Branching Stein Variational Gradient Descent for sampling multimodal distributions

TL;DR

This paper introduces BSVGD, a particle-based variational inference method that enhances exploration of multimodal distributions by incorporating a branching mechanism, with theoretical convergence guarantees and empirical validation.

Contribution

The paper presents BSVGD, a novel extension of SVGD that includes branching to better explore multimodal distributions, with proven convergence and improved performance.

Findings

BSVGD effectively explores multimodal distributions.

Theoretical convergence guarantees are established.

Empirical results show improved sampling efficiency.

Abstract

We propose a novel particle-based variational inference method designed to work with multimodal distributions. Our approach, referred to as Branched Stein Variational Gradient Descent (BSVGD), extends the classical Stein Variational Gradient Descent (SVGD) algorithm by incorporating a random branching mechanism that encourages the exploration of the state space. In this work, a theoretical guarantee for the convergence in distribution is presented, as well as numerical experiments to validate the suitability of our algorithm. Performance comparisons between the BSVGD and the SVGD are presented using the Wasserstein distance between samples and the corresponding computational times.