TY  - JOUR
VL  - 57
EP  - 558
PB  - IEEE
SP  - 549
A1  - Gnecco, Giorgio
A1  - Sanguineti, Marcello
AV  - none
ID  - eprints1719
TI  - On a Variational Norm Tailored to Variable-Basis Approximation Schemes
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5673958&isnumber=5673678
IS  - 1
KW  - ${cal L}_1$-norm
KW  -  Approximation schemes
KW  -  convex hulls
KW  -    infinite-dimensional optimization
KW  -  upper and lower bounds
KW  -   variation with respect to a set
SN  - 0018-9448
Y1  - 2011///
JF  - IEEE Transactions on Information Theory
N2  - 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.
ER  -