Rates of convergence for density estimation with generative adversarial networks

Nikita Puchkin; Sergey Samsonov; Denis Belomestny; Eric Moulines; Alexey Naumov

In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shannon (JS) divergence between the underlying density

$\mathsf{p}^*$ and the GAN estimate with a significantly better statistical error term compared to the previously known results. The advantage of our bound becomes clear in application to nonparametric density estimation. We show that the JS-divergence between the GAN estimate and

$\mathsf{p}^*$ decays as fast as

$(\log{n}/n)^{2\beta/(2\beta + d)}$ , where

$n$ is the sample size and

$\beta$ determines the smoothness of

$\mathsf{p}^*$ . This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities.

Rates of convergence for density estimation with generative adversarial networks

Abstract