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Handbook on Neural Information Processing pp 143–181Cite as

Approximating Multivariable Functions by Feedforward Neural Nets

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 49))

Abstract

Theoretical results on approximation of multivariable functions by feedforward neural networks are surveyed. Some proofs of universal approximation capabilities of networks with perceptrons and radial units are sketched. Major tools for estimation of rates of decrease of approximation errors with increasing model complexity are proven. Properties of best approximation are discussed. Recent results on dependence of model complexity on input dimension are presented and some cases when multivariable functions can be tractably approximated are described

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Georgetown University, Washington, D.C., 20057-1233, USA

    Paul C. Kainen

  2. Academy of Sciences of the Czech Republic, Pod Vodáarenskou věží 2, 182 07, Prague 8, Czech Republic

    Věra Kůrková

  3. DIBRIS, University of Genova, via Opera Pia 13, 16145, Genova, Italy

    Marcello Sanguineti

Authors
  1. Paul C. Kainen
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  2. Věra Kůrková
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  3. Marcello Sanguineti
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Corresponding author

Correspondence to Paul C. Kainen .

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Editors and Affiliations

  1. , Dipto. Ingegneria dell'Informazione, Università degli Studi di Siena, Via Roma 56, Siena, 53100, Italy

    Monica Bianchini

  2. Fac. Ingegneria, Dipto. Ingegneria dell'Informazione, Università Siena, Via Roma 56, Siena, 53100, Italy

    Marco Maggini

  3. University of Canberra, School of Electrical and Information, Adjunct Professor, Mawson Lakes Campus, ACT, 2601, Australia

    Lakhmi C. Jain

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Kainen, P.C., Kůrková, V., Sanguineti, M. (2013). Approximating Multivariable Functions by Feedforward Neural Nets. In: Bianchini, M., Maggini, M., Jain, L. (eds) Handbook on Neural Information Processing. Intelligent Systems Reference Library, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36657-4_5

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