Rates of convergence for density estimation with generative adversarial networks

Understand

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 $\mathsf{p}^*$.