Some Comparisons of the Worst-Case Errors in Linear and Neural Network Approximation

0403860 - UIVT-O 20000039 RIV FR eng C - Konferenční příspěvek (zahraniční konf.)
Kůrková, Věra - Sanguineti, M.
Some Comparisons of the Worst-Case Errors in Linear and Neural Network Approximation.
Proceedings CD of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems. Perpignan: Université de Perpignan, 2000, nestr.
[MTNS'2000. International Symposium of Mathematical Theory of Networks and Systems /14./. Perpignan (FR), 19.06.2000-23.06.2000]
Grant CEP: GA ČR GA201/99/0092
Grant ostatní: MURST(IT) 96.02472.CT07; MURST(IT) 97.00048.PF42
Výzkumný záměr: AV0Z1030915
Klíčová slova: linear and neural approximation * Kolmogorov n-width * dimension-independent approximation * one-hidden-layer perceptron networks * curse of dimensionality
Kód oboru RIV: BA - Obecná matematika

Worst-case errors in linear and neural-network approximation are investigated in a more general framework of fixed versus variable-basis approximation. Such errors are compared for balls in certain norms, tailored to variable-basis. Estimates are applied to sets of functions either computable by perceptrons with periodic or sigmoidal activations, or approximable with dimension-independent rates by one-hidden-layer networks with such perceptrons.
Trvalý link: http://hdl.handle.net/11104/0124148