Learning a function from noisy samples at a finite sparse set of points

Authors:
Andreas Hofinger;Friedrich Pillichshammer
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraíe 69, A-4040 Linz, Austria;University of Linz, Institute for Financial Mathematics, Altenbergerstraíe 69, A-4040 Linz, Austria
Venue:
Journal of Approximation Theory
Year:
2009

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Abstract

In learning theory the goal is to reconstruct a function defined on some (typically high dimensional) domain @W, when only noisy values of this function at a sparse, discrete subset @w@?@W are available. In this work we use Koksma-Hlawka type estimates to obtain deterministic bounds on the so-called generalization error. The resulting estimates show that the generalization error tends to zero when the noise in the measurements tends to zero and the number of sampling points tends to infinity sufficiently fast.