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Activity Number: 309
Type: Contributed
Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #316516 View Presentation
Title: Innovated Interaction Screening for High-Dimensional Nonlinear Classification
Author(s): Yinfei Kong* and Yingying Fan and Daoji Li and Zemin Zheng
Companies: and University of Southern California and University of Southern California and University of Southern California
Keywords: Classification ; dimension reduction ; discriminant analysis ; interaction screening ; sparsity ; sure screening property
Abstract:

This paper is concerned with interaction screening and nonlinear classification in high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original p-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and simultaneously conducting classification. The IIS screens important interactions by examining only p features instead of all two-way interactions. Our theory shows that the proposed method enjoys sure screening property in interaction selection in the high-dimensional setting of p growing exponentially with the sample size. In the selection and classification step, we establish a sparse inequality on the estimate of SQDA and prove that the classification error of our procedure can be upper-bounded by the oracle classification error plus some smaller order term. Extensive simulation studies and real data analysis show that our proposal compares favorably with existing methods in interaction selection and high-dimensional classification.


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