%0 Journal Article
%@ 0018-9448
%A Gnecco, Giorgio
%A Sanguineti, Marcello
%D 2011
%F eprints:1719
%I IEEE
%J IEEE Transactions on Information Theory
%K ${cal L}_1$-norm, Approximation schemes, convex hulls,   infinite-dimensional optimization, upper and lower bounds,  variation with respect to a set
%N 1
%P 549-558
%T On a Variational Norm Tailored to Variable-Basis Approximation Schemes
%U http://eprints.imtlucca.it/1719/
%V 57
%X 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.