Understanding and Accelerating Particle-Based Variational Inference

TL;DR

This paper provides a unified theoretical framework for particle-based variational inference, introduces acceleration and bandwidth-selection methods, and demonstrates improved convergence and accuracy in Bayesian inference tasks.

Contribution

It unifies existing ParVIs through Wasserstein gradient flows, introduces novel acceleration and bandwidth-selection techniques, and offers practical improvements for Bayesian inference.

Findings

Accelerated convergence of ParVIs demonstrated.

Enhanced sample accuracy with bandwidth selection.

Theoretical insights unify and extend existing ParVIs.

Abstract

Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.