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
published in: Journal of machine learning research, 10 (2009), p. 2115-2132
Keywords and phrases: sampling inequality, radial basis functions, approximation theory, reproducing kernel Hilbert space, Sobolev space
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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.