Variable Selection for Support Vector Machines in Moderately High Dimensions

Journal of the Royal Statistical Society. Series B, Statistical Methodology
Xiang ZhangRunze Li

Abstract

The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when the number of predictors diverges to infinity. In this work, we establish a unified theory for a general class of nonconvex penalized SVMs. We first prove that in ultra-high dimensions, there exists one local minimizer to the objective function of nonconvex penalized SVMs possessing the desired oracle property. We further address the problem of nonunique local minimizers by showing that the local linear approximation algorithm is guaranteed to converge to the oracle estimator even in the ultra-high dimensional setting if an appropriate initial estimator is available. This condition on initial estimator is verified to be automatically valid as long as the dimensions are moderately high. Numerical examples provide supportive evidence.

References

Oct 27, 2005·Bioinformatics·Hao Helen ZhangCheolwoo Park
Jan 27, 2009·Annals of Statistics·Jianqing Fan, Yingying Fan
Jan 1, 2008·Journal of the Royal Statistical Society. Series B, Statistical Methodology·Hao Helen Zhang
Aug 1, 2008·Annals of Statistics·Hui Zou, Runze Li
Oct 20, 2012·Journal of the American Statistical Association·Lan WangRunze Li
Jun 21, 2014·Annals of Statistics·Lan WangRunze Li
Jan 1, 2011·Journal of the American Statistical Association·Rahul MazumderTrevor Hastie
Jan 20, 2015·Annals of Statistics·Jianqing FanHui Zou

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Citations

Dec 15, 2018·Biometrical Journal. Biometrische Zeitschrift·Guang-Hui FuJianxin Pan

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