Cumulant-based parameter estimation using structured networks

A two-level three-layer structured network is developed to estimate the moving-average model parameters based on second-order and third-order cumulant matching. The structured network is a multilayer feedforward network composed of linear summers in which the weights of these summers have a clear physical meaning. The first level is composed of random access memory units, which are used to control the connectivities of the second-level summers. The second level is composed of three layers of linear summers in which the weight of any summer represents the moving-average parameter to be estimated. The connectivities among these summers are controlled by the first-level memory units in such a way that the outputs of the second-level structured network equal the desired second-order or third-order statistics if the summer weights equal their corresponding true moving-average parameter values. Each second-order and third-order cumulant is viewed as a pattern which the structured network needs to learn, and a steepest-descent algorithm is proposed for training the structured network. The author also presents extensions to particular sorts of estimation, and results of simulations.