A Note on Support Vector Machines with Polynomial Kernels

We present a better theoretical foundation of support vector machines with polynomial kernels. The sample error is estimated under Tsybakov's noise assumption. In bounding the approximation error, we take advantage of a geometric noise assumption that was introduced to analyze gaussian kernels. Compared with the previous literature, the error analysis in this note does not require any regularity of the marginal distribution or smoothness of Bayes' rule. We thus establish the learning rates for polynomial kernels for a wide class of distributions.