Networks and the best approximation property

✍ Scribed by F. Girosi; T. Poggio

• Book ID: 104658894
• Publisher: Springer-Verlag
• Year: 1990
• Tongue: English
• Weight: 815 KB
• Volume: 63
• Category: Article
• ISSN: 0340-1200
• DOI: 10.1007/bf00195855

✦ Synopsis

Networks can be considered as approximation schemes. Multilayer networks of the perceptron type can approximate arbitrarily well continuous functions (Cybenko 1988(Cybenko , 1989;;Funahashi 1989;Stinchcombe and White 1989). We prove that networks derived from regularization theory and including Radial Basis Functions (Poggio and Girosi 1989), have a similar property. From the point of view of approximation theory, however, the property of approximating continuous functions arbitrarily well is not sufficient for characterizing good approximation schemes. More crit-