Sup-norm approximation bounds for networks through probabilistic methods

Author

Yukich, Joseph E. ; Stinchcombe, Maxwell B. ; White, Halbert

Author_Institution

Dept. of Math., Lehigh Univ., Bethlehem, PA, USA

Volume

41

Issue

4

fYear

1995

fDate

7/1/1995 12:00:00 AM

Firstpage

1021

Lastpage

1027

Abstract

We consider the problem of approximating a smooth target function and its derivatives by networks involving superpositions and translations of a fixed activation function. The approximation is with respect to the sup-norm and the rate is shown to be of order O(n^-1/2); that is, the rate is independent of the dimension d. The results apply to neural and wavelet networks and extend the work of Barren(see Proc. 7th Yale Workshop on Adaptive and Learning Systems, May, 1992, and ibid., vol.39, p.930, 1993). The approach involves probabilistic methods based on central limit theorems for empirical processes indexed by classes of functions

Keywords

approximation theory; neural nets; probability; wavelet transforms; central limit theorems; empirical processes; fixed activation function; neural networks; probabilistic methods; smooth target function; sup-norm approximation bounds; superpositions; translations; wavelet networks; Artificial neural networks; Chaos; Fourier transforms; Mathematics; Neural networks; Robots;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.391247

Filename

391247