Robust Estimation and Generative Adversarial Nets
Time: 2019-01-04
Published By: Xiaoni Tan
Speaker(s): Yuan Yao (The Hong Kong University of Science and Technology)
Time: 10:30-12:00 January 4, 2019
Venue: Room 29, Quan Zhai, BICMR
Robust estimation under Huber's ε-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 ε- contamination model. Interestingly, the hidden layers for the neural net structure in the discriminator class is shown to be necessary for robust estimation.
