Scalable Bayesian variable selection regression models for count data

Abstract Variable selection, also known as feature selection in the machine learning literature, plays an indispensable role in scientific studies. In many research areas with massive data, finding a subset of representative features that best explain the outcome of interest has become a critical component in any researcher's workflow. In this chapter, we focus on Bayesian variable selection regression models for count data, and specifically on the negative binomial linear regression model and on the Dirichlet-multinomial regression model. We address the variable selection problem via spike-and-slab priors. For posterior inference, we review standard MCMC methods and also investigate computationally more efficient variational inference approaches that use data augmentation techniques and concrete relaxation methods. We investigate performance of the methods via simulation studies and benchmark data sets.