In this paper we present the soft-computing method Group Method of Data Handling (GMDH), a method which allows to address a problem that frequently arises in different disciplines: the approximation of an unknown relationship between a variable “to explain” and a given set of potentially “explanatory” variables. In short, this methodology works as follow. After a starting generation of simple models (characterized by a polynomial analytical form), the problem of approximating the unknown relationship is faced by iterating for an appropriate number of times the following phases: first, the selection of the best model among the previously generated ones (in this phase only the most suitable models can survive: survival of the fittest); second, the evolution of the selected models to a next generation of new “child” models (also characterized by a polynomial analytical form), potentially more explanatory than their “parents”. This methodology belongs to the family of inductive and self-organizing techniques. Note that, in the eyes of an expert of the “classic” neuro-computation techniques, the GMDH methodology could recall a MLP feedforward ANN. Nevertheless, GMDH methodology differs from the classic neural approach for, at least, the following reasons: first, the GMDH methodology specifies a polynomial function that approximates the unknown investigated relation (while, generally, the neural networks specify a black-box model); second, the GMDH methodology determines the evolution and optimizes the organization of its architecture endogenously (while, generally, the architectural aspects of the MLP have to be specified exogenously); third, every element of the structure developed by the GMDH methodology tries to pursue the final result alone (while, generally, in the neural networks the knowledge of the final result is distributed among all the elements of their structure). At the end of the paper, a financial application of GMDH is presented.

Un approccio "Group Method of Data Handling" alla soft-computation: i polinomi approssimanti di Ivakhnenko

CORAZZA, Marco
2000

Abstract

In this paper we present the soft-computing method Group Method of Data Handling (GMDH), a method which allows to address a problem that frequently arises in different disciplines: the approximation of an unknown relationship between a variable “to explain” and a given set of potentially “explanatory” variables. In short, this methodology works as follow. After a starting generation of simple models (characterized by a polynomial analytical form), the problem of approximating the unknown relationship is faced by iterating for an appropriate number of times the following phases: first, the selection of the best model among the previously generated ones (in this phase only the most suitable models can survive: survival of the fittest); second, the evolution of the selected models to a next generation of new “child” models (also characterized by a polynomial analytical form), potentially more explanatory than their “parents”. This methodology belongs to the family of inductive and self-organizing techniques. Note that, in the eyes of an expert of the “classic” neuro-computation techniques, the GMDH methodology could recall a MLP feedforward ANN. Nevertheless, GMDH methodology differs from the classic neural approach for, at least, the following reasons: first, the GMDH methodology specifies a polynomial function that approximates the unknown investigated relation (while, generally, the neural networks specify a black-box model); second, the GMDH methodology determines the evolution and optimizes the organization of its architecture endogenously (while, generally, the architectural aspects of the MLP have to be specified exogenously); third, every element of the structure developed by the GMDH methodology tries to pursue the final result alone (while, generally, in the neural networks the knowledge of the final result is distributed among all the elements of their structure). At the end of the paper, a financial application of GMDH is presented.
Finanza Computazionale. Atti della Scuola Estiva 2000
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/10868
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