Open Access
dec 2006 Classifiers of support vector machine type with \ell1 complexity regularization
Bernadetta Tarigan, Sara A. Van De Geer
Author Affiliations +
Bernoulli 12(6): 1045-1076 (dec 2006). DOI: 10.3150/bj/1165269150


We study the binary classification problem with hinge loss. We consider classifiers that are linear combinations of base functions. Instead of an 2 penalty, which is used by the support vector machine, we put an 1 penalty on the coefficients. Under certain conditions on the base functions, hinge loss with this complexity penalty is shown to lead to an oracle inequality involving both model complexity and margin.


Download Citation

Bernadetta Tarigan. Sara A. Van De Geer. "Classifiers of support vector machine type with \ell1 complexity regularization." Bernoulli 12 (6) 1045 - 1076, dec 2006.


Published: dec 2006
First available in Project Euclid: 4 December 2006

zbMATH: 1118.62067
MathSciNet: MR2274857
Digital Object Identifier: 10.3150/bj/1165269150

Keywords: Binary classification , hinge loss , margin , Oracle inequality , penalized classification rule , Sparsity

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

Vol.12 • No. 6 • dec 2006
Back to Top