Determinantal Point Process Priors for Bayesian Variable Selection in Linear Regression

Abstract

We propose discrete determinantal point processes (DPPs) for priors on the model parameter in Bayesian variable selection. By our variable selection method, collinear predictors are less likely to be selected simultaneously because of the repulsion property of discrete DPPs. Three types of DPP priors are proposed. We show the efficiency of the proposed priors through numerical experiments and applications to collinear datasets.