributes. The attributes are continuous and discrete as well as categorical variables. <br />
The data attributes, their types and the description is shown in Table 1 below:<br />
<br />
[[File:Data Attributes Types and Description.png]]<br />
<br />
'''Data Pre-Processing'''<br />
<br />
----<br />
<br />
<br />
In the data preprocessing step, missing values in the data are either imputed or those entries are dropped and some of the attributes are either transformed in a different form to make the subsequent processing of data easier. This decision is made after determining the mechanism of missingness, that is if the data is Missing Completely at Random (MCAR), Missing at Random (MAR), or Missing Not at Random (MNAR). <br />
<br />
'''Dimensionality Reduction''' <br />
<br />
In this paper, there are two methods that have been used for dimensionality reduction – <br />
<br />
1.Correlation based Feature Selection (CFS): This is a feature selection method in which a subset of features from the original features is selected. In this method, the algorithm selects features from the dataset that are highly correlated with the output but are not correlated with each other. The user does not need to specify the number of features to be selected. The correlation values are calculated based on measures such a Pearson’s coefficient, minimum description length, symmetrical uncertainty, and relief. <br />
<br />
2.Principal Components Analysis (PCA): PCA is a feature extraction method that transforms existing features into new sets of features such that the correlation between them is zero and these transformed features explain the maximum variability in the data. <br />
<br />
<br />
'''Supervised Learning Algorithms'''<br />
<br />
----<br />
<br />
<br />
The four Algorithms that have been used in this paper are the following:<br />
<br />
1.Multiple Linear Regression: In MLR, the relationship between the dependent and the two or more independent variables is predicted by fitting a linear model. The model parameters are calculated by minimizing the sum of squares of the errors. The significance of the variables is determined by tests like the F test and the p-values. <br />
<br />
2.REPTree: REPTree stands for reduced error pruning tree. It can build both classification and regression trees, depending on the type of the response variable. In this case, it uses regression tree logic and creates many trees across several iterations. This algorithm develops these trees based on the principles of information gain and variance reduction. At the time of pruning the tree, the algorithm uses the lowest mean square error to select the best tree. <br />
<br />
3.Random Tree (Also known as the Random Forest): A random tree selects some of the attributes at each node in the decision tree and builds a tree based on random selection of data as well as attributes. Random Tree does not do pruning. Instead, it estimates class probabilities based on a hold-out set.<br />
<br />
4.Artificial Neural Network: In a neural network, the inputs are transformed into outputs via a series of layered units where each of these units transforms the input received via a function into an output that gets further transmitted to units down the line. The weights that are used to weigh the inputs are improved after each iteration via a method called backpropagation in which errors propagate backward in the network and are used to update the weights to make the computed output closer to the actual output.<br />
<br />
'''Experiments and Results'''<br />
<br />
----<br />
<br />
<br />
'''Missing Data Mechanism'''<br />
<br />
Attributes, where more than 30% of Data was missing, were dropped from the analysis. The data were tested for Missing Completely at Random (MCAR), one form of the nature of missing values using the Little Test. The null hypothesis that the missing data was completely random had a p-value of 0 meaning, MCAR was rejected. Then, all the variables were plotted to check how many missing values that they had, and the results are shown in the figure below:<br />
<br />
[[File: Missing Value Plot of Training Data.png]]<br />
<br />
The variables that have the most number of missing variables are plotted at the top and that have the least number of missing variables are plotted at the bottom of the y-axis in the figure above. There does not seem to a pattern to the missing variables and therefore they are assumed to be Missing at Random (MAR), meaning the tendency for the variables to be missing is not related to the missing data, but it is related to the observed data.<br />
<br />
'''Missing Data Imputation'''<br />
<br />
Assuming that missing data follows a MAR pattern, multiple imputations are used as a technique to fill in the values of missing data. The steps involved in Multiple Imputation are the following: <br />
<br />
Imputation: Imputation of the missing values is done over several steps and this results in a number of complete data sets. Imputation is done via a predictive model like linear regression to predict these missing values based on other variables in the data set.<br />
<br />
Analysis: The complete data sets that are formed are analyzed and parameter estimates and standard errors are calculated.<br />
<br />
Pooling: The analysis results are then integrated to form a final data set that is then used for further analysis.<br />
<br />
'''Comparison of Feature Selection and Feature Extraction'''<br />
<br />
The Correlation-based Feature Selection (CFS) method was performed using the Waikato Environment for Knowledge Analysis. It was implemented using a Best-first search method on a CfsSubsetEval attribute evaluator. 33 variables were selected out of the total of 117 features. <br />
PCA was implemented via a RankerSearch Method using a Principal Components Attributes Evaluator. Out of the 117 features, those that had a standard deviation of more than 0.5 times the standard deviation of the first principal component were selected and this resulted in 20 features for further analysis. <br />
After dimensionality reduction, this reduced data set was exported and used for building prediction models using the four machine learning algorithms discussed before – REPTree, Multiple Linear Regression, Random Tree, and ANNs. The results are shown in the table below: <br />
<br />
[[File: Comparison of Results between CFS and PCA.png]]<br />
<br />
For CFS, the REPTree model had the lowest MAE and RMSE. For PCA, the Multiple Linear Regression Model had the lowest MAE as well as RMSE. So, for this dataset, it seems that overall, Multiple Linear Regression and REPTree Models are the two best ones in terms of the lowest error rates. In terms of dimensionality reduction, it seems that CFS is a better method than PCA for this data set as the MAE and RMSE values are lower for all ML methods except ANNs.<br />
<br />
'''Conclusion and Further Work'''<br />
<br />
----<br />
<br />
<br />
Predictive Analytics in the Life Insurance Industry is enabling faster customer service and lower costs by helping automate the process of Underwriting, thereby increasing satisfaction and loyalty. <br />
In this study, the authors analyzed data obtained from Prudential Life Insurance to predict risk scores via Supervised Machine Learning Algorithms. The data was first pre-processed to first replace the missing values. Attributes having more than 30% of missing data were eliminated from the analysis. <br />
Two methods of dimensionality reduction – CFS and PCA were used and the number of attributes used for further analysis was reduced to 33 and 20 via these two methods. The Machine Learning Algorithms that were implemented were – REPTree, Random Tree, Multiple Linear Regression, and Artificial Neural Networks. Model validation was performed via ten-fold cross-validation. The performance of the models was evaluated using MAE and RMSE measures. <br />
Using the PCA method, Multiple Linear Regression showed the best results with MAE and RMSE values of 1.64 and 2.06 respectively. With CFS, REPTree had the highest accuracy with MAE and RMSE values of 1.52 and 2.02 respectively. <br />
Further work can be directed towards dealing with all the variables rather than deleting the ones where more than 30% of the values are missing. Customer segmentation, i.e. grouping customers based on their profiles can help companies come up with a customized policy for each group. This can be done via unsupervised algorithms like clustering. Work can also be done to make the models more explainable especially if we are using PCA and ANNs to analyze data. We can also get indirect data about the prospective applicant like their driving behavior, education record, etc to see if these attributes contribute to better risk profiling than the already available data.<br />
<br />
<br />
'''Critiques'''<br />
<br />
----<br />
The project built multiple models and had utilized various methods to evaluate the result. They could potentially ensemble the prediction, such as averaging the result of the different models, to achieve a better accuracy result. Another method is model stacking, we can input the result of one model as input into another model for better results. However, they do have some major setbacks: sometimes, the result could be effect negatively (ie: increase the RMSE). In addition, if the improvement is not prominent, it would make the process much more complex thus cost time and effort. In a research setting, stacking and ensembling are definitely worth a try. In a real-life business case, it is more of a trade-off between accuracy and effort/cost. <br />
<br />
This project only used unsupervised dimensionality reduction techniques to analyze the data and did not explore supervised methods such as linear discriminant analysis, quadratic discriminant analysis, Fisher discriminant analysis, or supervised PCA. The supervisory signal could've been the normalized risk score, which determines whether someone is granted the policy. The supervision might have provided insight on factors contributing to risk that would not have been captured with unsupervised methods.<br />
<br />
In addition, the dimensionality reduction techniques seem to contradict each other. If we do select features based on their correlation, there is no need to do further PCA on the dataset. Even if we perform PCA, the resulting columns would have a similar number of columns compared to the original ones and it would lose interpretability of the features, which is crucial in real-life practices. <br />
<br />
<br />
'''References'''<br />
<br />
----<br />
<br />
<br />
Chen, T. (2016). Corporate reputation and financial performance of Life Insurers. Geneva Papers Risk Insur Issues Pract, 378-397.<br />
<br />
Cummins J, S. B. (2013). Risk classification in Life Insurance. Springer 1st Edition.<br />
<br />
J Carson, C. E. (2017). Sunk costs and screening: two-part tariffs in life insurance. SSRN Electron J, 1-26.<br />
<br />
Jayabalan, N. B. (2018). Risk prediction in life insurance industry using supervised learning algorithms. Complex & Intelligent Systems, 145-154.<br />
<br />
Mishr, K. (2016). Fundamentals of life insurance theories and applications. PHI Learning Pvt Ltd.<br />
<br />
Prince, A. (2016). Tantamount to fraud? Exploring non-disclosure of genetic information in life insurance applications as grounds for policy recession. Health Matrix, 255-307.</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=stat441F21&diff=45557stat441F212020-11-21T19:55:22Z<p>Q58yu: /* Paper presentation */</p>
<hr />
<div><br />
<br />
== [[F20-STAT 441/841 CM 763-Proposal| Project Proposal ]] ==<br />
<br />
<!--[https://goo.gl/forms/apurag4dr9kSR76X2 Your feedback on presentations]--><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="wikitable"<br />
<br />
{| border="1" cellpadding="3"<br />
|-<br />
|width="60pt"|Date<br />
|width="250pt"|Name <br />
|width="15pt"|Paper number <br />
|width="700pt"|Title<br />
|width="15pt"|Link to the paper<br />
|width="30pt"|Link to the summary<br />
|width="30pt"|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&t=539]<br />
|-<br />
|Week of Nov 16 ||Sharman Bharat, Li Dylan,Lu Leonie, Li Mingdao || 1|| Risk prediction in life insurance industry using supervised learning algorithms || [https://rdcu.be/b780J Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Bsharman Summary] ||<br />
[https://www.youtube.com/watch?v=TVLpSFYgF0c&feature=youtu.be]<br />
|-<br />
|Week of Nov 16 || Delaney Smith, Mohammad Assem Mahmoud || 2|| Influenza Forecasting Framework based on Gaussian Processes || [https://proceedings.icml.cc/static/paper_files/icml/2020/1239-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Influenza_Forecasting_Framework_based_on_Gaussian_Processes Summary]|| [https://www.youtube.com/watch?v=HZG9RAHhpXc&feature=youtu.be]<br />
|-<br />
|Week of Nov 16 || Tatianna Krikella, Swaleh Hussain, Grace Tompkins || 3|| Processing of Missing Data by Neural Networks || [http://papers.nips.cc/paper/7537-processing-of-missing-data-by-neural-networks.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Gtompkin Summary] || [https://learn.uwaterloo.ca/d2l/ext/rp/577051/lti/framedlaunch/6ec1ebea-5547-46a2-9e4f-e3dc9d79fd54]<br />
|-<br />
|Week of Nov 16 ||Jonathan Chow, Nyle Dharani, Ildar Nasirov ||4 ||Streaming Bayesian Inference for Crowdsourced Classification ||[https://papers.nips.cc/paper/9439-streaming-bayesian-inference-for-crowdsourced-classification.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Streaming_Bayesian_Inference_for_Crowdsourced_Classification Summary] || [https://www.youtube.com/watch?v=UgVRzi9Ubws]<br />
|-<br />
|Week of Nov 16 || Matthew Hall, Johnathan Chalaturnyk || 5|| Neural Ordinary Differential Equations || [https://papers.nips.cc/paper/7892-neural-ordinary-differential-equations.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_ODEs Summary]||<br />
|-<br />
|Week of Nov 16 || Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun || 6|| Adversarial Attacks on Copyright Detection Systems || Paper [https://proceedings.icml.cc/static/paper_files/icml/2020/1894-Paper.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems Summary] || [https://www.youtube.com/watch?v=bQI9S6bCo8o]<br />
|-<br />
|Week of Nov 16 || Casey De Vera, Solaiman Jawad || 7|| IPBoost – Non-Convex Boosting via Integer Programming || [https://arxiv.org/pdf/2002.04679.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=IPBoost Summary] || [https://www.youtube.com/watch?v=4DhJDGC4pyI&feature=youtu.be]<br />
|-<br />
|Week of Nov 16 || Yuxin Wang, Evan Peters, Yifan Mou, Sangeeth Kalaichanthiran || 8|| What Game Are We Playing? End-to-end Learning in Normal and Extensive Form Games || [https://arxiv.org/pdf/1805.02777.pdf] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=what_game_are_we_playing Summary] || [https://www.youtube.com/watch?v=9qJoVxo3hnI&feature=youtu.be]<br />
|-<br />
|Week of Nov 16 || Yuchuan Wu || 9|| || || ||<br />
|-<br />
|Week of Nov 16 || Zhou Zeping, Siqi Li, Yuqin Fang, Fu Rao || 10|| A survey of neural network-based cancer prediction models from microarray data || [https://www.sciencedirect.com/science/article/pii/S0933365717305067 Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Y93fang Summary] || [https://youtu.be/B8pPUU8ypO0]<br />
|-<br />
|Week of Nov 23 ||Jinjiang Lian, Jiawen Hou, Yisheng Zhu, Mingzhe Huang || 11|| DROCC: Deep Robust One-Class Classification || [https://proceedings.icml.cc/static/paper_files/icml/2020/6556-Paper.pdf paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:J46hou Summary] || [https://www.youtube.com/watch?v=tvCEvvy54X8&ab_channel=JJLian]<br />
|-<br />
|Week of Nov 23 || Bushra Haque, Hayden Jones, Michael Leung, Cristian Mustatea || 12|| Combine Convolution with Recurrent Networks for Text Classification || [https://arxiv.org/pdf/2006.15795.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Cvmustat Summary] || [https://www.youtube.com/watch?v=or5RTxDnZDo]<br />
|-<br />
|Week of Nov 23 || Taohao Wang, Zeren Shen, Zihao Guo, Rui Chen || 13|| Deep multiple instance learning for image classification and auto-annotation || [https://jiajunwu.com/papers/dmil_cvpr.pdf paper] || ||<br />
|-<br />
|Week of Nov 23 || Qianlin Song, William Loh, Junyue Bai, Phoebe Choi || 14|| Task Understanding from Confusing Multi-task Data || [https://proceedings.icml.cc/static/paper_files/icml/2020/578-Paper.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Task_Understanding_from_Confusing_Multi-task_Data Summary] ||<br />
|-<br />
|Week of Nov 23 || Rui Gong, Xuetong Wang, Xinqi Ling, Di Ma || 15|| Semantic Relation Classification via Convolution Neural Network|| [https://www.aclweb.org/anthology/S18-1127.pdf paper] || ||<br />
|-<br />
|Week of Nov 23 || Xiaolan Xu, Robin Wen, Yue Weng, Beizhen Chang || 16|| Graph Structure of Neural Networks || [https://proceedings.icml.cc/paper/2020/file/757b505cfd34c64c85ca5b5690ee5293-Paper.pdf Paper] ||[https://wiki.math.uwaterloo.ca/statwiki/index.php?title= Summary] ||<br />
|-<br />
|Week of Nov 23 ||Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty || 17|| Superhuman AI for multiplayer poker || [https://www.cs.cmu.edu/~noamb/papers/19-Science-Superhuman.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 ||Guanting Pan, Haocheng Chang, Zaiwei Zhang || 18|| Point-of-Interest Recommendation: Exploiting Self-Attentive Autoencoders with Neighbor-Aware Influence || [https://arxiv.org/pdf/1809.10770.pdf Paper] || ||<br />
|-<br />
|Week of Nov 23 || Jerry Huang, Daniel Jiang, Minyan Dai || 19|| Neural Speed Reading Via Skim-RNN ||[https://arxiv.org/pdf/1711.02085.pdf?fbclid=IwAR3EeFsKM_b5p9Ox7X9mH-1oI3U3oOKPBy3xUOBN0XvJa7QW2ZeJJ9ypQVo Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Neural_Speed_Reading_via_Skim-RNN Summary]||<br />
|-<br />
|Week of Nov 23 ||Ruixian Chin, Yan Kai Tan, Jason Ong, Wen Cheen Chiew || 20|| DivideMix: Learning with Noisy Labels as Semi-supervised Learning || [https://openreview.net/pdf?id=HJgExaVtwr Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=User:Yktan Summary]||<br />
|-<br />
|Week of Nov 30 || Banno Dion, Battista Joseph, Kahn Solomon || 21|| Music Recommender System Based on Genre using Convolutional Recurrent Neural Networks || [https://www.sciencedirect.com/science/article/pii/S1877050919310646] || ||<br />
|-<br />
|Week of Nov 30 || Sai Arvind Budaraju, Isaac Ellmen, Dorsa Mohammadrezaei, Emilee Carson || 22|| A universal SNP and small-indel variant caller using deep neural networks||[https://www.nature.com/articles/nbt.4235.epdf?author_access_token=q4ZmzqvvcGBqTuKyKgYrQ9RgN0jAjWel9jnR3ZoTv0NuM3saQzpZk8yexjfPUhdFj4zyaA4Yvq0LWBoCYQ4B9vqPuv8e2HHy4vShDgEs8YxI_hLs9ov6Y1f_4fyS7kGZ Paper] || ||<br />
|-<br />
|Week of Nov 30 || Daniel Fagan, Cooper Brooke, Maya Perelman || 23|| Efficient kNN Classification With Different Number of Nearest Neighbors || [https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7898482 Paper] || ||<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 Infarction Detection in Electrocardiograms || [https://arxiv.org/pdf/1912.07618.pdf?fbclid=IwAR0RwATSn4CiT3qD9LuywYAbJVw8YB3nbex8Kl19OCExIa4jzWaUut3oVB0 Paper] || Summary [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Learning_for_Cardiologist-level_Myocardial_Infarction_Detection_in_Electrocardiograms&fbclid=IwAR1Tad2DAM7LT6NXXuSYDZtHHBvN0mjZtDdCOiUFFq_XwVcQxG3hU-3XcaE] ||<br />
|-<br />
|Week of Nov 30 || Stan Lee, Seokho Lim, Kyle Jung, Daehyun Kim || 27|| Bag of Tricks for Efficient Text Classification || [https://arxiv.org/pdf/1607.01759.pdf paper] || ||<br />
|-<br />
|Week of Nov 30 || Yawen Wang, Danmeng Cui, ZiJie Jiang, Mingkang Jiang, Haotian Ren, Haris Bin Zahid || 28|| A Brief Survey of Text Mining: Classification, Clustering and Extraction Techniques || [https://arxiv.org/pdf/1707.02919.pdf Paper] || [https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Describtion_of_Text_Mining Summary] ||<br />
|-<br />
|Week of Nov 30 || Qing Guo, XueGuang Ma, James Ni, Yuanxin Wang || 29|| Mask R-CNN || [https://arxiv.org/pdf/1703.06870.pdf Paper] || ||<br />
|-<br />
|Week of Nov 30 || Bertrand Sodjahin, Junyi Yang, Jill Yu Chieh Wang, Yu Min Wu, Calvin Li || 30|| Research paper classifcation systems based on TF‑IDF and LDA schemes || [https://hcis-journal.springeropen.com/articles/10.1186/s13673-019-0192-7?fbclid=IwAR3swO-eFrEbj1BUQfmomJazxxeFR6SPgr6gKayhs38Y7aBG-zX1G3XWYRM Paper] || ||<br />
|-<br />
|Week of Nov 30 || Daniel Zhang, Jacky Yao, Scholar Sun, Russell Parco, Ian Cheung || 31 || Speech2Face: Learning the Face Behind a Voice || [https://arxiv.org/pdf/1905.09773.pdf?utm_source=thenewstack&utm_medium=website&utm_campaign=platform Paper] || ||<br />
|-<br />
|Week of Nov 30 || Siyuan Xia, Jiaxiang Liu, Jiabao Dong, Yipeng Du || 32 || Evaluating Machine Accuracy on ImageNet || [https://proceedings.icml.cc/static/paper_files/icml/2020/6173-Paper.pdf] || ||<br />
|-<br />
|Week of Nov 30 || Msuhi Wang, Siyuan Qiu, Yan Yu || 33 || Surround Vehicle Motion Prediction Using LSTM-RNN for Motion Planning of Autonomous Vehicles at Multi-Lane Turn Intersections || [https://ieeexplore.ieee.org/abstract/document/8957421 paper] || ||</div>Q58yuhttp://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems&diff=44665Adversarial Attacks on Copyright Detection Systems2020-11-15T20:22:14Z<p>Q58yu: /* Audio Fingerprinting Model */</p>
<hr />
<div>== Presented by == <br />
Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun<br />
<br />
==Introduction ==<br />
Copyright detection system is one of the most commonly used machine learning systems; however, the hardiness of copyright detection and content control systems to adversarial attacks, inputs intentionally designed by people to cause the model to make a mistake, has not been widely addressed by public. 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 open which means 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 />
<br />
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. Next, the paper talks about how to generate audio fingerprints using convolutional neural network 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 onto industrial systems like AudioTag and YouTube Content ID to evaluate the effectiveness of the systems, and the conclusion is made at the end.<br />
<br />
== Types of copyright detection systems ==<br />
Fingerprinting algorithm is to extract the features of the source file as a hash and then compare that to the materials protected by copyright in the database. If enough matches are found between the source and existing data, 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 & 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 that these algorithms 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 fingerprinting 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 the most of time, the hash is generated by extracting hand-crafted features rather than training a neural network. But 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. Shazam is a popular music recognization application, which uses one of the most well-known fingerprinting models. With three principles: temporally localized, translation invariant, and robustness, the Shazam algorithm is treated as a good fingerprint algorithm. It shows strong robustness even in presence of noise by using local maximum in spectrogram to form hashes.<br />
<br />
=== Interpreting the fingerprint extractor as a CNN ===<br />
The intention of this section is to build a differentiable neural network whose function resembling 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 audio format (Group et al., 2005). The generic neural network will then be used as an example of implementing black-box attacks on many popular real-world systems, in this case, YouTube and AudioTag. <br />
<br />
The generic neural network model consists two convolutional layers and a max-pooling layer, depicted in the figure below. As mentioned above, the convolutional neural network is well-known for its properties of temporarily localized and transformational invariant. 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 time 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 />
$$ f_{1}(n)=\frac {sin^2(\frac{\pi n} {N})} {\sum sin^2(\frac{\pi n}{N})} $$ <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 <math>{\in}</math> 0,1,...,N-1 (output channel index) and n <math>{\in}</math> 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. 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 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 <math>{\delta}</math>, 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 <math>{||\delta||_p\le\epsilon}</math> is the <math>{l_p}</math>-norm of the perturbation and <math>{\epsilon}</math> 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 <math>{\psi(x)}</math> and <math>{\psi(y)}</math> be two binary fingerprints outputted from the model, the number of peaks shared by <math>{x}</math> and <math>{y}</math> can be found through <math>{|\psi(x)\cdot\psi(y)|}</math>. 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 with 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 which involves more movements of the local maxima of the spectrogram is proposed. The idea is to move the locations of peaks in <math>{\psi(x)}</math> outside of neighborhood of the peaks of <math>{\psi(y)}</math>. In order to implement the model more efficiently, two max-pooling layers are used. One of the layers has a bigger width <math>{w_1}</math> while the other one has a smaller width <math>{w_2}</math>. For any location, if the output of <math>{w_1}</math> pooling is strictly greater than the output of <math>{w_2}</math> pooling, then it can be concluded that no peak is in that location with radius <math>{w_2}</math>. <br />
<br />
The loss function is as the following:<br />
<br />
$$J(x,y) = \sum_i\bigg(ReLU\bigg(c-\bigg(\underset{|j| \leq w_1}{\max}\phi(i+j;x)-\underset{|j| \leq w_2}{\max}\phi(i+j;x)\bigg)\bigg)\cdot\psi(i;y)\bigg)$$<br />
The equation above penalizes the peaks of <math>{x}</math> which are in neighborhood of peaks of <math>{y}</math> with radius of <math>{w_2}</math>. The activation function uses <math>{ReLU}</math>. <math>{c}</math> is the difference between the output 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 <math>{\alpha}</math> is a smoothing hyper parameter. When <math>{\alpha}</math> approaches positive infinity, <math>{S_\alpha}</math> 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 <math>{x}</math> is the input signal, <math>{J}</math> is the loss function with the smoothed max function.<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 signal 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 <math>{\lambda}</math> is a scalar parameter that controls the similarity of <math>{x+\delta}</math> and <math>{y}</math>.<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. <math>{l_{\infty}}</math> norm and <math>{l_{2}}</math> 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 are used to provide the baseline of adversarial examples’ effectiveness. Loss function <math>{J(x,y)=|\phi(x)\cdot\psi(x)\cdot\psi(y)|}</math> 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 />
<div align="center">Table 1: Norms of the perturbations for white-box attacks</div><br />
<br />
In black-box attacks, 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 <math>{\epsilon}</math> is required. YouTube Content ID system has a more robust fingerprint model.<br />
<br />
<br />
[[File:Table_2_Black-box.jpg |center]]<br />
<br />
<div align="center">Table 2: Norms of the perturbations for black-box attacks</div><br />
<br />
[[File:YouTube_Figure.jpg |center]]<br />
<br />
<div align="center">Figure 2: YouTube’s copyright detection recall against the magnitude of noise</div><br />
<br />
== Conclusion ==<br />
In conclusion, many industrial copyright detection systems used in the popular video and music website 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 neural network and attack it by the well-known gradient method, this paper firmly proved the lack of robustness of the current online detector. 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 enhancing our copyright detection system. More approach, such as adversarial training needs to be developed and examined, in order to protect us against the threat of adversarial copyright attack.<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; 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>Q58yu