

Preprint 152/2006
Deterministic Error Analysis of Support Vector Regression and Related Regularized Kernel Methods
Christian Rieger and Barbara Zwicknagl
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Submission date: 15. Dec. 2006
Pages: 16
published in: Journal of machine learning research, 10 (2009), p. 2115-2132
Bibtex
Keywords and phrases: sampling inequality, radial basis functions, approximation theory, reproducing kernel Hilbert space, Sobolev space
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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 - and
-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.