eprintid: 1719
rev_number: 6
eprint_status: archive
userid: 46
dir: disk0/00/00/17/19
datestamp: 2013-09-13 11:34:55
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-13 11:34:55
type: article
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: On a Variational Norm Tailored to Variable-Basis Approximation Schemes
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: ${cal L}_1$-norm, Approximation schemes, convex hulls,   infinite-dimensional optimization, upper and lower bounds,  variation with respect to a set
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.
date: 2011
date_type: published
publication: IEEE Transactions on Information Theory
volume: 57
number: 1
publisher: IEEE
pagerange: 549-558
id_number: 10.1109/TIT.2010.2090198
refereed: TRUE
issn: 0018-9448
official_url: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5673958&isnumber=5673678
citation:   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)