Dimension for Regression in Reproducing Kernel Hilbert Spaces
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
dimension for
regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for
the Support Vector Machine (SVM) regression
-insensitive loss function L, and general Lp
loss functions.
Finiteness of the
dimension is shown,
which also proves uniform convergence in probability for regression machines in
RKHS subspaces that use the
L 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
dimension
under some conditions, that leads to an approach for the estimation of the
empirical dimension
given a set of training data.
©Copyright 1999 Springer-Verlag