Stochastic Gradient MCMC with Repulsive Forces

TL;DR

This paper unifies SG-MCMC and SVGD into a novel sampling algorithm that incorporates repulsive forces and noise, enhancing exploration and avoiding particle collapse in Bayesian inference.

Contribution

It introduces a new sampling scheme combining SG-MCMC and SVGD with repulsive forces, improving exploration and convergence in Bayesian inference.

Findings

Enhanced exploration of parameter space

Avoidance of particle collapse

Improved sampling efficiency

Abstract

We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCMC method. Instead of treating each parallel chain independently from others, our proposed algorithm implements a repulsive force between particles, avoiding collapse and facilitating a better exploration of the parameter space. We also show how the addition of this noise term is necessary to obtain a valid SG-MCMC sampler, a significant difference with SVGD. Experiments with both synthetic distributions and real datasets illustrate the benefits of the proposed scheme.