The article is devoted to the development and possibility of using a new mathematical form of connection between the output variable and input factors in regression analysis. For this purpose, previously studied simpler modular linear regression models were used, in which one or more input factors are transformed once using the modulus operation. A symbiosis of linear regression and modular regression with a multiary operation module is proposed. On its basis, a multilayer modular regression is formulated, built on the “module within a module” principle, that is, each new layer uses a module from the value of the previous layer. The problem of estimating multilayer modular regression with a given number of layers using the least modulus method is reduced to a partial-Boolean linear programming problem. Using the proposed regressions, the problem of modeling timber reserves in the Irkutsk region was solved. In this case, single-layer, two-layer and three-layer modular regression were constructed. The new models turned out to be significantly better in quality than linear regression, and with an increase in the number of layers, a decrease in the sum of the residual modules was observed. In the three-layer model, all residuals turned out to be zero. The developed mathematical apparatus can be successfully used to solve many data analysis problem.
1. Chicco D., Warrens M.J., Jurman G. The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Computer Science. 2021;7. https://doi.org/10.7717/peerj-cs.623
2. Westfall P.H., Arias A.L. Understanding Regression Analysis: A Conditional Distribution Approach. New York: Chapman and Hall/CRC; 2020. 514 p. https://doi.org/10.1201/9781003025764
3. Nguyen Ph.-M., Pham H.T. A rigorous framework for the mean field limit of multilayer neural networks. Mathematical Statistics and Learning. 2023;6(3):201–357. https://doi.org/10.4171/msl/42
4. Talaat M., Farahat M.A., Mansour N., Hatata A.Y. Load forecasting based on grasshopper optimization and a multilayer feed-forward neural network using regressive approach. Energy. 2020;196. https://doi.org/10.1016/j.energy.2020.117087
5. Ivakhnenko A.G. Induktivnyi metod samoorganizatsii modelei slozhnykh sistem. Kyiv: Naukova dumka; 1982. 296 p. (In Russ.).
6. Muravina O.M. The metod of the group account of arguments in the analysis of geophysical date. Geofizika = Journal of Geophysics. 2012;(6):16–20. (In Russ.).
7. Bazilevskiy M.P., Oydopova A.B. Estimation of modular linear regression models using the least absolute deviations. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniya = Bulletin of Perm National Research Polytechnic University. Electrotechnics, Informational Technologies, Control Systems. 2023;(45):130–146. (In Russ.).
8. Bazilevskiy M.P. Software for estimating modular linear regressions. Informatsionnye i matematicheskie tekhnologii v nauke i upravlenii = Information and mathematical technologies in science and management. 2023;(3):136–146. (In Russ.). https://doi.org/10.25729/ESI.2023.31.3.013
9. Bazilevskiy M.P. Improving the algorithm for exact estimation of modular linear regressions using the least absolute deviations. Vestnik Tekhnologicheskogo universiteta = Herald of Technological University. 2024;27(4):97–102. (In Russ.).
10. Bazilevskiy M.P. Estimation of regression models with multiary modulus operation using least absolute deviations. Inzhenernyi vestnik Dona = Engineering Journal of Don. 2024;(5). (In Russ.). URL: http://www.ivdon.ru/ru/magazine/archive/n5y2024/9188
11. Thanoon F.H. Robust Regression by Least Absolute Deviations Method. International Journal of Statistics and Applications. 2015;5(3):109–112.
12. Liu Zh., Yang Y. Least absolute deviations estimation for uncertain regression with imprecise observations. Fuzzy Optimization and Decision Making. 2020;19(1):33–52. https://doi.org/10.1007/s10700-019-09312-w
13. Carrizosa E., Molero-Río C., Romero Morales D. Mathematical optimization in classification and regression trees. TOP. 2021;29(1):5–33. https://doi.org/10.1007/s11750-021-00594-1
14. Park Y.W., Klabjan D. Subset selection for multiple linear regression via optimization. Journal of Global Optimization. 2020;77(3):543–574. https://doi.org/10.1007/s10898-020-00876-1
15. Bazilevskiy M.P. An approximate ordinary least squares estimation algorithm for two-layer non-elementary linear regressions with two explanatory variables. Sovremennye naukoemkie tekhnologii = Modern high technologies. 2024;(4):10–14. (In Russ.). https://doi.org/10.17513/snt.39966
16. Voronkov P.T., Voronkov A.P., Belov A.N., Dudina E.A., Ilyukhina L.A. Modelirovanie ekonomicheskoi dostupnosti lesnykh resursov s ispol'zovaniem regressionnogo analiza. Lesokhozyaistvennaya informatsiya = Forestry Information. 2009;(1-2):7–13. (In Russ.).
17. Soldatov M.S., Malkhazova S.M., Rumyantsev V.Yu., Leonova N.B. Forecast of Change in Wood Growth in Forests of European Russia Due to Global Warming. Izvestiya Rossiiskoi Akademii Nauk. Seriya Geograficheskaya. 2014;(2):96–102. (In Russ.). https://doi.org/10.15356/0373-2444-2014-2-96-102
Bazilevskiy Mikhail Pavlovich
ORCID | eLibrary |
Irkutsk State Transport University
Irkutsk, Russia
