Statistical Science

Neural Networks: A Review from a Statistical Perspective

Bing Cheng and D. M. Titterington

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Abstract

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.

Article information

Source
Statist. Sci., Volume 9, Number 1 (1994), 2-30.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177010638

Digital Object Identifier
doi:10.1214/ss/1177010638

Mathematical Reviews number (MathSciNet)
MR1278678

Zentralblatt MATH identifier
0955.62589

JSTOR
links.jstor.org

Keywords
Artificial neural networks artificial intelligence statistical pattern recognition discriminant analysis nonparametric regression cluster analysis incomplete data Gibbs distributions

Citation

Cheng, Bing; Titterington, D. M. Neural Networks: A Review from a Statistical Perspective. Statist. Sci. 9 (1994), no. 1, 2--30. doi:10.1214/ss/1177010638. https://projecteuclid.org/euclid.ss/1177010638


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See also

  • See Comment: S. Amari. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 31--32.
  • See Comment: Andrew R. Barron. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 33--35.
  • See Comment: Elie Bienenstock, Stuart Geman. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 36--38.
  • See Comment: Leo Breiman. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 38--42.
  • See Comment: James L. McClelland. [Neural Networks: A Review from Statistical Perspective]: Comment: Neural Networks and Cognitive Science: Motivations and Applications. Statist. Sci., Volume 9, Number 1 (1994), 42--45.
  • See Comment: B. D. Ripley. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 45--48.
  • See Comment: Robert Tibshirani. [Neural Networks: A Review from Statistical Perspective]: Comment. Statist. Sci., Volume 9, Number 1 (1994), 48--49.
  • See Comment: Bing Cheng, D. M. Titterington. [Neural Networks: A Review from Statistical Perspective]: Rejoinder. Statist. Sci., Volume 9, Number 1 (1994), 49--54.