Geometrical Insights for Implicit Generative Modeling
This provides theoretical insights for researchers in machine learning, particularly in generative modeling, though it appears incremental as it builds on existing distance metrics.
The paper analyzed the geometric properties of distances like Wasserstein, Energy, and Maximum Mean Discrepancy in implicit generative modeling, finding that the 1-Wasserstein distance allows for approximate global convergence guarantees even with nonconvex generator parametrizations.
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.