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Relationships Between the A Priori and A Posteriori Errors in Nonlinear Adaptive Neural Filters

School of Information Systems, University of East Anglia, Norwich, U.K.

Jonathon A. Chambers

Signal Processing Section, Department of Electrical and Electronic Engineering, Imperial College of Science, Technology and Medicine, London, U.K.

The lower bounds for the a posteriori prediction error of a nonlinear predictor realized as a neural network are provided. These are obtained for a priori adaptation and a posteriori error networks with sigmoid nonlinearities trained by gradient-descent learning algorithms. A contractivity condition is imposed on a nonlinear activation function of a neuron so that the a posteriori prediction error is smaller in magnitude than the corresponding a priori one. Furthermore, an upper bound is imposed on the learning rate so that the approach is feasible. The analysis is undertaken for both feedforward and recurrent nonlinear predictors realized as neural networks.

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