MCMC with Strings and Branes: The Suburban Algorithm (Extended Version)

TL;DR

This paper introduces a novel class of MCMC algorithms inspired by string and brane physics, called suburban samplers, which use coupled parallel Metropolis-Hastings chains to improve convergence and overcome energy barriers.

Contribution

The paper proposes a new MCMC method involving coupled extended objects on a grid, demonstrating how neighbor interactions affect sampling efficiency and convergence.

Findings

Performance improves with increased neighbors up to a critical point.

Beyond the critical connectivity, performance declines due to groupthink.

Suburban samplers can better overcome free energy barriers.

Abstract

Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis-Hastings (MH) samplers, we place them on an auxiliary grid, and couple them together via nearest neighbor interactions. This leads to a class of "suburban samplers" (i.e., spread out Metropolis). Coupling the samplers in this way modifies the mixing rate and speed of convergence for the Markov chain, and can in many cases allow a sampler to more easily overcome free energy barriers in a target distribution. We test these general theoretical considerations by performing several numerical experiments. For suburban samplers with a fluctuating grid topology, performance is strongly correlated with the average number of neighbors. Increasing the average number of neighbors above zero initially leads to an increase in performance, though there is a critical connectivity with effective dimension d_eff ~ 1, above which "groupthink" takes over, and the performance of the sampler declines.