Wasserstein generative adversarial networks are minimax optimal distribution estimators
Wasserstein生成对抗网络作为极小极大最优分布估计量
We provide nonasymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and discriminators which yield a GAN that achieves the minimax optimal rate for estimating a certain probability measure μ with support in Rp. The probability μ is considered to be the push forward of the Lebesgue measure on the d-dimensional torus Td by a map g⋆:Td→Rp of smoothness β+1. Measuring the…