SPARSITY IN MULTIPLE KERNEL LEARNING

被引：100

作者：

Koltchinskii, Vladimir ^{[1
]}

Yuan, Ming ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Georgia Inst Technol, Sch Ind & Syst Engn, Atlanta, GA 30332 USA

来源：

ANNALS OF STATISTICS | 2010年 / 38卷 / 06期

基金：

美国国家科学基金会;

关键词：

High dimensionality; multiple kernel learning; oracle inequality; reproducing kernel Hilbert spaces; restricted isometry; sparsity; DANTZIG SELECTOR; LASSO;

D O I：

10.1214/10-AOS825

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical L-2 norms and the reproducing kernel Hilbert space (RKHS) norms induced by the kernels with a data-driven choice of regularization parameters. The main focus is on the case when the total number of kernels is large, but only a relatively small number of them is needed to represent the target function, so that the problem is sparse. The goal is to establish oracle inequalities for the excess risk of the resulting prediction rule showing that the method is adaptive both to the unknown design distribution and to the sparsity of the problem.

引用

页码：3660 / 3695

页数：36

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