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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.
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https://hal.sorbonne-universite.fr/hal-01737975
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Submitted on : Tuesday, March 20, 2018 - 9:52:46 AM
Last modification on : Thursday, August 27, 2020 - 3:22:40 AM
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Gérard Biau, Benoît Cadre, M. Sangnier, U. Tanielian. Some Theoretical Properties of GANs. Annals of Statistics, Institute of Mathematical Statistics, 2020, 48 (3), pp.1539-1566. ⟨10.1214/19-AOS1858⟩. ⟨hal-01737975⟩

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