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--- seminars:stat:220331 [2022/03/29 22:13] – created qyu
+++ seminars:stat:220331 [2022/03/29 22:15] (current) – qyu
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+<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
+<WRAP 70% center>
+^  **DATE:**|Thursday, March 31, 2022 |
+^  **TIME:**|1:15pm -- 2:15pm |
+^  **LOCATION:**|Zoom meeting |
+^  **SPEAKER:**|Jingze Liu, Binghamton University |
+^  **TITLE:**|How Well Generative Adversarial Networks Learn Distributions  |
+</WRAP>
+\\
+<WRAP center box 80%>
+<WRAP centeralign>**Abstract**</WRAP>
+This paper studies the rates of convergence for learning
+distributions implicitly with the adversarial framework and Generative
+Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD  GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases. We study a wide range of parametric and nonparametric  target distributions under a host of objective evaluation metrics. We  investigate how to obtain valid statistical guarantees for GANs through the lens of regularization. On  the nonparametric end, we derive the optimal minimax rates for distribution estimation  under the adversarial framework. On the parametric end, we establish a theory for general neural network classes (including deep leaky ReLU networks) that characterizes the interplay on  the choice of generator and discriminator pair. We discover and isolate  a new notion of regularization, called the generator-discriminator-pair regularization, that sheds light on the  advantage of GANs compared to classical parametric and nonparametric approaches for  explicit distribution estimation. We develop novel oracle inequalities as the main technical  tools for analyzing
+GANs, which are of independent interest.
+</WRAP>