Abstract
This work presents a rigorous statistical analysis of adversarial training
for generative models, advancing recent work by Arjovsky and Bottou 2. A key
element is the distinction between the objective function with respect to the
(unknown) data distribution, and its empirical counterpart. This yields a
straight-forward explanation for common pathologies in practical adversarial
training such as vanishing gradients. To overcome such issues, we pursue the
idea of smoothing the Jensen-Shannon Divergence (JSD) by incorporating noise in
the formulation of the discriminator. As we show, this effectively leads to an
empirical version of the JSD in which the true and the generator densities are
replaced by kernel density estimates. We analyze statistical consistency of
this objective, and demonstrate its practical effectiveness.
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