Title :
On the least square error and prediction square error of function representation with discrete variable basis
Author :
Hayasaka, Taichi ; Toda, Naohiro ; Usui, Shiro ; Hagiwara, Katsuyuki
Author_Institution :
Dept. of Inf. & Comput. Sci., Toyohashi Univ. of Technol., Japan
Abstract :
One of the most important features of 3-layered neural networks is the adaptability of the basis functions. In this paper, in order to focus on the adaptability in a context of the regression or curve-fitting, we restricted our attention to function representation in which the basis functions are modified according to the associated discrete parameters. For such function representation, we derived the expectations of the least square error and prediction square error with respect to the distribution of a set of samples using the extreme value theory, provided that the given set of samples is an independent Gaussian noise sequence and the basis functions satisfy an appropriate orthonormality condition
Keywords :
Gaussian noise; curve fitting; multilayer perceptrons; 3-layered neural networks; adaptability; basis functions; curve-fitting; discrete variable basis; extreme value theory; function representation; independent Gaussian noise sequence; least square error; orthonormality condition; prediction square error; regression; Computer errors; Computer networks; Curve fitting; Electronic mail; Function approximation; Gaussian noise; Least squares methods; Neural networks; Stochastic resonance; Stochastic systems;
Conference_Titel :
Neural Networks for Signal Processing [1996] VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop
Conference_Location :
Kyoto
Print_ISBN :
0-7803-3550-3
DOI :
10.1109/NNSP.1996.548337
