An Approach to Variable Selection Employing Dirichlet Lasso

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marc Sobel*+ and Kiranmoy Das and Zhigen Zhao
• Companies: Temple University and Temple University and Temple University
• Keywords: Dirichlet Process Priors ; Group Lasso ; Metropolis-Hastings ; Gibbs Sampling ; Bayesian Lasso

Abstract

One of the key problems in statistical research is concerned with selecting important predictor variables in regression settings. The Bayesian (and Bayesian grouped) Lasso have played a crucial role in this research. We propose a Bayesian methodology, Dirichlet Lasso, to solve this problem. In many modern regression settings, large groups of predictor variables play the same inferential role; we say in this case that they exhibit a group structure. Dirichlet Lasso employs Dirichlet process priors to infer the missing group label information present in this group structure. Dirichlet process priors have the advantage of simultaneously clustering the variable coefficients and selecting the best predictor variables. We show, using a variety of examples, that the predictive performance of the Dirichlet Lasso is frequently superior to (non-Dirichlet) Bayesian and Bayesian grouped Lasso in high dimensional settings where all or most group label information is missing.