Distribution-Dissimilarities in Machine Learning

Abstract

Any binary classifier (or score-function) can be used to define a dissimilarity between two distributions. Many well-known distribution-dissimilarities are actually classifier-based: total variation, KL- or JS-divergence, Hellinger distance, etc. And many recent popular generative modeling algorithms compute or approximate these distribution-dissimilarities by explicitly training a classifier: e.g. generative adversarial networks (GAN) and their variants.

This thesis introduces and studies such classifier-based distribution-dissimilarities. After a general introduction, the first part analyzes the influence of the classifiers' capacity on the dissimilarity's strength for the special case of maximum mean discrepancies (MMD) and provides applications. The second part studies applications of classifier-based distribution-dissimilarities in the context of generative modeling and presents two new algorithms: Wasserstein Auto-Encoders (WAE) and AdaGAN. The third and final part focuses on adversarial examples, i.e. targeted but imperceptible input-perturbations that lead to drastically different predictions of an artificial classifier. It shows that adversarial vulnerability of neural network based classifiers typically increases with the input-dimension, independently of the network topology.