  Generative Adversarial Networks (GANs) have become a widely popular framework
for generative modelling of high-dimensional datasets. However their training
is well-known to be difficult. This work presents a rigorous statistical
analysis of GANs providing straight-forward explanations for common training
pathologies such as vanishing gradients. Furthermore, it proposes a new
training objective, Kernel GANs, and demonstrates its practical effectiveness
on large-scale real-world data sets. A key element in the analysis is the
distinction between training with respect to the (unknown) data distribution,
and its empirical counterpart. To overcome issues in GAN training, we pursue
the idea of smoothing the Jensen-Shannon Divergence (JSD) by incorporating
noise in the input distributions 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, which leads to
Kernel GANs.
