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June 2015 Innovated interaction screening for high-dimensional nonlinear classification
Yingying Fan, Yinfei Kong, Daoji Li, Zemin Zheng
Ann. Statist. 43(3): 1243-1272 (June 2015). DOI: 10.1214/14-AOS1308

Abstract

This paper is concerned with the problems of interaction screening and nonlinear classification in a 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. Our IIS approach screens important interactions by examining only $p$ features instead of all two-way interactions of order $O(p^{2})$. 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 estimated coefficient vector for QDA 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.

Citation

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Yingying Fan. Yinfei Kong. Daoji Li. Zemin Zheng. "Innovated interaction screening for high-dimensional nonlinear classification." Ann. Statist. 43 (3) 1243 - 1272, June 2015. https://doi.org/10.1214/14-AOS1308

Information

Received: 1 October 2014; Published: June 2015
First available in Project Euclid: 15 May 2015

zbMATH: 1328.62383
MathSciNet: MR3346702
Digital Object Identifier: 10.1214/14-AOS1308

Subjects:
Primary: 62H30
Secondary: 62F05 , 62J12

Keywords: ‎classification‎ , Dimension reduction , discriminant analysis , interaction screening , Sparsity , sure screening property

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 3 • June 2015
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