The Bayesian Group Bridge for Bilevel Variable Selection

• Activity Number: 305
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Himel Mallick* and Nengjun Yi
• Companies: The University of Alabama at Birmingham and The University of Alabama at Birmingham
• Keywords: Bayesian Regularization ; Bayesian Variable Selection ; Bi-level Variable Selection ; Group Bridge ; Group Variable Selection ; MCMC

Abstract

Group bridge is a flexible regularization method that uses a specially designed L1 penalty on the coefficients associated with a group of variables. It is particularly useful when there is some grouping structure among the predictors. This paper proposes a Bayesian method to solve the group bridge model using a Gibbs sampler. The fundamental difference between the frequentist and Bayesian approach is that, here we can obtain valid standard errors based on a geometrically ergodic Markov chain besides an appropriate point estimator. In addition, the concavity parameter can be estimated from the data along with other parameters in the model. The proposed method is adaptive to the signal level by adopting different shrinkage for different groups of predictors. Empirical evidence of the attractiveness of the method is illustrated by simulations and real data analysis. We find that the Bayesian group bridge outperforms existing group variable selection methods in estimation and prediction. We also discuss possible extensions of this new approach and present a unified framework for bi-level variable selection in general models with other flexible penalties.