Sampling using Adaptive Regenerative Processes

TL;DR

This paper introduces an adaptive regeneration process for Markov chain Monte Carlo methods that automatically adjusts the regeneration distribution, reducing the need for manual tuning and improving sampling efficiency especially for skewed target distributions.

Contribution

The authors propose a novel adaptive method for selecting regeneration distributions in Markov processes, eliminating the need for computing a constant and improving sampling robustness.

Findings

Adaptive method reduces regeneration frequency.

Improves accuracy of Monte Carlo estimates.

Effective for skewed target distributions.

Abstract

Enriching Brownian motion with regenerations from a fixed regeneration distribution $\mu$ at a particular regeneration rate $\kappa$ results in a Markov process that has a target distribution $\pi$ as its invariant distribution. For the purpose of Monte Carlo inference, implementing such a scheme requires firstly selection of regeneration distribution $\mu$, and secondly computation of a specific constant $C$. Both of these tasks can be very difficult in practice for good performance. We introduce a method for adapting the regeneration distribution, by adding point masses to it. This allows the process to be simulated with as few regenerations as possible and obviates the need to find said constant $C$. Moreover, the choice of fixed $\mu$ is replaced with the choice of the initial regeneration distribution, which is considerably less difficult. We establish convergence of this resulting self-reinforcing process and explore its effectiveness at sampling from a number of target distributions. The examples show that adapting the regeneration distribution guards against poor choices of fixed regeneration distribution and can reduce the error of Monte Carlo estimates of expectations of interest, especially when $\pi$ is skewed.