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  • Research Article
  • 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:


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.


  • Approximation Error
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Authors’ Affiliations

Department of Mathematics (DIMA), University of Genova, Via Dodecaneso 35, 16146 Genova, Italy
Department of Communications, Computer, and System Sciences (DIST), University of Genova, Via Opera Pia 13, 16145 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.