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**Neural networks: A review from a statistical perspective. With comments and a rejoinder by the authors.**
*(English)*
Zbl 0955.62589

Summary: This paper informs the 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 unsupervised learning rules. Perceptrons are shown to have strong associations with discriminant analysis and regression, and unsupervised networks with cluster analysis. The paper concludes with some thoughts on the future of the interface between neural networks and statistics.