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Abstract Details

Activity Number: 345
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #304901
Title: Structured Dimension Reduction
Author(s): Bo Zhang*+ and Lexin Li
Companies: North Carolina State University and North Carolina State University
Address: Department of Statistics, Raleigh, NC, 27695-8203, United States
Keywords: Dimension reduction ; conditional independence ; reproducing kernel

We consider high-dimensional regression problem where the predictors have some structural constraint. For instance, in cognitive science, a battery of cognitive measures belong to different cognitive domains; in computational biology, genes belong to different biological pathways; and in brain imaging analysis, images come in the form of matrix/arrays. We propose a new class of dimension reduction approaches for aggregating high-dimensional predictors while incorporating predictor structural information. Our solution is based upon a general nonparametric characterization of conditional independence using covariance operators on reproducing kernel Hilbert spaces. Through simulation and real data analyses, we show that the proposed methods achieve greater accuracy and interpretability than the dimension reduction solutions that ignore predictor structural information.

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