Rates of convergence for density estimation with generative adversarial networks

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 ${\mathsf{p}}^{\ast }$ 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 ${\mathsf{p}}^{\ast }$ decays as fast as $(\log n/n{)}^{2\beta /(2\beta +d)}$, where $n$ is the sample size and $\beta$ determines the smoothness of ${\mathsf{p}}^{\ast }$. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities.

To appear in Journal of Machine Learning Research

References in corpus (9)

• Energy-based Generative Adversarial Network
• On Convergence and Stability of GANs
• Sample Complexity of Sinkhorn divergences
• Connecting Generative Adversarial Networks and Actor-Critic Methods
• Spatial aggregation of local likelihood estimates with applications to classification
• Some Theoretical Insights into Wasserstein GANs
• Statistical guarantees for generative models without domination
• Generalization Properties of Optimal Transport GANs with Latent Distribution Learning
• Minimax density estimation for growing dimension

Cited by in corpus (2)

• Some Theoretical Insights into Wasserstein GANs
• Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution