CLASSIFICATION WITH POLYNOMIAL KERNELS AND $l^1-$COEFFICIENT REGULARIZATION

Abstract

In this paper we investigate a class of learning algorithms for classification generated by regularization schemes with polynomial kernels and $l^1-$regularizer. The novelty of our analysis lies in the estimation of the hypothesis error. A Bernstein-Kantorovich polynomial is introduced as a regularizing function. Although the hypothesis spaces and the regularizers in the schemes are sample dependent, we prove the hypothesis error can be removed from the error decomposition with confidence. As a result, we derive some explicit learning rates for the produced classifiers under some assumptions.