Article ID Journal Published Year Pages File Type
4609031 Journal of Complexity 2009 12 Pages PDF
Abstract

Complexity of Gaussian-radial-basis-function networks, with varying widths, is investigated. Upper bounds on rates of decrease of approximation errors with increasing number of hidden units are derived. Bounds are in terms of norms measuring smoothness (Bessel and Sobolev norms) multiplied by explicitly given functions a(r,d)a(r,d) of the number of variables dd and degree of smoothness rr. Estimates are proven using suitable integral representations in the form of networks with continua of hidden units computing scaled Gaussians and translated Bessel potentials. Consequences on tractability of approximation by Gaussian-radial-basis function networks are discussed.

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Physical Sciences and Engineering Mathematics Analysis
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