Ensemble Markov chain Monte Carlo with teleporting walkers

TL;DR

This paper introduces an ensemble MCMC method with teleporting walkers that enhances sampling efficiency by overcoming metastability, with theoretical analysis and application to Bayesian hyperparameter estimation.

Contribution

It proposes a novel ensemble MCMC approach with teleportation, providing theoretical convergence analysis and demonstrating effectiveness in high-dimensional Bayesian problems.

Findings

Rapid mixing once modes are populated

Asymptotic convergence independent of spectral gap

Effective application to Gaussian process hyperparameter estimation

Abstract

We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in which one chain's state is cloned as another's is deleted. This effective teleportation of states can overcome issues of metastability in the underlying chain, as the scheme enjoys rapid mixing once the modes of the target density have been populated. We derive a mean-field limit for the evolution of the ensemble. We analyze the global and local convergence of this mean-field limit, showing asymptotic convergence independent of the spectral gap of the underlying Markov chain, and moreover we interpret the limiting evolution as a gradient flow. We explain how interaction can be applied selectively to a subset of state variables in order to maintain advantage on very high-dimensional problems. Finally we present the application of our methodology to Bayesian hyperparameter estimation for Gaussian process regression.