Minimization of Error Functionals over Variable-Basis Functions

Generalized Tikhonov well-posedness is investigated for the problem of minimization of error functionals over admissible sets formed by variable-basis functions, i.e., linear combinations of a fixed number of elements chosen from a given basis without a prespecified ordering. For variable-basis func...

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Bibliographic Details
Published in:SIAM journal on optimization 2004-01, Vol.14 (3), p.732-742
Main Authors: Kainen, Paul C., Kurková, Vera, Sanguineti, Marcello
Format: Article
Language:English
Subjects:
Boolean
Investigations
Mathematical functions
Neural networks
Optimization
Variables
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Summary:Generalized Tikhonov well-posedness is investigated for the problem of minimization of error functionals over admissible sets formed by variable-basis functions, i.e., linear combinations of a fixed number of elements chosen from a given basis without a prespecified ordering. For variable-basis functions of increasing complexity, rates of decrease of infima of error functionals are estimated. Upper bounds are derived on such rates which do not exhibit the curse of dimensionality with respect to the number of variables of admissible functions. Consequences are considered for Boolean functions and decision trees.
ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623402401233