Joint Bayesian Variable and DAG Selection Consistency for High-Dimensional Regression Models with Network-Structured Covariates

• Activity Number: 28 - Advances in Bayesian Theory and Methods on Network Data Modeling
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xuan Cao* and Kyoungjae Lee
• Companies: University of Cincinnati and Inha University

Abstract

We consider the joint sparse estimation of regression coefficients and the covariance matrix for covariates in a high-dimensional regression model, where the predictors are both relevant to a response variable of interest and functionally related to one another via a Gaussian directed acyclic graph (DAG) model. In this talk, we consider a hierarchical model with spike and slab priors on the regression coefficients and a flexible and general class of DAG-Wishart distributions with multiple shape parameters on the Cholesky factors of the inverse covariance matrix. Under mild regularity assumptions, we establish the joint selection consistency for both the variable and the underlying DAG of the covariates when the dimension of predictors is allowed to grow much larger than the sample size. We demonstrate that our method outperforms existing methods in selecting network-structured predictors in several simulation settings. This is joint work with Kyoungjae Lee.