ACCURACY ANALYSIS FOR WAVELET APPROXIMATIONS

Citation
B. Delyon et al., ACCURACY ANALYSIS FOR WAVELET APPROXIMATIONS, IEEE transactions on neural networks, 6(2), 1995, pp. 332-348
Citations number
24
Categorie Soggetti
Computer Application, Chemistry & Engineering","Engineering, Eletrical & Electronic","Computer Science Artificial Intelligence","Computer Science Hardware & Architecture","Computer Science Theory & Methods
ISSN journal
10459227
Volume
6
Issue
2
Year of publication
1995
Pages
332 - 348
Database
ISI
SICI code
1045-9227(1995)6:2<332:AAFWA>2.0.ZU;2-F
Abstract
''Constructive wavelet networks'' are investigated as a universal tool for function approximation. The parameters of such networks are obtai ned via some ''direct'' Monte-Carlo procedures. Approximation bounds a re given. Typically, it is shown that such networks with one layer of ''wavelons'' achieve an L(2)-error of order O(N--rho/d), where N is th e number of nodes, d is the problem dimension and rho is the number of summable derivatives of the approximated function, An algorithm is al so proposed to estimate this approximation based on noisy input-output data observed from the function under consideration. Unlike neural ne twork training, this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated ''backpropagation,'' a nd it completely avoids the problem of poor convergence or undesirable local minima.