Bayesian Indicator Model Selection Approaches for Structured Sparse Regressions

Abstract

In this talk, the structure selection problems are considered. Given a linear regression model, the variables (regressors) can form certain structures or patterns based on the prior background knowledge and we are interested in identifying these important structures for explaining the response variable due to the different structure sparse assumptions. One of the most common structures is group, for example, genes in the same biological pathway can form a group, and under sparse group assumption, we not only want to identify the important groups but also select the active variables within these important groups. To accomplish selection goal, the different binary indicators are introduced to denote the structures (or variables) are selected or not. Thus the structure selection problems can be solved by sampling from the posterior distributions of these indicators. Several MCMC algorithms are proposed for the indicator posterior sampling. Simulations and real examples are used to illustrate the performance of the proposed Bayesian approaches. In addition to the single response model, we extend the proposed approaches to deal with the selection problems raised in the multiple response regression model. Other related works and on-going projects are also briefly introduced at the end of the talk.