Complexity of Gaussian-radial-basis networks approximating smooth functions
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 IneaStiring smoothness (Bessel and Sobolev norms) multiplied by explicitly given functions a(r, d) of the number of variables d and degree of smoothness r. 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. (C) 2008 Elsevier Inc. All rights reserved.
gaussian-radial-basis-function networks bessel and sobolev norms tractability of approximation rates of approximation model complexity variation norms