Statistical inference for generative adversarial networks and other minimax problems

TL;DR

This paper explores the statistical properties of GAN solutions, demonstrating consistent estimation and confidence set construction, applicable to general minimax problems with multiple solutions.

Contribution

It introduces the first statistical inference framework for GANs, establishing consistency and confidence sets for generator and discriminator parameters.

Findings

Sample GAN solutions are Hausdorff consistent estimators of population solutions.

Confidence sets can be constructed to contain true solutions with desired coverage.

Results extend to general minimax problems beyond GANs, including non-convex and non-concave cases.

Abstract

This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be non-convex, non-concave, and have multiple solutions.