BIVAS: A Scalable Bayesian Method for Bi-Level Variable Selection With Applications

In this article, we consider a Bayesian bi-level variable selection problem in high-dimensional regressions. In many practical situations, it is natural to assign group membership to each predictor. Examples include that genetic variants can be grouped at the gene level and a covariate from different tasks naturally forms a group. Thus, it is of interest to select important groups as well as important members from those groups. The existing Markov chain Monte Carlo methods are often computationally intensive and not scalable to large datasets. To address this problem, we consider variational inference for bi-level variable selection. In contrast to the commonly used mean-field approximation, we propose a hierarchical factorization to approximate the posterior distribution, by using the structure of bi-level variable selection. Moreover, we develop a computationally efficient and fully parallelizable algorithm based on this variational approximation. We further extend the developed method to model datasets from multitask learning. The comprehensive numerical results from both simulation studies and real data analysis demonstrate the advantages of BIVAS for variable selection, parameter estimation, and computational efficiency over existing methods. The method is implemented in R package “bivas” available at Supplementary materials for this article are available online.