Open Access

Estimates of the Approximation Error Using Rademacher Complexity: Learning Vector-Valued Functions

Journal of Inequalities and Applications20082008:640758

Received: 15 January 2008

Accepted: 20 October 2008

Published: 30 December 2008


For certain families of multivariable vector-valued functions to be approximated, the accuracy of approximation schemes made up of linear combinations of computational units containing adjustable parameters is investigated. Upper bounds on the approximation error are derived that depend on the Rademacher complexities of the families. The estimates exploit possible relationships among the components of the multivariable vector-valued functions. All such components are approximated simultaneously in such a way to use, for a desired approximation accuracy, less computational units than those required by componentwise approximation. An application to -stage optimization problems is discussed.

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Authors’ Affiliations

Department of Mathematics (DIMA), University of Genova, Genova, Italy
Department of Communications, Computer, and System Sciences (DIST), University of Genova, Genova, Italy


© G. Gnecco and M. Sanguineti. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.