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An Error Analysis of Generative Adversarial Networks for Learning Distributions.
- Source :
-
Journal of Machine Learning Research . 2022, Vol. 23, p1-43. 43p. - Publication Year :
- 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 Hölder 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 Hölder 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15324435
- Volume :
- 23
- Database :
- Academic Search Index
- Journal :
- Journal of Machine Learning Research
- Publication Type :
- Academic Journal
- Accession number :
- 164775339