Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Estimates of the Approximation Error Using Rademacher Complexity: Learning Vector-Valued Functions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 640758 16 pages doi 2008 640758 Research Article Estimates of the Approximation Error Using Rademacher Complexity Learning Vector-Valued Functions Giorgio Gnecco1 2 and Marcello Sanguineti2 1 Department of Mathematics DIMA University of Genova Via Dodecaneso 35 16146 Genova Italy 2 Department of Communications Computer and System Sciences DIST University of Genova Via Opera Pia 13 16145 Genova Italy Correspondence should be addressed to Marcello Sanguineti marcello@ Received 15 January 2008 Revised 13 August 2008 Accepted 20 October 2008 Recommended by Ulrich Abel 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 N-stage optimization problems is discussed. Copyright 2008 G. Gnecco and M. Sanguineti. 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. 1. Introduction Various authors have derived upper bounds on the approximation error of certain linear combinations of computational units containing adjustable parameters called variable-basis approximation schemes 1 for various families of functions to be approximated see . 211 and the references therein . In these schemes the number of computational .
