Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the 1-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.
@article{arxiv.1712.07822,
title = {Geometrical Insights for Implicit Generative Modeling},
author = {Leon Bottou and Martin Arjovsky and David Lopez-Paz and Maxime Oquab},
journal= {arXiv preprint arXiv:1712.07822},
year = {2019}
}