SOME THEORETICAL PROPERTIES OF GANS
成果类型：
Article
署名作者：
Biau, Gerard; Cadre, Benoit; Sangnier, Maxime; Tanielian, Ugo
署名单位：
Universite Paris Cite; Sorbonne Universite; Ecole Normale Superieure de Rennes (ENS Rennes); Universite de Rennes
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/19-AOS1858
发表日期：
2020
页码：
1539-1566
关键词：
摘要：
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.