Jtg. Hwang et Aa. Ding, PREDICTION INTERVALS FOR ARTIFICIAL NEURAL NETWORKS, Journal of the American Statistical Association, 92(438), 1997, pp. 748-757
The artificial neural network (ANN) is becoming a very popular model f
or engineering and scientific applications. Inspired by brain architec
ture, artificial neural networks represent a class of nonlinear models
capable of learning from data. Neural networks have been applied in m
any areas, including pattern matching, classification, prediction, and
process control. This article focuses on the construction of predicti
on intervals. Previous statistical theory for constructing confidence
intervals for the parameters (or the weights in an ANN), is inappropri
ate, because the parameters are unidentifiable. We show in this articl
e that the problem disappears in prediction. We then construct asympto
tically Valid prediction intervals and also show how to use the predic
tion intervals to choose the number of nodes in the network. We then a
pply the theory to an example for predicting the electrical load.