Ultra High-Dimensional Variable Selection: Beyond the Linear Model

• Activity Number: 494
• Type: Invited
• Date/Time: Wednesday, August 5, 2009 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Richard Samworth*+ and Jianqing Fan and Yichao Wu
• Companies: University of Cambridge and Princeton University and North Carolina State University
• Keywords: Feature screening ; variable selection ; pseudo-likelihood models

Abstract

In the linear model, Fan and Lv (2008) showed that simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iterated sure independence screening (ISIS), is needed when features are marginally unrelated but jointly related to the response variable. We extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process, and we can also select important features in high-dimensional classification where the frequently used two-sample t-method may fail. A new technique is introduced to reduce the false discovery rate in the feature screening stage, and we illustrate the methodology on simulated and real data.