Relations between the a priori and a posteriori errors in nonlinear adaptive neural filters

Danilo P. Mandic, Jonathon A. Chambers

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1285-1292
Number of pages8
JournalNeural Computation
Issue number6
Publication statusPublished - 1999

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