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Can Dictionary-based Computational Models Outperform the Best Linear Ones?
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SYSNO ASEP 0360287 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Can Dictionary-based Computational Models Outperform the Best Linear Ones? Author(s) Gnecco, G. (IT)
Kůrková, Věra (UIVT-O) RID, SAI, ORCID
Sanguineti, M. (IT)Source Title Neural Networks. - : Elsevier - ISSN 0893-6080
Roč. 24, č. 8 (2011), s. 881-887Number of pages 7 s. Language eng - English Country GB - United Kingdom Keywords dictionary-based approximation ; linear approximation ; rates of approximation ; worst-case error ; Kolmogorov width ; perceptron networks Subject RIV IN - Informatics, Computer Science R&D Projects OC10047 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000295105700012 EID SCOPUS 80051786839 DOI 10.1016/j.neunet.2011.05.014 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2012
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