Support vector machines are universally consistent

Abstract

We show that support vector machines of the 1-norm soft margin type are universally consistent provided that the regularization parameter is chosen in a distinct manner and the kernel belongs to a specific class-the so-called universal kernels-which has recently been considered by the author. In particular it is shown that the 1-norm soft margin classifier with Gaussian RBF kernel on a compact subsect X of ℝd and regularization parameter cn = nβ-1 is universally consistent, if n is the training set size and 0