Linear and nonlinear associative memories for parameter estimation

Abstract

This paper proposes the use of associative memories for obtaining preliminary parameter estimates for nonlinear systems. For each parameter vector r, in a selected training set, the system equations are used to determine a vector s, of system outputs, An associative memory matrix M is then constructed which optimally, in the least squares sense, associates each system output vector s, with its corresponding parameter vector I-,. Given any observed system output vector s*, an estimate i for the system parameters is obtained by setting i = Ms*. Numerical experiments are reported which indicate the effectiveness of this approach, especially for the nonlinear associative memory case in which the training vectors s, include not only the system output levels but also products of these levels.

Time Series and Turning Point Forecasts: A Comparison of Associative Memories and Bayesian Econometric Techniques Applied to Lesage's Data*

“…The numerical problems posed by relatively large elements in M** can be addressed in a number of ways. For example, (1) can be modified by attaching a penalty to the size of the elements in the associative memory matrix (Kalaba and Tesfatsion, 1992; Kalaba and Udwadia, 1991). Computing such a multicriteria associative memory matrix MA involves a trade-off.…”

Associative Memory Techniques for Quick Estimation of Network Performance Measures

“…AM techniques have been applied in a number of situations in which unknown system parameter estimation was involved, including nonlinear system identification, passive ranging, remote sensing, and image processing (9,10). Kalaba et al (9) further showed the application of AM techniques even when the data available were noisy.…”

Nonlinear Estimation with Associative Memories and Machine Evaluation of Derivatives: An Application to Calibrating Spatial Interaction Models

“…Kohonen (1989), Murakami and Aibara (1987), and Poggio (1975) have generated these and related ideas and applied them to neural computing schemes. Applications of associative memories to mathematical and social systems can be found in 1992a;1992b), Kalaba and Tesfatsion (1991a), Moore II et al (1991;1993;1994a;1994b).…”