Statistical inference for generative adversarial networks

This paper studies generative adversarial networks (GANs) from a statistical perspective. 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 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. The assumptions employed in our results are weak and hold in many practical GAN applications. To the best of our knowledge, this paper provides the first results on statistical inference for GANs in the empirically relevant case of multiple solutions.