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On a Variational Norm Tailored to Variable-Basis Approximation Schemes

Gnecco, Giorgio and Sanguineti, Marcello On a Variational Norm Tailored to Variable-Basis Approximation Schemes. IEEE Transactions on Information Theory, 57 (1). pp. 549-558. ISSN 0018-9448 (2011)

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A variational norm associated with sets of computational units and used in function approximation, learning from data, and infinite-dimensional optimization is investigated. For sets Gk obtained by varying a vector y of parameters in a fixed-structure computational unit K(-,y) (e.g., the set of Gaussians with free centers and widths), upper and lower bounds on the GK -variation norms of functions having certain integral representations are given, in terms of the £1-norms of the weighting functions in such representations. Families of functions for which the two norms are equal are described.

Item Type: Article
Identification Number: 10.1109/TIT.2010.2090198
Uncontrolled Keywords: ${cal L}_1$-norm, Approximation schemes, convex hulls, infinite-dimensional optimization, upper and lower bounds, variation with respect to a set
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Giorgio Gnecco
Date Deposited: 13 Sep 2013 11:34
Last Modified: 16 Sep 2013 12:03
URI: http://eprints.imtlucca.it/id/eprint/1719

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