  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.
