Fast Rates for Support Vector Machines
We establish learning rates to the Bayes risk for support vector machines (SVMs) using a regularization sequence λ n = n -α , where a ∈ (0,1) is arbitrary. Under a noise condition recently proposed by Tsybakov these rates can become faster than n -1/2 . In order to deal with the approximation error we present a general concept called the approximation error function which describes how well the infinite sample versions of the considered SVMs approximate the data-generating distribution. In addition we discuss in some detail the relation between the classical approximation error and the approximation error function. Finally, for distributions satisfying a geometric noise assumption we establish some learning rates when the used RKHS is a Sobolev space.