Rates of convergence for density estimation with GANs

February 9, 2021 Nikita Puchkin, Junior Research Fellow, International Laboratory of Stochastic Algorithms and High-Dimensional Inference We undertake a precise study of the non-asymptotic properties of vanilla generative adversarial networks (GANs) and derive theoretical guarantees in the problem of estimating an unknown $d$-dimensional density $p^*$ under a proper choice of the class of generators and discriminators. We prove that the resulting density estimate converges to $p^*$ in terms of Jensen-Shannon (JS) divergence at the rate $n^{-2\beta/(2\beta d)}$ where $n$ is the sample size and $\beta$ determines the smoothness of $p^*.$ This is the first result in the literature on density estimation using vanilla GANs with JS rates faster than $n^{-1/2}$ in the regime $\beta}d/2.$ HDI Lab: Faculty of Computer Science: