An Error Analysis of Generative Adversarial Networks for Learning Distributions

被引：0

作者：

Huang, Jian ^{[1
]}

Jiao, Yuling ^{[2
]}

Li, Zhen ^{[1
]}

Liu, Shiao ^{[1
]}

Wang, Yang ^{[3
]}

Yang, Yunfei ^{[3
]}

机构：

[1] Department of Statistics and Actuarial Science, University of Iowa, Iowa City,IA, United States

[2] School of Mathematics and Statistics, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China

[3] Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

来源：

Journal of Machine Learning Research | 2022年 / 23卷

基金：

中国国家自然科学基金;

关键词：

Risk assessment - Deep neural networks - Errors - Sampling - Network architecture - Probability distributions;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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 Holder 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 Holder 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. © 2022 Jian Huang, Yuling Jiao, Zhen Li, Shiao Liu, Yang Wang and Yunfei Yang.

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