eprintid: 1751
rev_number: 4
eprint_status: archive
userid: 46
dir: disk0/00/00/17/51
datestamp: 2013-09-17 07:44:28
lastmod: 2013-09-17 07:44:28
status_changed: 2013-09-17 07:44:28
type: article
succeeds: 1720
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Kůrková, Věra
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
creators_id: 
title: Can Dictionary-Based Computational Models Outperform the Best Linear Ones? 
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Dictionary-based approximation; Linear approximation; Rates of approximation; Worst-case error; Kolmogorov width; Perceptron networks
note: Special Issue "Artificial Neural Networks: Selected Papers from ICANN 2010"
abstract: Approximation capabilities of two types of computational models are explored: dictionary-based models (i.e., linear combinations of n -tuples of basis functions computable by units belonging to a set called “dictionary”) and linear ones (i.e., linear combinations of n fixed basis functions). The two models are compared in terms of approximation rates, i.e., speeds of decrease of approximation errors for a growing number n of basis functions. Proofs of upper bounds on approximation rates by dictionary-based models are inspected, to show that for individual functions they do not imply estimates for dictionary-based models that do not hold also for some linear models. Instead, the possibility of getting faster approximation rates by dictionary-based models is demonstrated for worst-case errors in approximation of suitable sets of functions. For such sets, even geometric upper bounds hold. 
date: 2011
date_type: published
publication: Neural Networks 
volume: 24
number: 8
publisher: Elseviers
pagerange: 881 - 887
id_number: 10.1016/j.neunet.2011.05.014
refereed: TRUE
issn: 0893-6080
official_url: http://www.sciencedirect.com/science/article/pii/S0893608011001560
citation:   Gnecco, Giorgio and Kůrková, Věra and Sanguineti, Marcello  Can Dictionary-Based Computational Models Outperform the Best Linear Ones?  Neural Networks , 24 (8).  881 - 887.  ISSN 0893-6080      (2011)