An error analysis of generative adversarial networks for learning distributions
It provides theoretical guarantees for GANs in distribution learning, which is important for researchers in machine learning and statistics, though it is incremental as it builds on existing error analysis frameworks.
This paper analyzes the convergence rates of generative adversarial networks (GANs) for learning probability distributions from finite samples, showing that GANs can achieve rates independent of high ambient dimensions for low-dimensional structured data.
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.