Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609031 | Journal of Complexity | 2009 | 12 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Paul C. Kainen, Věra Kůrková, Marcello Sanguineti,