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Optimal Design in Flexible Models, Including Feed-Forward Networks and Nonparametric Regression

  • D. M. Titterington
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

Abstract

Feed-forward networks, also known as multilayer perceptrons, are the most frequently implemented type of neural network. In statistical terminology, they can be regarded as a class of nonlinear regression or classification models, depending on the context, nonlinear in terms of both the explanatory variables and the parameters. An attempt at optimal design therefore leads to a nonlinear design problem. In principle, statistical work in this area can be applied to this context, and a major aim of the paper will be to survey relevant material that has appeared in the neural-computing literature, where it is described under headings such as ‘active learning’, as well as ‘optimal design’. This part of the chapter will reinforce the contribution of Haines (1998).

A major reason for the attraction of feed-forward networks is that they can provide parametric but flexible regression models. One can consider going further and discuss the question of optimal design in nonparametric regression scenarios. The chapter discusses this issue and in particular the approach taken by Cheng et al. (1998) in the context of local linear smoothing.

Keywords

active learning Bayesian design local linear smoothing neural networks nonlinear nonparametric regression sequential design 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • D. M. Titterington
    • 1
  1. 1.Department of StatisticsUniversity of GlasgowGlasgowUK

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