%0 Generic %1 biau2018theoretical %A Biau, G. %A Cadre, B. %A Sangnier, M. %A Tanielian, U. %D 2018 %K 2018 GAN arxiv deep-learning paper %T Some Theoretical Properties of GANs %U http://arxiv.org/abs/1803.07819 %X 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.

@misc{biau2018theoretical, 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.}, added-at = {2018-03-22T16:47:11.000+0100}, author = {Biau, G. and Cadre, B. and Sangnier, M. and Tanielian, U.}, biburl = {https://www.bibsonomy.org/bibtex/202a1cbdb828ae05ab93678859ab5cca2/achakraborty}, description = {[1803.07819] Some Theoretical Properties of GANs}, interhash = {2f300accc9475371698b9402d46bd0c5}, intrahash = {02a1cbdb828ae05ab93678859ab5cca2}, keywords = {2018 GAN arxiv deep-learning paper}, note = {cite arxiv:1803.07819}, timestamp = {2018-03-22T16:47:11.000+0100}, title = {Some Theoretical Properties of GANs}, url = {http://arxiv.org/abs/1803.07819}, year = 2018 }