Geometrical Insights for Implicit Generative Modeling

Understand

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.