@article{eprints1719,
           pages = {549--558},
       publisher = {IEEE},
            year = {2011},
          author = {Giorgio Gnecco and Marcello Sanguineti},
         journal = {IEEE Transactions on Information Theory},
           title = {On a Variational Norm Tailored to Variable-Basis Approximation Schemes},
          number = {1},
          volume = {57},
        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 {\pounds}1-norms of the weighting functions in such representations. Families of functions for which the two norms are equal are described.},
        keywords = {\$\{cal L\}\_1\$-norm, Approximation schemes, convex hulls,   infinite-dimensional optimization, upper and lower bounds,  variation with respect to a set},
             url = {http://eprints.imtlucca.it/1719/}
}