Aggregation of SVM Classifiers Using Sobolev Spaces

This paper investigates statistical performances of Support Vector Machines (SVM) and considers the problem of adaptation to the margin parameter and to complexity. In particular we provide a classifier with no tuning parameter. It is a combination of SVM classifiers. Our contribution is two-fold: (1) we propose learning rates for SVM using Sobolev spaces and build a numerically realizable aggregate that converges with same rate; (2) we present practical experiments of this method of aggregation for SVM using both Sobolev spaces and Gaussian kernels.