Multilevel Gibbs Sampling for Bayesian Regression

TL;DR

This paper introduces a multilevel Gibbs sampling method for Bayesian linear mixed models that accelerates computation in large-scale applications by leveraging data clustering and correlated sampling, maintaining predictive accuracy.

Contribution

It proposes a novel multilevel Gibbs sampler that reduces computational time for Bayesian regression with large datasets, incorporating data clustering and correlated samples for efficiency.

Findings

Achieves significant speed-up in Bayesian regression computations.

Maintains predictive performance comparable to traditional methods.

Effective across diverse datasets.

Abstract

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known computational burden of Markov Chain Monte Carlo approach for Bayesian regression, we developed a multilevel Gibbs sampler for Bayesian regression of linear mixed models. The level hierarchy of data matrices is created by clustering the features and/or samples of data matrices. Additionally, the use of correlated samples is investigated for variance reduction to improve the convergence of the Markov Chain. Testing on a diverse set of data sets, speed-up is achieved for almost all of them without significant loss in predictive performance.