Article information

2017 , Volume 22, ¹ 1, p.37-47

Mikhov E.D., Mikhova E.D., Nepomnyashchiy O.V.

Comparative analysis of nonparametric algorithms on the example of modelling of stochastic processes

The problem of modelling of stochastic processes without inertia in the space of input-output variables is considered. The general scheme of the studied processes is described. Some differences between nonparametric algorithms of modelling, namely modelling by means of nuclear approximation and by means of Rosenblat - Parsena’s perceptron are considered. The question of identification in “broad” and “narrow” sense is briefly discussed. Distinction between these types of identification is described in detail. The fact that identification in the “broad” sense corresponds more to real problems of modelling rather than identification in “narrow” sense is proved. Principles of neural networks and it’s training algorithms are described. The structure of the perseptron used in research is described. The modelling algorithm based on the core approximation is considered. The vectors of the “smooth core” optimization result is shown. Optimization was performed by the Nedler - Midd algorithm. Further results of modelling by means of Rosenblat perceptron and core approximation were presented. It is shown that between the model designed to use neural network algorithm and the model, that designed to employ core approximation’s algorithm, there is no essential difference in accuracy. It is shown that neural networks give the forecast quicker than the method of local approximation, but at the same time neural networks training is much longer.

[full text]
Keywords: stochastic processes simulating, core approximation, neural networks, comparison of algorithms

Author(s):
Mikhov Evgeniy Dmitriyevich
Position: Student
Office: Siberian Federal Institute of Space and Information Technologies University
Address: 660074, Russia, Krasnoyarsk, Kirensky St. 26B
E-mail: edmihov@mail.ru

Mikhova Evgeniya Dmitriyevna
Position: The master of mathematics
Office: Siberian State Aerospace University
Address: 660037, Russia, Krasnoyarsk, ave. of gas. "The Krasnoyarsk worker", 31
E-mail: soldatova90@mail.ru

Nepomnyashchiy Oleg Vladimirovich
PhD. , Associate Professor
Position: Professor
Office: Siberian Federal University
Address: 660074, Russia, Krasnoyarsk, Kirensky St. 26B
E-mail: ONepomnuashy@sfu-kras.ru

References:
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[2] Tsypkin, Ya.Z. Adaptatsiya i obuchenie v avtomaticheskikh sistemakh [Adaptation and learning in automatic systems]. Moscow: Nauka; 1968: 400. (In Russ.)
[3] Medvedev, A.V. SOME NOTES ON H-MODELS FOR NON-INERTIA SYSTEMS WITH A DELAY. Vestnik SibGAU. 2014; 2(54): 50-55. (In Russ.)
[4] Minskiy, M., Peypert, S. Perseptrony [Perceptrons]. Moscow: Mir; 1971: 261. (In Russ.)
[5] Mikhov, E.D. OPTIMIZATION OF COEFFICIENT OF BLURRING OF THE KERNEL IN NONPARAMETRIC MODELLING. Vestnik SibGAU. 2015. No. 2(16). P. 338–342. (In Russ.)

Bibliography link:
Mikhov E.D., Mikhova E.D., Nepomnyashchiy O.V. Comparative analysis of nonparametric algorithms on the example of modelling of stochastic processes // Computational technologies. 2017. V. 22. ¹ 1. P. 37-47
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