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June 2020 Some theoretical properties of GANS
Gérard Biau, Benoît Cadre, Maxime Sangnier, Ugo Tanielian
Ann. Statist. 48(3): 1539-1566 (June 2020). DOI: 10.1214/19-AOS1858


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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Gérard Biau. Benoît Cadre. Maxime Sangnier. Ugo Tanielian. "Some theoretical properties of GANS." Ann. Statist. 48 (3) 1539 - 1566, June 2020.


Received: 1 March 2018; Revised: 1 November 2018; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241602
MathSciNet: MR4124334
Digital Object Identifier: 10.1214/19-AOS1858

Primary: 62F12
Secondary: 68T01

Keywords: adversarial principle , central limit theorem , generative models , Jensen–Shannon divergence , neural networks

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.48 • No. 3 • June 2020
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