DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework

TL;DR

DPVI introduces a dynamic-weight particle-based variational inference framework that adjusts particle weights during optimization, leading to faster convergence and improved approximation of target distributions compared to fixed-weight methods.

Contribution

The paper proposes a novel DPVI framework with a continuous composite flow that evolves particle positions and weights simultaneously, enhancing approximation capabilities.

Findings

DPVI achieves faster decrease of the dissimilarity functional than fixed-weight methods.

Empirical results show DPVI algorithms outperform fixed-weight ParVI algorithms.

The mean-field limit of DPVI corresponds to a Wasserstein-Fisher-Rao gradient flow.

Abstract

The recently developed Particle-based Variational Inference (ParVI) methods drive the empirical distribution of a set of \emph{fixed-weight} particles towards a given target distribution $\pi$ by iteratively updating particles' positions. However, the fixed weight restriction greatly confines the empirical distribution's approximation ability, especially when the particle number is limited. In this paper, we propose to dynamically adjust particles' weights according to a Fisher-Rao reaction flow. We develop a general Dynamic-weight Particle-based Variational Inference (DPVI) framework according to a novel continuous composite flow, which evolves the positions and weights of particles simultaneously. We show that the mean-field limit of our composite flow is actually a Wasserstein-Fisher-Rao gradient flow of certain dissimilarity functional $\mathcal{F}$, which leads to a faster decrease of $\mathcal{F}$ than the Wasserstein gradient flow underlying existing fixed-weight ParVIs. By using different finite-particle approximations in our general framework, we derive several efficient DPVI algorithms. The empirical results demonstrate the superiority of our derived DPVI algorithms over their fixed-weight counterparts.