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2008 Structured variable selection in support vector machines
Seongho Wu, Hui Zou, Ming Yuan
Electron. J. Statist. 2: 103-117 (2008). DOI: 10.1214/07-EJS125

Abstract

When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection techniques have been successfully used in the SVM to perform automatic variable selection. In some problems, there is a natural hierarchical structure among the variables. Thus, in order to have an interpretable SVM classifier, it is important to respect the heredity principle when enforcing the sparsity in the SVM. Many variable selection methods, however, do not respect the heredity principle. In this paper we enforce both sparsity and the heredity principle in the SVM by using the so-called structured variable selection (SVS) framework originally proposed in [20]. We minimize the empirical hinge loss under a set of linear inequality constraints and a lasso-type penalty. The solution always obeys the desired heredity principle and enjoys sparsity. The new SVM classifier can be efficiently fitted, because the optimization problem is a linear program. Another contribution of this work is to present a nonparametric extension of the SVS framework, and we propose nonparametric heredity SVMs. Simulated and real data are used to illustrate the merits of the proposed method.

Citation

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Seongho Wu. Hui Zou. Ming Yuan. "Structured variable selection in support vector machines." Electron. J. Statist. 2 103 - 117, 2008. https://doi.org/10.1214/07-EJS125

Information

Published: 2008
First available in Project Euclid: 22 February 2008

zbMATH: 1320.62154
MathSciNet: MR2386088
Digital Object Identifier: 10.1214/07-EJS125

Subjects:
Primary: 68T10
Secondary: 62G05

Keywords: ‎classification‎ , Heredity , nonparametric estimation , Support Vector Machine , Variable selection

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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