Penalized empirical risk minimization over Besov spaces

Abstract

Kernel methods are closely related to the notion of reproducing kernel Hilbert space (RKHS). A kernel machine is based on the minimization of an empirical cost and a stabilizer (usually the norm in the RKHS). In this paper we propose to use Besov spaces as alternative hypothesis spaces. We study statistical performances of a penalized empirical risk minimization for classification where the stabilizer is a Besov norm. More precisely, we state fast rates of convergence to the Bayes rule. These rates are adaptive with respect to the regularity of the Bayes.