Mini-batch Tempered MCMC

TL;DR

This paper introduces Mini-batch Tempered MCMC (MINT-MCMC), a scalable method for Bayesian inference that efficiently explores multi-modal posteriors using mini-batch data and a novel parallel sampling algorithm.

Contribution

It proposes a new framework for mini-batch MCMC that estimates the Metropolis-Hastings ratio from data subsets and develops a parallel algorithm based on the Equi-Energy sampler.

Findings

Efficiently explores multiple modes of complex posteriors.

Samples from the true posterior raised to a known temperature.

Demonstrates scalability and effectiveness in high-dimensional settings.

Abstract

In this paper we propose a general framework of performing MCMC with only a mini-batch of data. We show by estimating the Metropolis-Hasting ratio with only a mini-batch of data, one is essentially sampling from the true posterior raised to a known temperature. We show by experiments that our method, Mini-batch Tempered MCMC (MINT-MCMC), can efficiently explore multiple modes of a posterior distribution. Based on the Equi-Energy sampler (Kou et al. 2006), we developed a new parallel MCMC algorithm based on the Equi-Energy sampler, which enables efficient sampling from high-dimensional multi-modal posteriors with well separated modes.