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MiS Preprint
152/2006

Deterministic Error Analysis of Support Vector Regression and Related Regularized Kernel Methods

Christian Rieger and Barbara Zwicknagl

Abstract

This paper introduces a new technique for the analysis of kernel-based regression problems. The basic tools are sampling inequalities which apply to all machine learning problems involving penalty terms induced by kernels related to Sobolev spaces. They lead to explicit deterministic results concerning the worst case behaviour of $\epsilon$- and $\nu$-SVRs. Using these, we show how to adjust regularization parameters to get best possible approximation orders for regression. The results are illustrated by some numerical examples.

Received:
Dec 15, 2006
Published:
Dec 15, 2006
Keywords:
sampling inequality, radial basis functions, approximation theory, reproducing kernel Hilbert space, Sobolev space

Related publications

inJournal
2009 Journal Open Access
Christian Rieger and Barbara Zwicknagl

Deterministic error analysis of support vector regression and related regularized kernel methods

In: Journal of machine learning research, 10 (2009), pp. 2115-2132