On the V_ gamma Dimension for Regression in Reproducing Kernel Hilbert Spaces

摘要

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