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Sample sizes for sigmoidal neural networks

Shawe-Taylor, J; (1995) Sample sizes for sigmoidal neural networks. In: UNSPECIFIED (pp. 258-264).

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Abstract

© 1995 ACM. This paper applies the theory of Probably Approximately Correct (PAC) learning to feedforward neural networks with sigmoidal activation functions. Despite the best known upper bound on the VC dimension of such networks being O((WN)2), for W parameters and TV computational nodes, it is shown that the asymptotic bound on the sample size required for learning with increasing accuracy 1 - e and decreasing probability of failure δ is (Equation presented) For practical values of ∈ and δ the formula obtained for the sample sizes is a factor 2 log(2e/∈) smaller than a naive use of the VC dimension result would give. Similar results are obtained for learning where the hypothesis is only guaranteed to correctly classify a given proportion of the training sample. The results are formulated in general terms and show that for many learning classes defined by smooth functions thresholded at the output, the sample size for a class with VC-dimension d and L parameters is (Equation presented).

Type: Book chapter
Title: Sample sizes for sigmoidal neural networks
ISBN: 0897917235
ISBN-13: 9780897917230
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/79196
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