Classifiers of support vector machine type with ℓ1complexity regularization

Abstract

We study the binary classification problem with hinge loss. We consider classifiers that are linear combinations of base functions. Instead of an ∓2penalty, which is used by the support vector machine, we put an ∓1penalty 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. © 2006 ISI/BS. © 2006 Applied Probability Trust.