  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.
