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Networks and the Best Approximation Property

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Show simple item record Girosi, Federico en_US Poggio, Tomaso en_US 2004-10-04T14:36:01Z 2004-10-04T14:36:01Z 1989-10-01 en_US
dc.identifier.other AIM-1164 en_US
dc.description.abstract Networks can be considered as approximation schemes. Multilayer networks of the backpropagation type can approximate arbitrarily well continuous functions (Cybenko, 1989; Funahashi, 1989; Stinchcombe and White, 1989). We prove that networks derived from regularization theory and including Radial Basis Function (Poggio and Girosi, 1989), have a similar property. From the point of view of approximation theory, however, the property of approximating continous functions arbitrarily well is not sufficient for characterizing good approximation schemes. More critical is the property of best approximation. The main result of this paper is that multilayer networks, of the type used in backpropagation, are not best approximation. For regularization networks (in particular Radial Basis Function networks) we prove existence and uniqueness of best approximation. en_US
dc.format.extent 22 p. en_US
dc.format.extent 104037 bytes
dc.format.extent 421671 bytes
dc.format.mimetype application/octet-stream
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.relation.ispartofseries AIM-1164 en_US
dc.subject learning en_US
dc.subject networks en_US
dc.subject regularization en_US
dc.subject best approximation en_US
dc.subject sapproximation theory en_US
dc.title Networks and the Best Approximation Property en_US

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