Scalable Bayesian Variable Selection

• Activity Number: 229
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Feng Liang* and Jin Wang and Yuan Ji and Yitan Zhu
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign and The University of Chicago and Northshore University HealthSystem
• Keywords: Bayesian Variable selection ; Variation method ; EM ; Sparsity

Abstract

We propose a new computational framework for Bayesian variable selection. The key idea is to seek an approximation of the posterior distribution via a deterministic optimization procedure. The classical EM algorithm that gives the MAP estimate and the Variational Bayes algorithm (VB) are special cases of this framework. The algorithm we propose is a combination of VB and EM. The big advantage of our algorithm compared to the traditional MCMC is its scalability: it runs very fast and can handle large scale data easily. Although our algorithm provides just an approximation of the full posterior distribution, theoretical study shows that it still achieves model selection consistency asymptotically. We compare the performance of our algorithm with other alternatives on several simulated data sets. We also apply our algorithm on an RNA-sequence data of ovarian cancer, and identify three miRNAs that play an important role in mRNA expression verified by literature.