Determinantal Point Process Priors for Bayesian Variable Selection in Linear Regression

TL;DR

This paper introduces determinantal point process priors for Bayesian variable selection in linear regression, effectively reducing the selection of collinear predictors due to their repulsive properties.

Contribution

It proposes three types of DPP priors for Bayesian variable selection, demonstrating their effectiveness in handling collinearity in datasets.

Findings

DPP priors reduce collinearity in variable selection

Numerical experiments validate the efficiency of DPP priors

Applications show improved model selection in collinear datasets

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.