Home Page

Papers

Submissions

News

Editorial Board

Special Issues

Open Source Software

Proceedings (PMLR)

Transactions (TMLR)

Search

Statistics

Login

Frequently Asked Questions

Contact Us



RSS Feed

An Error Analysis of Generative Adversarial Networks for Learning Distributions

Jian Huang, Yuling Jiao, Zhen Li, Shiao Liu, Yang Wang, Yunfei Yang; 23(116):1−43, 2022.

Abstract

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through H\"{o}lder classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have H\"{o}lder densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

[abs][pdf][bib]       
© JMLR 2022. (edit, beta)