Networks and the Best Approximation Property
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 Bas...
| Main Authors: | , |
|---|---|
| Language: | en_US |
| Published: |
2004
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/6017 |
| _version_ | 1826200593540055040 |
|---|---|
| author | Girosi, Federico Poggio, Tomaso |
| author_facet | Girosi, Federico Poggio, Tomaso |
| author_sort | Girosi, Federico |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:38:51Z |
| id | mit-1721.1/6017 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:38:51Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/60172019-04-10T17:24:46Z Networks and the Best Approximation Property Girosi, Federico Poggio, Tomaso learning networks regularization best approximation sapproximation theory 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. 2004-10-04T14:36:01Z 2004-10-04T14:36:01Z 1989-10-01 AIM-1164 http://hdl.handle.net/1721.1/6017 en_US AIM-1164 22 p. 104037 bytes 421671 bytes application/octet-stream application/pdf application/octet-stream application/pdf |
| spellingShingle | learning networks regularization best approximation sapproximation theory Girosi, Federico Poggio, Tomaso Networks and the Best Approximation Property |
| title | Networks and the Best Approximation Property |
| title_full | Networks and the Best Approximation Property |
| title_fullStr | Networks and the Best Approximation Property |
| title_full_unstemmed | Networks and the Best Approximation Property |
| title_short | Networks and the Best Approximation Property |
| title_sort | networks and the best approximation property |
| topic | learning networks regularization best approximation sapproximation theory |
| url | http://hdl.handle.net/1721.1/6017 |
| work_keys_str_mv | AT girosifederico networksandthebestapproximationproperty AT poggiotomaso networksandthebestapproximationproperty |