Grouped Variable Selection via Nested Spike and Slab Priors

Abstract

Grouped Variable Selection via Nested Spike and Slab Priors Dr. Tso-Jung Yen (顏 佐 榕 博士) Postdoctoral Fellow, Institute of Statistical Science, Academia Sinica ? In this paper we study grouped variable selection problems. We propose a specified prior, called the nested spike and slab prior, to model collective behavior of regression coefficients. At the group level, the nested spike and slab prior puts positive mass on the probability that the l2-norm of the grouped coefficients is equal to zero. At the individual level, it assigns each coefficient a spike and slab prior. To estimate the model, we adopt a maximum a posteriori approach. The estimation problem involves an approximate objective function modified with the majorization-minimization technique. Simulation studies show that the proposed estimator performs relatively well when both the true and redundant covariates are included in the same group. Asymptotic analysis further shows that the proposed estimator can achieve a smaller l2 estimation error if groups that include the true covariates do not include too many redundant covariates. In addition, given some regular conditions hold, the proposed estimator can achieve model selection consistency regardless of the irrepresentable-type conditions.