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.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/6017 |
| Date | 01 October 1989 |
| Creators | Girosi, Federico, Poggio, Tomaso |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Format | 22 p., 104037 bytes, 421671 bytes, application/octet-stream, application/pdf |
| Relation | AIM-1164 |
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