Bridging the Gap Between Variational Inference and Wasserstein Gradient Flows

Understand

Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families.

• On the other hand, Wasserstein gradient flows describe optimization within the space of probability measures where they do not necessarily admit a parametric density function.
• In this paper, we bridge the gap between these two methods.
• We demonstrate that, under certain conditions, the Bures-Wasserstein gradient flow can be recast as the Euclidean gradient flow where its forward Euler scheme is the standard black-box variational inference algorithm.