27 septembre 2018

Gérard Biau (Sorbonne Université - LPSM)
Some theoretical properties of GANs

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Lieu : salle 3L15

Résumé : 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 presentation, 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.
Joint work with B. Cadre (ENS Rennes), M. Sangnier (Sorbonne University), and U. Tanielian (Sorbonne University & Criteo)

Some theoretical properties of GANs  Version PDF