On Variable Selection Using Additive Conditional Independence

• Activity Number: 651
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Kuang-Yao Lee*+ and Bing Li and Hongyu Zhao
• Companies: Yale University and The Pennsylvania State University and Yale University
• Keywords: reproducing kernel ; additive conditional covariance operator ; high-dimensional regression ; sparsity ; heterogeneity

Abstract

We propose a novel variable selection method for high-dimensional data where the number of features is much larger than the sample size. Our approach is built upon additive conditional independence - a new type of statistical relation introduced recently by Li, Chun, and Zhao (2013) in the context of graphical models, which covers a wide variety contemporary statistical models. In contrast to most recent work that aims at searching predictors among features that are associated with the conditional mean of a response, our method can capture features that are not exclusively related to regression (or conditional mean) function. In this talk, we will first introduce our procedures to identify the active sets at both the population and the sample levels, and then discuss the asymptotic behavior of the proposed estimator. Finally, we will present some application and simulation results.