Function estimation by feedforward sigmoidal networks with bounded weights

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The authors address the problem of PAC (probably and approximately correct) learning functions f : [0, 1]{sup d} {r_arrow} [{minus}K, K] based on iid (independently and identically distributed) sample generated according to an unknown distribution, by using feedforward sigmoidal networks. They use two basic properties of the neural networks with bounded weights, namely: (a) they form a Euclidean class, and (b) for hidden units of the form tanh ({gamma}z) they are Lipschitz functions. Either property yields sample sizes for PAC function learning under any Lipschitz cost function. The sample size based on the first property is tighter compared to the ... continued below

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11 p.

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Rao, N.S.V.; Protopoescu, V. & Qiao, H. May 1, 1996.

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  • Rao, N.S.V.
  • Protopoescu, V. Oak Ridge National Lab., TN (United States). Center for Engineering Systems Advanced Research
  • Qiao, H. Fort Valley State Coll., GA (United States). Dept. of Mathematics and Physics

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Description

The authors address the problem of PAC (probably and approximately correct) learning functions f : [0, 1]{sup d} {r_arrow} [{minus}K, K] based on iid (independently and identically distributed) sample generated according to an unknown distribution, by using feedforward sigmoidal networks. They use two basic properties of the neural networks with bounded weights, namely: (a) they form a Euclidean class, and (b) for hidden units of the form tanh ({gamma}z) they are Lipschitz functions. Either property yields sample sizes for PAC function learning under any Lipschitz cost function. The sample size based on the first property is tighter compared to the known bounds based on VC-dimension. The second estimate yields a sample size that can be conveniently adjusted by a single parameter, {gamma}, related to the hidden nodes.

Physical Description

11 p.

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OSTI as DE96008788

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  • 9. annual conference on computational learning theory, Desenzano del Garda (Italy), 23 Jun 1996

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  • Other: DE96008788
  • Report No.: CONF-9606113--2
  • Grant Number: AC05-96OR22464
  • DOI: 10.2172/217721 | External Link
  • Office of Scientific & Technical Information Report Number: 238556
  • Archival Resource Key: ark:/67531/metadc671625

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  • May 1, 1996

Added to The UNT Digital Library

  • June 29, 2015, 9:42 p.m.

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  • Jan. 19, 2016, 1:52 p.m.

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Rao, N.S.V.; Protopoescu, V. & Qiao, H. Function estimation by feedforward sigmoidal networks with bounded weights, article, May 1, 1996; Tennessee. (digital.library.unt.edu/ark:/67531/metadc671625/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.