Methods for Bayesian Variable Selection with Binary Response Data using the EM Algorithm

TL;DR

This paper extends the EMVS Bayesian variable selection method to binary response data using logistic and probit models, demonstrating faster computation and accurate variable selection compared to existing methods.

Contribution

The authors develop and implement EMVS extensions for binary data with SDCA, providing a faster alternative to MCMC and SSVS methods for high-dimensional variable selection.

Findings

EMVS methods outperform SSVS in speed and accuracy

Simulation studies confirm quick identification of sparse models

Real data applications show reduced computational cost

Abstract

High-dimensional Bayesian variable selection problems are often solved using computationally expensive Markov Chain Montle Carlo (MCMC) techniques. Recently, a Bayesian variable selection technique was developed for continuous data using the EM algorithm called EMVS. We extend the EMVS method to binary data by proposing both a logistic and probit extension. To preserve the computational speed of EMVS we also implemented the Stochastic Dual Coordinate Descent (SDCA) algorithm. Further, we conduct two extensive simulation studies to show the computational speed of both methods. These simulation studies reveal the power of both methods to quickly identify the correct sparse model. When these EMVS methods are compared to Stochastic Search Variable Selection (SSVS), the EMVS methods surpass SSVS both in terms of computational speed and correctly identifying significant variables. Finally, we illustrate the effectiveness of both methods on two well-known gene expression datasets. Our results mirror the results of previous examinations of these datasets with far less computational cost.