Rates of convergence for density estimation with generative adversarial networks
Nikita Puchkin, Sergey Samsonov, Denis Belomestny, Eric Moulines, Alexey Naumov; 25(29):1−47, 2024.
Abstract
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.
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