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Generative Adversarial Networks (GANs) have become a widely popular frameworkfor generative modelling of high-dimensional datasets. However their trainingis well-known to be difficult. This work presents a rigorous statisticalanalysis of GANs providing straight-forward explanations for common trainingpathologies such as vanishing gradients. Furthermore, it proposes a newtraining objective, Kernel GANs, and demonstrates its practical effectivenesson large-scale real-world data sets. A key element in the analysis is thedistinction between training with respect to the (unknown) data distribution,and its empirical counterpart. To overcome issues in GAN training, we pursuethe idea of smoothing the Jensen-Shannon Divergence (JSD) by incorporatingnoise in the input distributions of the discriminator. As we show, thiseffectively leads to an empirical version of the JSD in which the true and thegenerator densities are replaced by kernel density estimates, which leads toKernel GANs.

Non-parametric estimation of Jensen-Shannon Divergence in Generative Adversarial Network training