  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.
