**Statistics Seminar (2019- 22)**

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**Title:** Robust Statistics and Generative Adversarial Networks

**Speaker: **Yuan Yao, Hong Kong University of Science and Technology

**Time:** Thursday, October 31, 14:00-15:00

**Place:** Room 217, Guanghua Building 2

**Abstract:**

Robust estimation under Huber's contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on 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-GANs, we show that these depth functions that lead to statistically 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 in both theory and experiments that some appropriate structures of discriminator networks with hidden layers in GANs lead to statistically optimal robust location estimators for both Gaussian distribution and general elliptical distributions where first moment may not exist. This is a joint work with Chao Gao, Jiyi Liu, and Weizhi Zhu.

**Introduction:**

Yuan Yao is currently an associate professor of mathematics, chemical & biological engineering, and by courtesy, computer science & engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, P.R. China. He received the BSE and MSE degrees in control engineering both from the Harbin Institute of Technology, China, in 1996 and 1998, respectively, the MPhil degree in mathematics from the City University of Hong Kong, in 2002, and the PhD degree in mathematics from the University of California, Berkeley, in 2006. Since then, he has been with Stanford University and in 2009, he joined the Department of Probability and Statistics, School of Mathematical Sciences, Peking University, Beijing, China. His current research interests include topological and geometric methods for high dimensional data analysis and statistical machine learning, with applications in computational biology, computer vision, and information retrieval.

http://repository.ust.hk/ir/AuthorProfile/yao-yuan

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