COMBINING ALTERNATIVE OPTIONS OF THE REGRESSION MODEL BASED ON THE BEHAVIOR CONSISTENCY CRITERION

DOI: 10.47026/1810-1909-2024-2-92-101

УДК 519.852

ББК 22.1

Key words

regression equation, ensemble of models, combination of options, weighting coefficients, behavior consistency criterion, gross product

Abstract

The purpose of the study is to develop an algorithm for calculating the coefficients of a convex combination of alternative variants of a regression model of a complex object, based on the use of the criterion of behavior consistency between the actual and calculated values of the output variable, specified in continuous form, introduced in previous works by one of the authors.

Methods. To solve the problem formulated in the paper, the authors use both the traditional criteria for model adequacy in regression analysis – multiple determination, Fisher, average relative error of approximation – and the behavior consistency criterion previously developed by one of the authors.

Results. The study demonstrates the application of the developed method to create an ensemble of regression models for the construction of a mathematical model of the gross domestic product of the Russian Federation. This approach, due to its invariance to the nature of the analyzed systems, does not require special adaptation in the study of objects of technical nature.

Conclusions. The proposed algorithm for combining alternative options for a regression model of an object, based on the use of a behavior consistency criterion between the actual and calculated values of the output variable, can be effectively used in the study of complex systems of various natures.

References

1. Bobrova T.V., Panchenko P.M. Tekhnicheskoe normirovanie rabochikh protsessov v stroitel’stve na osnove prostranstvenno-vremennogo modelirovaniya [Technical normalization of working processes in construction based on spatial-temporal modeling]. Magazine of Civil Engineering, 2017, no. 8(76), pp. 84–97.
2. Bolotov A.N., Rachishkin A.A., Sutyagin O.V. Komp’yuternoe modelirovanie fizicheskikh vzaimodeistvii tekhnicheskikh poverkhnostei na mikrourovne [Computer modeling of physical interactions of technical phenomena at the micro level]. Programmnye produkty i sistemy, 2019, no. 1, pp. 109–114.
3. Dreiper N., Smit G. Applied Regression Analysis, Wiley & Sons Publ., 2016, 912 p. (Russ. ed.: Prikladnoi regressionnyi analiz, Moscow, Williams Publ., 2016).
4. Interdepartmental Information and Statistical System (EMISS): site. Available at: https://www.fedstat.ru/ (Access Date: 2023, Nov. 19).
5. Eliseeva M.A., Malovik K.N. Prikladnye zadachi modelirovaniya tekhnicheskikh riskov [Applied problems of technical risk modeling]. In: Nauka i obrazovanie v XXI veke: nauch. tr. po materialam Mezhdunar. nauch.-prakt. konf. [Proc. of Int. Sci. Conf. «Science and education in the 21^st century»].Tabmov, Consalting company Ukom Publ., 2014, vol. 17, pp. 36–38.
6. Finance. News: website. Available at: https://inflatio.ru/ (Access Date: 2023, Nov. 19).
7. Levin M.Sh. Primer kombinatornoi evolyutsii i prognozirovaniya trebovanii k kommunikatsionnym sistemam [An example of combinatorial evolution and forecasting of requirements for communication systems]. Informatsionnye protsessy, 2017, vol. 17, no. 2, pp. 92–100.
8. Mutushev D.M. Matematicheskoe modelirovanie v zadachakh upravleniya kachestvom tekhnicheskikh i ekspluatatsionnykh kharakteristik transportnykh ob”ektov [Mathematical modeling in problems of quality management of technical and operational characteristics of transport facilities]. Kachestvo i zhizn’, 2019, no. 2(22), pp. 118–123.
9. Nikolaichuk O.A., Berman A.F., Pavlov A.I. Prognozirovanie tekhnicheskogo sostoyaniya opasnykh ob”ektov metodom imitatsionnogo modelirovaniya [Forecasting the technical condition of hazardous objects using simulation modeling]. Problemy mashinostroeniya i nadezhnosti mashin, 2017, no. 2, pp. 131–142.
10. Noskov S.I. Postroenie svertki kriteriev adekvatnosti regressionnykh modelei [Construction of a Convolution of Adequacy Criteria for Regression Models]. Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve, 2022, no. 1, pp. 73–81.
11. Noskov S.I. Realizatsiya konkursa regressionnykh modelei s primeneniem kriteriya soglasovannosti povedeniya [Implementation of the Regression Models Contest Using the Criterion of Behavior Consistency]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Ser. Sistemnyi analiz i informatsionnye tekhnologii, 2021, no. 2, pp. 153–160.
12. Noskov S.I., Bychkov Yu.A. Vychislitel’nye eksperimenty s nepreryvnoi formoi metoda maksimal’noi soglasovannosti v regressionnom analize [Computational Experiments with the Continuous Form of the Method of Maximum Consistency in Regression Analysis]. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta, 2022, vol. 18, no. 2, pp. 7–12.
13. Popova T.P. Ansambli modelei kak sovremennyi instrument analiza dannykh [Ensembles of Models as a Modern Tool for Data Analysis]. In: Konkurentosposobnost’ territorii: materialy XX Vseros. ekon. foruma molodykh uchenykh i studentov: v 8 ch. [Proc. of 20^th Economic Forum of Young Scientists and Students Competitiveness of Territories. 8 parts]. Yekaterinburg, Ural State Economic University Publ., 2017, Part 7, pp. 256–259.
14. Noskov S.I., Pashkov D.V. Programmnyi kompleks realizatsii konkursa lineinykh regressionnykh modelei po kriteriyu Fishera [Software Complex for the Implementation of the Linear Regression Models Contest According to Fisher’s Criterion]. Certificate of State Registration of the Computer Program, no. 2021619297, 2021.
15. Reference Tables: website. Available at: https://infotables.ru.
16. Federal State Statistics Service: website. Available at: https://rosstat.gov.ru (Access Date: 2023, Nov. 19).
17. Acar E., Rais-Rohani M. Ensemble of metamodels with optimized weight factors. Structural and Multidisciplinary Optimization, 2009, vol. 37, pp. 279–294.
18. Branicki M., Majda A.J. Imperfect Dynamical Predictions Via Multi-Model Ensemble Forecasts. Journal of Nonlinear Science, 2015, vol. 25, pp. 489–538.
19. Dua M., Shakshi, Singla R. et al. Deep CNN models-based ensemble approach to driver drowsiness detection. Neural Computing and Applications, 2021, vol. 33, pp. 3155–3168.
20. Elish M.O., Aljamaan H., Ahmad I. Three empirical studies on predicting software maintainability using ensemble methods. Soft Computing, 2015, 19, pp. 2511–2524.
21. Iglesias M.A. Iterative regularization for ensemble data assimilation in reservoir models. Computational Geosciences, 2015, 19, pp. 177–212.
22. Lee Y., Choi D.-H. Pointwise ensemble of meta-models using v nearest points cross-validation. Structural and Multidisciplinary Optimization, 2014, 50, pp. 383–394.
23. Prayogo D., Cheng M.-Y., Wu Y.-W., Tran D.-H. Combining machine learning models via adaptive ensemble weighting for prediction of shear capacity of reinforced-concrete deep beams. Engineering with Computers, 2020, vol. 36, pp. 1135–1153.
24. Statista: website. Available at: https://www.statista.com (Access Date: 2023, Nov. 19).
25. Uchida M., Maehara Y., Shioya H. Unsupervised Weight Parameter Estimation Method for Ensemble Learning. Journal of Mathematical Modelling and Algorithms, 2011, vol. 10, pp. 307–322.

Information about the authors

Sergey I. NoskoV – Doctor of Technical Sciences, Professor, Department of Information Systems and Information Security, Irkutsk State Transport University, Russia, Irkutsk (sergey.noskov.57@mail.ru ORCID: https://orcid.org/0000-0003-4097-2720).

Ivan V. Ovsyannikov – 4^th Year Student, Faculty of Transport Management and Information Technology, Irkutsk State University of Transport, Russia, Irkutsk (bidanocka@gmail.com).

For citations

Noskov S.I., Ovsyannikov I.V. COMBINING ALTERNATIVE OPTIONS OF THE REGRESSION MODEL BASED ON THE BEHAVIOR CONSISTENCY CRITERION. Vestnik Chuvashskogo universiteta, 2024, no. 2, pp. 92–101. DOI: 10.47026/1810-1909-2024-2-92-101 (in Russian).

Download the full article