Selective Properties of the GMDH Criteria for Inductive Modeling. V.S.Stepashko

Abstract. The problem of construction (structural identification) of optimum model on the basis of a short data sample in the class of structures linear in parameters is investigated. The choice of a model structure having minimum variance of the forecasting error, or the noise-immunity model, is accepted as a primary objective of the problem solution. The features and regularities of the optimum model construction depending on the noise level and the sample volume are investigated; efficiency of the GMDH external criteria in this problem is studied.

Keywords. Inductive modelling, GMDH, forecasting error, noise-immunity model, optimal complexity.

References.
1 Ivakhnenko A.G.: Group method of data handling as competitor to the method of stochastic approximation. Soviet Automatic Control: No. 3, 1968.
2. Ivakhnenko A.G.: Long-term forecasting and control of complex systems. Kiev: Tekhnika, 1975. (In Russian)
3. Ivakhnenko A.G.: Inductive methods of self-organization of models of complex systems. Kiev: Naukova dumka, 1982. (In Russian)
4. Ivachnenko A.G., Mueller J.A.: Selbstorganization von Vorherzagemodellen. Berlin: VEB Verlag Technik, 1984. (In German)
5. Farlow S.J.: Self-organizing methods in modelling: GMDH type algorithms:/ Edited by .- New-York, Bazel: Marcel Decker Inc., 1984.
6. Ivakhnenko A.G., Karpinsky A.M.: Self-organization of models by computer in terms of the general communication theory (information theory). Soviet Automatic Control: No. 4, 1982.
7. Stepashko V.S.: The potential noise immunity of modeling on the basis of a combinatorial GMDH algorithm without taking the information about the noise into account. Soviet Automatic Control: No. 3, 1983.
8. Ivakhnenko A.G., Stepashko V.S.: Noise-immunity of modelling. Kiev: Naukova dumka, 1985. (In Russian)
9. Rao H.M., Ivakhnenko A.G.: Inductive learning algorithms for complex systems modelling. London, Tokyo: CRC Press, 1994.
10. Stepashko V.S.: Structural identification of predicting models for a planned experiment conditions. Journal of Automation and Information Sciences: No. 1, 1992.
11. Stepashko V.S.: Efficiency analysis of criteria of structural identification of forecasting models. Journal of Automation and Information Sciences: No. 3-4, 1994.