On the Vgamma Dimension for Regression in Reproducing Kernel Hilbert Spaces

Authors: Theodoros Evgeniou and Massimiliano Pontil.

Source: Lecture Notes in Artificial Intelligence Vol. 1720, 1999, 106 - 117.

Abstract. This paper presents a computation of the Vgamma dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression epsilon-insensitive loss function Lepsilon, and general Lp loss functions. Finiteness of the Vgamma dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the Lepsilon or general Lp loss functions. This paper presents a novel proof of this result. It also presents a computation of an upper bound of the Vgamma dimension under some conditions, that leads to an approach for the estimation of the empirical Vgamma dimension given a set of training data.

©Copyright 1999 Springer-Verlag