Metropolis-adjusted interacting particle sampling

TL;DR

This paper explores the use of Metropolis adjustments in interacting particle samplers to improve their accuracy and convergence when sampling from complex distributions, especially in Bayesian inverse problems.

Contribution

It introduces a Metropolization technique for ensemble-based samplers, providing theoretical convergence guarantees and demonstrating improved performance in numerical experiments.

Findings

Metropolization improves sampler accuracy.

Theoretical proof of convergence to the target distribution.

Enhanced performance in Bayesian inverse problems.

Abstract

In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and implemented as ensembles of particles that move in the product state space according to coupled stochastic differential equations. The ensemble approximation and numerical time stepping used to simulate these systems can introduce bias and affect the invariance of the particle system with respect to the target distribution. To correct for this, we investigate the use of a Metropolization step, similar to the Metropolis-adjusted Langevin algorithm. We examine Metropolization of either the whole ensemble or smaller subsets of the ensemble, and prove basic convergence of the resulting ensemble Markov chain to the target distribution. Our numerical results demonstrate the benefits of this correction in numerical examples for popular interacting particle samplers such as ALDI, CBS, and stochastic SVGD.