eprintid: 1749
rev_number: 4
eprint_status: archive
userid: 46
dir: disk0/00/00/17/49
datestamp: 2013-09-17 07:39:34
lastmod: 2013-09-17 07:39:34
status_changed: 2013-09-17 07:39:34
type: article
succeeds: 1701
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: Approximation Error Bounds via Rademacher's Complexity 
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: public
keywords: approximation error, model complexity, curse of dimensionality, Rademacher's complexity, Talagrand's inequality, union bounds, VC dimension.
abstract: Approximation properties of some connectionistic models, commonly used to construct approximation schemes for optimization problems with multivariable functions as admissible solutions, are investigated. Such models are made up of linear combinations of computational units
with adjustable parameters. The relationship between model complexity (number of computational units) and approximation error is investigated using tools from Statistical Learning Theory, such as Talagrand's
inequality, fat-shattering dimension, and Rademacher's complexity. For some families of multivariable functions, estimates of the approximation accuracy of models with certain computational units are derived in dependence of the Rademacher's complexities of the families. The
estimates improve previously-available ones, which were expressed in terms of V C dimension and derived by exploiting union-bound techniques. The results are applied to approximation schemes with certain radial-basis-functions as computational units, for which it is shown that
the estimates do not exhibit the curse of dimensionality with respect to the number of variables.
date: 2008
date_type: published
publication: Applied Mathematical Sciences
volume: 2
number: 4
publisher: Hikari Ltd
pagerange: 153-176
refereed: TRUE
issn: 1312-885X
official_url: http://www.m-hikari.com/ams/ams-password-2008/ams-password1-4-2008/
citation:   Gnecco, Giorgio and Sanguineti, Marcello  Approximation Error Bounds via Rademacher's Complexity.  Applied Mathematical Sciences, 2 (4).  pp. 153-176.  ISSN 1312-885X      (2008)  
document_url: http://eprints.imtlucca.it/1749/1/Applied%20Mathematical%20Sciences_Gnecco_Sanguinetti_2008.pdf