An Error Analysis of Generative Adversarial Networks for Learning Distributions

Jian Huang; Yuling Jiao; Zhen Li; Shiao Liu; Yang Wang; Yunfei Yang

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An Error Analysis of Generative Adversarial Networks for Learning Distributions

Journal article

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An Error Analysis of Generative Adversarial Networks for Learning Distributions

Jian Huang, Yuling Jiao, Zhen Li, Shiao Liu, Yang Wang and Yunfei Yang

Journal of machine learning research, Vol.23, 116

01/01/2022

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https://jmlr.org/papers/v23/21-0732.htmlView

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Abstract

This paper studies how well generative adversarial networks (GANs) learn probability dis-tributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through Ho center dot 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 Ho center dot 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.

Computer Science

Technology

Automation & Control Systems

Computer Science, Artificial Intelligence

Science & Technology

Details

Title: Subtitle: An Error Analysis of Generative Adversarial Networks for Learning Distributions
Creators: Jian Huang - Actuarial Sci Univ Iowa, Dept Stat, Iowa City, IA USA
Yuling Jiao - Wuhan University
Zhen Li - Actuarial Sci Univ Iowa, Dept Stat, Iowa City, IA USA
Shiao Liu - Actuarial Sci Univ Iowa, Dept Stat, Iowa City, IA USA
Yang Wang - University of Hong Kong
Yunfei Yang - University of Hong Kong
Resource Type: Journal article
Publication Details: Journal of machine learning research, Vol.23, 116
Publisher: Microtome Publ
ISSN: 1532-4435
eISSN: 1533-7928
Number of pages: 43
Grant note: ITS/044/18FX / HK Innovation Technology Fund 16308518 / HK RGC; Hong Kong Research Grants Council 2020B1212030001 / Guangdong -Hong Kong -Macao Joint Laboratory for Data Driven Fluid Dynamics and Engineering Applications 11871474 / National Science Foundation of China; National Natural Science Foundation of China (NSFC)
Language: English
Date published: 01/01/2022
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984438957302771

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