Nonparametric Density Estimation under Adversarial Losses

Abstract

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical ${\mathcal{L}}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.

Cited by in corpus (9)

• How Well Generative Adversarial Networks Learn Distributions
• Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs
• Minimax Distribution Estimation in Wasserstein Distance
• An error analysis of generative adversarial networks for learning distributions
• The Inductive Bias of Restricted f-GANs
• Estimating Certain Integral Probability Metric (IPM) is as Hard as Estimating under the IPM
• On Energy-Based Models with Overparametrized Shallow Neural Networks
• Support-weighted Adversarial Imitation Learning
• Robust Density Estimation under Besov IPM Losses