Rates of convergence for density estimation with generative adversarial networks
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 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 𝗉∗ decays as fast as (logn/n)2β/(2β+d), where n is the sample size and β determines the smoothness of 𝗉∗. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities.