CONSTRUCTION OF CONFIDENCE INTERVALS IN NEURAL MODELING USING A LINEAR TAYLOR EXPANSION
Isabelle Rivals, L. Personnaz · 1998
: We introduce the theoretical results on the construction of confidence intervals for a nonlinear regression, based on the linear Taylor expansion of the corresponding nonlinear model output. The case of neural black-box modeling is then analyzed, and illustrated on an industrial application. We show that the linear Taylor expansion not only provides a confidence interval at any point of interest, but also gives a tool to detect overfitting. Keywords: backpropagation algorithm, black-box modeling, bootstrap methods, confidence intervals, least squares estimator, linear Taylor expansion, neural networks, overfitting detection. I. INTRODUCTION In neural network modeling studies, generally only an average estimate of a neural model reliability is given through its mean square error on a test set. Yet, the problem of the estimation of a given model reliability has been investigated to a great extent in nonlinear regression theory (see for example [Bates & Watts 88] [Seber & Wild 89]). ...