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.
2010 Mathematics Subject Classification : 68T05, 62J02.
Key words and phrases : Classification, Coefficient regularization, Polynomial kernels, Bernstein-Kantorovich polynomial, Learning rates.