
<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>

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^  **DATE:**|Thursday, Nov. 11, 2021 |
^  **TIME:**|1:15pm -- 2:15pm |
^  **LOCATION:**|Zoom meeting |
^  **SPEAKER:**|Jingze Liu, Binghamton University |
^  **TITLE:**|Some Theoretical Properties of GANs  |
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<WRAP centeralign>**Abstract**</WRAP>
Generative Adversarial Networks (GANs) are a class of generative 
algorithms that have been shown to produce state-of-the art samples,
especially in the domain of image creation. The fundamental principle of 
GANs is to approximate the unknown distribution of a given data set by 
optimizing an
objective function through an adversarial game between a family of 
generators and a family of discriminators. In this paper, we offer a 
better theoretical
understanding of GANs by analyzing some of their mathematical and 
statistical properties. We study the deep connection between the 
adversarial
principle underlying GANs and the Jensen-Shannon divergence, together 
with some optimality characteristics of the problem. An analysis of the 
role
of the discriminator family via approximation arguments is also 
provided.In addition, taking a statistical point of view, we study the 
large sample
properties of the estimated distribution and prove in particular a 
central limit
theorem. Some of our results are illustrated with simulated examples.
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