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

Mingxuan Cai, Mingwei Dai, Jingsi Ming, Heng PENG, Jin Liu, Can YANG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)40-52
Number of pages13
JournalJournal of Computational and Graphical Statistics
Issue number1
Publication statusPublished - 2 Jan 2020

Scopus Subject Areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Bayesian variable selection
  • Group sparsity
  • Parallel computing
  • Variational inference


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