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

摘要

The lower bounds for the a posteriori prediction error of a nonlinear pre- dictor realized as a neural network are provided. These are obtained for a priori adaptation and a posteriori error networks with sigmoid nonlin- earities 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.