An error analysis of generative adversarial networks for learning distributions

• URL: http://arxiv.org/abs/2105.13010v1
• Date: Thu, 27 May 2021 08:55:19 GMT
• Title: An error analysis of generative adversarial networks for learning distributions
• Authors: Jian Huang, Yuling Jiao, Zhen Li, Shiao Liu, Yang Wang, Yunfei Yang
• Abstract summary: generative adversarial networks (GANs) learn probability distributions from finite samples. GANs are able to adaptively learn data distributions with low-dimensional structure or have H"older densities. Our analysis is based on a new oracle inequality decomposing the estimation error into generator and discriminator approximation error and statistical error.
• Score: 11.842861158282265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results estimate the convergence rates of GANs under a collection of integral probability metrics defined through H\"older classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structure or have H\"older densities, when the network architectures are chosen properly. In particular, for distributions concentrate around a low-dimensional set, it is proved 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 generator and discriminator approximation error and statistical error, which may be of independent interest.

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