A Neural Network Architecture That Computes Its Own Reliability

~emical reactors, distillation columns, ~gineering science. Jity, safety, scheduling) lication of computing to one or more nputer methods and programs. Others I methods. Comparisons of alternative , and significant computing developed should describe in reasonable detail Yherever possible the authors should ity suitable for chemical engineering ,the methods are oriented to chemical ion. or Contributors. on Press Ltd ,rial have not been published and will a manuscript, the authors agree that the article is accepted for publication. nork for organizations which d o not reproduce and distribute the article, r reproductions of similar nature and I a retrieval system or transmitted in chanical, photocopying, recording or : for this publication indicates that I by the copyright holder for libraries :C) Transactional Reporting Service 07 or 108 of the U.S. hat no inaccurate or misleading data, that the data and opinions appearing : contributor or advertiser concerned. pective employees, officers and agents ly such inaccurate or misleading data, Abstract-Artificial neural networks (ANNs) have been used to construct empirical nonlinear models of process data. Because network models are not based on physical theory and contain nonlinearities, their predictions are suspect when extrapolating beyond the range of the original training data. With multiple correlated inputs, it is difficult to recognize when the network is extrapolating. Furthermore, due to non-uniform distribution of the training examples and noise over the domain, the network may have local areas of poor fit even when not extrapolating. Standard measures of network performance give no indication of regions of locally poor fit or possible errors due to extrapolation. This paper introduces the "validity index network" (VI-net), an extension of radial basis function networks (RBFN), that calculates the reliability and the confidence of its output and indicates local regions of poor fit and extrapolation. Because RBFNs use a composition of local fits to the data, they are readily adapted to predict local fitting accuracy. The VI-net can also detect novel input patterns in classification problems, provided that the inputs to the classifier are real values. The reliability measures of the VI-net are implemented as additional output nodes of the underlying RBFN. Weights associated with the reliability nodes are given analytically based on training statistics from the fitting of the target function, and thus the reliability measures can be added to a standard RBFN with no additional training effort.