Nonparametric Variable Selection, Clustering, and Prediction for High-Dimensional Regression

• Activity Number: 130
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Subharup Guha*+ and Veera Baladandayuthapani
• Companies: University of Missouri and MD Anderson Cancer Center
• Keywords: Bayesian semiparametric models ; Markov chain Monte Carlo ; Poisson-Dirichlet process ; Dirichlet process ; Nonlinear functional relationships ; Small n, large p problems

Abstract

The development of parsimonious models for reliable inference and prediction of responses in high-dimensional regression settings is often challenging due to relatively small sample sizes and the presence of complex interaction patterns between a large number of covariates. We propose an efficient, nonparametric framework for simultaneous variable selection, clustering and prediction in high-throughput regression settings with continuous or discrete outcomes, called VariScan. The VariScan model utilizes the sparsity induced by Poisson-Dirichlet processes (PDPs) to group the covariates into lower-dimensional latent clusters consisting of covariates with similar patterns among the samples. Subsequently, the latent clusters are used to build a nonlinear prediction model for the responses using an adaptive mixture of linear and nonlinear elements, thus achieving a balance between model parsimony and flexibility. Through simulation studies and analyses of benchmark data sets, we demonstrate that VariScan compares favorably to and often outperforms existing methodologies in terms of the prediction accuracies of the subject-specific responses.