Weighted linear associative memory approach to nonlinear parameter estimation

The method of linear associative memory (LAM), a notion from the field of artificial neural nets, has been applied recently in nonlinear parameter estimation. In the LAM method, a model response, nonlinear with respect to the parameters, is approximated linearly by a matrix, which maps inversely from a response vector to a parameter vector. This matrix is determined from a set of initial training parameter vectors and their response vectors, and can be update recursively and adaptively with a pair of newly generated parameter response vectors. The LAM advantage is that it can yield a good estimation of the true parameters from a given observed response, even if the initial training parameter vectors are far from the true values.In this paper, we present a weighted linear associative memory (WLAM) for nonlinear parameter estimation. WLAM improves LAM by taking into account an observed response vector oriented weighting. The basic idea is to weight each pair of parameter response vectors in the cost function such that, if a response vector is closer to the observed one, then this pair plays a more important role in the cost function. This weighting algorithm improves significantly the accuracy of parameter estimation as compared to a LAM without weighting. In addition, we are able to construct the associative memory matrix recursively, while taking the weighting procedure into account, and simultaneously update the ridge parameter of the cost function further improving the efficiency of the WLAM estimation. These features enable WLAM to be a powerful tool for nonlinear parameter simulation.This work was supported by National Science Foundation, Grants BCS-93-15886 and INT-94-17206. We thank Mr. L. Yobas for fruitful discussions.