Abstract
Learning the true density in high-dimensional feature spaces is a well-known problem in machine learning. In this work, we consider generative autoencoders based on maximum-mean discrepancy (MMD) and provide theoretical insights. In particular, (i) we prove that MMD coupled with Coulomb kernels has optimal convergence properties, which are similar to convex functionals, thus improving the training of autoencoders, and (ii) we provide a probabilistic bound on the generalization performance, highlighting some fundamental conditions to achieve better generalization. We validate the theory on synthetic examples and on the popular dataset of celebrities faces, showing that our model, called Coulomb autoencoders, outperform the state-of-the-art.