GMDH Algorithm for Optimal Model Choice by the External Error Criterion with the Extension of Definition by Model Bias and Its Applications to the Committees and Neural Networks

In the case of substantial noise, i.e., for inaccurate and incomplete data, the use of the Group Method of Data Handling (GMDH) algorithm leads to sharp and rather deep minimums of dependency of external criterion of accuracy measured on testing sample on the complexity of model structure. This minimum indicates the optimal model. In practice, however, if the noise is just noticeable, i.e., if data are accurate, the minimum becomes indefinite or does not exist at all. In this case, an extension of definition is needed based on a new criterion such as, e.g., the value of a model bias measured on the two identical data samples. The combinatorial GMDH algorithm with an extension of definition by the model bias can be used as a neuron in committees and in repeatedly multilayered neural networks for solving the problems of medical monitoring. Received May 4, 2002