Training generative neural networks via Maximum Mean Discrepancy optimization
This provides an alternative method for generative modeling, potentially addressing training stability issues in adversarial approaches, but it is incremental as it builds on existing MMD and GAN frameworks.
The paper tackles the problem of training generative neural networks by minimizing the Maximum Mean Discrepancy (MMD) statistic as a two-sample test, comparing it to adversarial networks and proving generalization error bounds.
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.