Networks and the Best Approximation Property
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 functions (Poggio and Girosi, 1989), have a similar property. From the point of view of approximation theory, however, the property of approximation continuous 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1989
- Accession Number
- ADA216712
Entities
People
- Federico Girosi
- Tomaso Poggio
Organizations
- Massachusetts Institute of Technology