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 nonconvex, nonconcave, and have multiple solutions.

中文翻译：

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生成对抗网络和其他极小极大问题的统计推断

本文从统计推断的角度研究生成对抗网络（GAN）。 GAN 是一种流行的机器学习方法，其中估计两个神经网络（生成器和判别器）的参数来解决特定的极小极大问题。这个极小极大问题通常有多种解决方案，本文的重点是这些解决方案的统计特性。我们解决了生成器和鉴别器网络参数的两个关键统计问题：一致估计和置信集。我们首先证明样本 GAN 问题的解集是相应群体 GAN 问题的解集的（豪斯多夫）一致估计器。然后，我们设计一个计算密集型程序来形成置信集，并表明这些集包含具有所需覆盖概率的群体 GAN 解决方案。小型数值实验和蒙特卡罗研究说明了我们的结果并验证了我们的理论发现。我们还表明，我们的结果适用于一般的极小极大问题，这些问题可能是非凸、非凹的，并且有多个解决方案。