Least-Squares Learning and Approximation of Posterior Probabilities on Classification Problems by Neural Network Models
NAVAL OCEAN SYSTEMS CENTER SAN DIEGO CA
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We consider multilayer neural network models which are applied to stochastic classification problems and are trained with error back propagation methods. Expectations for network outputs are weighted least-squares approximations to posterior probabilities for the classes Gish 1990 Shoemaker, forthcoming White 1981. In an empirical study, networks were trained on small benchmark problems with known probability density functions, using training data comprising random samples generated according to those functions. Expected classification accuracy and goodness of fit of network outputs to posterior class probabilities were subsequently evaluated. Classification performance near the Bayes optimum was obtained for each problem, and fits to posterior class probabilities were judged reasonable, with root-mean-expected-square differences between outputs and probabilities below 0.05 seen in individual networks for both problems.
- Statistics and Probability