On a Variational Norm Tailored to Variable-Basis Approximation Schemes | IEEE Journals & Magazine | IEEE Xplore

On a Variational Norm Tailored to Variable-Basis Approximation Schemes


Abstract:

A variational norm associated with sets of computational units and used in function approximation, learning from data, and infinite-dimensional optimization is investigat...Show More

Abstract:

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.
Published in: IEEE Transactions on Information Theory ( Volume: 57, Issue: 1, January 2011)
Page(s): 549 - 558
Date of Publication: 23 December 2010

ISSN Information:


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