## ROBUST ESTIMATION VIA GENERATIVE ADVERSARIAL NETWORKS

Sep 27, 2018 ICLR 2019 Conference Blind Submission readers: everyone Show Bibtex
• Abstract: Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\epsilon$-contamination model. Interestingly, the hidden layers of the neural net structure in the discriminator class are shown to be necessary for robust estimation.
• Keywords: robust statistics, neural networks, minimax rate, data depth, contamination model, Tukey median, GAN
• TL;DR: GANs are shown to provide us a new effective robust mean estimate against agnostic contaminations with both statistical optimality and practical tractability.
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