arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2002.03938cs.LGstat.ML

Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks

Georgia Tech(佐治亚理工学院)

Minshuo Chen, Wenjing Liao, Hongyuan Zha, Tuo Zhao

英文摘要:

Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distributions that have densities in a Hölder space. Our main result shows that, if the generator and discriminator network architectures are properly chosen, GANs are consistent estimators of data distributions under strong discrepancy metrics, such as the Wasserstein-1 distance. Furthermore, when the data distribution exhibits low-dimensional structures, we show that GANs are capable of capturing the unknown low-dimensional structures in data and enjoy a fast statistical convergence, which is free of curse of the ambient dimensionality. Our analysis for low-dimensional data builds upon a universal approximation theory of neural networks with Lipschitz continuity guarantees, which may be of independent interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑