An Ensemble EM Algorithm for Bayesian Variable Selection

TL;DR

This paper introduces an efficient ensemble EM algorithm for Bayesian variable selection in linear regression, capable of handling large datasets and achieving consistent variable selection even as the number of variables grows.

Contribution

It proposes a novel ensemble EM algorithm that improves scalability and accuracy in Bayesian variable selection, addressing local optima issues.

Findings

Algorithm scales efficiently with big data

Achieves variable selection consistency as p diverges with n

Demonstrates superior empirical performance

Abstract

We study the Bayesian approach to variable selection in the context of linear regression. Motivated by a recent work by Rockova and George (2014), we propose an EM algorithm that returns the MAP estimate of the set of relevant variables. Due to its particular updating scheme, our algorithm can be implemented efficiently without inverting a large matrix in each iteration and therefore can scale up with big data. We also show that the MAP estimate returned by our EM algorithm achieves variable selection consistency even when $p$ diverges with $n$. In practice, our algorithm could get stuck with local modes, a common problem with EM algorithms. To address this issue, we propose an ensemble EM algorithm, in which we repeatedly apply the EM algorithm on a subset of the samples with a subset of the covariates, and then aggregate the variable selection results across those bootstrap replicates. Empirical studies have demonstrated the superior performance of the ensemble EM algorithm.