Oracle inequalities for support vector machines that are based on random entropy numbers

In this paper, we present a new technique for bounding local Rademacher averages of function classes induced by a loss function and a reproducing kernel Hilbert space (RKHS). At the heart of this technique lies the observation that certain expectations of random entropy numbers can be bounded by the eigenvalues of the integral operator associated with the RKHS. We then work out the details of the new technique by establishing two new oracle inequalities for support vector machines, which complement and generalize previous results.