Training generative neural networks via Maximum Mean Discrepancy optimization

TL;DR

This paper introduces a method for training generative neural networks by minimizing the maximum mean discrepancy (MMD), a statistical test, as an alternative to adversarial training, with theoretical bounds on generalization error.

Contribution

It proposes using MMD as a non-adversarial, kernel-based objective for training generative models, providing theoretical analysis and empirical comparisons.

Findings

MMD-based training performs comparably to adversarial methods.

Theoretical bounds on generalization error are established.

Empirical results demonstrate effectiveness across datasets.

Abstract

We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. As our two-sample test statistic, we use an unbiased estimate of the maximum mean discrepancy, which is the centerpiece of the nonparametric kernel two-sample test proposed by Gretton et al. (2012). We compare to the adversarial nets framework introduced by Goodfellow et al. (2014), in which learning is a two-player game between a generator network and an adversarial discriminator network, both trained to outwit the other. From this perspective, the MMD statistic plays the role of the discriminator. In addition to empirical comparisons, we prove bounds on the generalization error incurred by optimizing the empirical MMD.