Open Access
February, 1994 Neural Networks: A Review from a Statistical Perspective
Bing Cheng, D. M. Titterington
Statist. Sci. 9(1): 2-30 (February, 1994). DOI: 10.1214/ss/1177010638


This paper informs a statistical readership about Artificial Neural Networks (ANNs), points out some of the links with statistical methodology and encourages cross-disciplinary research in the directions most likely to bear fruit. The areas of statistical interest are briefly outlined, and a series of examples indicates the flavor of ANN models. We then treat various topics in more depth. In each case, we describe the neural network architectures and training rules and provide a statistical commentary. The topics treated in this way are perceptrons (from single-unit to multilayer versions), Hopfield-type recurrent networks (including probabilistic versions strongly related to statistical physics and Gibbs distributions) and associative memory networks trained by so-called unsuperviszd learning rules. Perceptrons are shown to have strong associations with discriminant analysis and regression, and unsupervized networks with cluster analysis. The paper concludes with some thoughts on the future of the interface between neural networks and statistics.


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Bing Cheng. D. M. Titterington. "Neural Networks: A Review from a Statistical Perspective." Statist. Sci. 9 (1) 2 - 30, February, 1994.


Published: February, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62589
MathSciNet: MR1278678
Digital Object Identifier: 10.1214/ss/1177010638

Keywords: Artificial intelligence , Artificial neural networks , cluster analysis , discriminant analysis , Gibbs distributions , incomplete data , Nonparametric regression , statistical pattern recognition

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.9 • No. 1 • February, 1994
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