Calculation of Cramer Rao maximum a posteriori lower bounds from training data

A neural network approach is presented to estimate the Cramer Rao maximum a posteriori (CRM) lower bounds on estimation error variances. First, from training data an additive statistical signal model is obtained by a feedforward neural network which maps output vectors back to input vectors. The CRM lower bounds are then calculated through the signal model. In neural network applications, the CRM lower bounds can be used: 1) to help determine when to stop training the network; and 2) to determine the importance of input features according to their contributions to the bounds. The convergence of the modeling procedure is shown. Examples are given to illustrate the proposed approach