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Register a new userDisentangling and Learning Robust Representations with Natural Clustering
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Learning representations that disentangle the underlying factors of variability in data is an intuitive way to achieve generalization in deep models. In this work, we address the scenario where generative factors present a multimodal distribution due to the existence of class distinction in the data. We propose N-VAE, a model which is capable of separating factors of variation which are exclusive to certain classes from factors that are shared among classes. This model implements an explicitly compositional latent variable structure by defining a class-conditioned latent space and a shared latent space. We show its usefulness for detecting and disentangling class-dependent generative factors as well as its capacity to generate artificial samples which contain characteristics unseen in the training data.
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The vulnerability to slight input perturbations is a worrying yet intriguing property of deep neural networks (DNNs). Despite many previous works studying the reason behind such adversarial behavior, the relationship between the generalization performance and adversarial behavior of DNNs is still little understood. In this work, we reveal such relation by introducing a metric characterizing the generalization performance of a DNN. The metric can be disentangled into an information-theoretic non-robust component, responsible for adversarial behavior, and a robust component. Then, we show by experiments that current DNNs rely heavily on optimizing the non-robust component in achieving decent performance. We also demonstrate that current state-of-the-art adversarial training algorithms indeed try to robustify the DNNs by preventing them from using the non-robust component to distinguish samples from different categories. Also, based on our findings, we take a step forward and point out the possible direction for achieving decent standard performance and adversarial robustness simultaneously. We believe that our theory could further inspire the community to make more interesting discoveries about the relationship between standard generalization and adversarial generalization of deep learning models.
In this paper, we study ordered representations of data in which different dimensions have different degrees of importance. To learn these representations we introduce nested dropout, a procedure for stochastically removing coherent nested sets of hidden units in a neural network. We first present a sequence of theoretical results in the simple case of a semi-linear autoencoder. We rigorously show that the application of nested dropout enforces identifiability of the units, which leads to an exact equivalence with PCA. We then extend the algorithm to deep models and demonstrate the relevance of ordered representations to a number of applications. Specifically, we use the ordered property of the learned codes to construct hash-based data structures that permit very fast retrieval, achieving retrieval in time logarithmic in the database size and independent of the dimensionality of the representation. This allows codes that are hundreds of times longer than currently feasible for retrieval. We therefore avoid the diminished quality associated with short codes, while still performing retrieval that is competitive in speed with existing methods. We also show that ordered representations are a promising way to learn adaptive compression for efficient online data reconstruction.
Unsupervised speech representation learning has shown remarkable success at finding representations that correlate with phonetic structures and improve downstream speech recognition performance. However, most research has been focused on evaluating the representations in terms of their ability to improve the performance of speech recognition systems on read English (e.g. Wall Street Journal and LibriSpeech). This evaluation methodology overlooks two important desiderata that speech representations should have: robustness to domain shifts and transferability to other languages. In this paper we learn representations from up to 8000 hours of diverse and noisy speech data and evaluate the representations by looking at their robustness to domain shifts and their ability to improve recognition performance in many languages. We find that our representations confer significant robustness advantages to the resulting recognition systems: we see significant improvements in out-of-domain transfer relative to baseline feature sets and the features likewise provide improvements in 25 phonetically diverse languages including tonal languages and low-resource languages.
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers. In this paper, we develop a provably robust spectral clustering algorithm that applies a simple rounding scheme to denoise a Gaussian kernel matrix built from the data points and uses vanilla spectral clustering to recover the cluster labels of data points. We analyze the performance of our algorithm under the assumption that the good data points are generated from a mixture of sub-gaussians (we term these inliers), while the outlier points can come from any arbitrary probability distribution. For this general class of models, we show that the misclassification error decays at an exponential rate in the signal-to-noise ratio, provided the number of outliers is a small fraction of the inlier points. Surprisingly, this derived error bound matches with the best-known bound for semidefinite programs (SDPs) under the same setting without outliers. We conduct extensive experiments on a variety of simulated and real-world datasets to demonstrate that our algorithm is less sensitive to outliers compared to other state-of-the-art algorithms proposed in the literature.
The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action representations from empirical trajectories. The method exploits the MDPs tensor structure by kernelization, importance sampling and low-Tucker-rank approximation. This method can be further used to cluster states and actions respectively and find the best discrete MDP abstraction. We provide sharp statistical error bounds for tensor concentration and the preservation of diffusion distance after embedding.
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