##Statistics Seminar##\\ Department of Mathematical Sciences
^ **DATE:**|Thursday, Nov. 11, 2021 |
^ **TIME:**|1:15pm -- 2:15pm |
^ **LOCATION:**|Zoom meeting |
^ **SPEAKER:**|Jingze Liu, Binghamton University |
^ **TITLE:**|Some Theoretical Properties of GANs |
\\
**Abstract**
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.