Some comparisons of model complexity in linear and neural-network approximation

Authors:
Giorgio Gnecco;Věra Kůrková;Marcello Sanguineti
Affiliations:
Department of Communications, Computer, and System Sciences, University of Genoa, Genova, Italy;Department of Communications, Computer, and System Sciences, University of Genoa, Genova, Italy;Department of Communications, Computer, and System Sciences, University of Genoa, Genova, Italy
Venue:
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part III
Year:
2010

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Abstract

Capabilities of linear and neural-network models are compared from the point of view of requirements on the growth of model complexity with an increasing accuracy of approximation. Upper bounds on worst-case errors in approximation by neural networks are compared with lower bounds on these errors in linear approximation. The bounds are formulated in terms of singular numbers of certain operators induced by computational units and high-dimensional volumes of the domains of the functions to be approximated.