Geometrical Insights for Implicit Generative Modeling

Research paper by Leon Bottou, Martin Arjovsky, David Lopez-Paz, Maxime Oquab

Indexed on: 21 Dec '17Published on: 21 Dec '17Published in: arXiv - Statistics - Machine Learning


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.