Parallelizing MCMC with Random Partition Trees

TL;DR

This paper introduces PART, a novel embarrassingly parallel MCMC method using random partition trees to improve accuracy, resampling, and scalability for large datasets in Bayesian inference.

Contribution

The paper proposes a new EP-MCMC algorithm that leverages random partition trees, addressing limitations of existing methods in approximation accuracy and resampling.

Findings

The PART algorithm is distribution-free and adaptable to multiple scales.

Extensive experiments show improved empirical performance over existing methods.

Theoretical analysis supports the effectiveness of the proposed approach.

Abstract

The modern scale of data has brought new challenges to Bayesian inference. In particular, conventional MCMC algorithms are computationally very expensive for large data sets. A promising approach to solve this problem is embarrassingly parallel MCMC (EP-MCMC), which first partitions the data into multiple subsets and runs independent sampling algorithms on each subset. The subset posterior draws are then aggregated via some combining rules to obtain the final approximation. Existing EP-MCMC algorithms are limited by approximation accuracy and difficulty in resampling. In this article, we propose a new EP-MCMC algorithm PART that solves these problems. The new algorithm applies random partition trees to combine the subset posterior draws, which is distribution-free, easy to resample from and can adapt to multiple scales. We provide theoretical justification and extensive experiments illustrating empirical performance.