Variable Selection in Complex High-Dimensional Data Based on Principal Fitted Components

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Moumita Karmakar*+ and Kofi Placid Adragni
• Companies: University of Maryland Baltimore County and University of Maryland, Baltimore County
• Keywords: Inverse regression ; Dimension reduction ; principal components ; Variable selection ; High dimensionality ; Likelihood ratio test

Abstract

Given a high dimensional p-vector of continuous predictors X and a univariate response Y , principal fitted components (PFC) provides a sufficient reduction of X that retains all regression information about Y in X while reducing the dimensionality. The reduction is a linear combination of all the p predictors, where with the use of a flexible set of basis functions, predictors related to Y via complex, nonlinear relationship can be detected. In the presence of possibly large number of irrelevant predictors, the accuracy of the sufficient reduction is hindered. We adapt a sequential Likelihood ratio test to the PFC to obtain a "pruned" sufficient reduction that shed of the irrelevant predictors. The sequential test is based on the likelihood ratio which expression is derived under different covariance structures of X|Y . The resulting reduction has an improved accuracy and also allows the identification of the relevant variables. We compare the variable selection performance of the proposed method to penalized least squares methods like the lasso and sparse PLS through simulations.