  We propose a method to optimize the representation and distinguishability of
samples from two probability distributions, by maximizing the estimated power
of a statistical test based on the maximum mean discrepancy (MMD). This
optimized MMD is applied to the setting of unsupervised learning by generative
adversarial networks (GAN), in which a model attempts to generate realistic
samples, and a discriminator attempts to tell these apart from data samples. In
this context, the MMD may be used in two roles: first, as a discriminator,
either directly on the samples, or on features of the samples. Second, the MMD
can be used to evaluate the performance of a generative model, by testing the
model's samples against a reference data set. In the latter role, the optimized
MMD is particularly helpful, as it gives an interpretable indication of how the
model and data distributions differ, even in cases where individual model
samples are not easily distinguished either by eye or by classifier.
