Russian Federation
Russian Federation
Russian Federation
UDK 004.891.3 Диагностические экспертные системы
The article considers the problem of increasing the reliability and statistical significance of regression models of research objects built on small experimental data samples. Insufficient amount of experimental data forces the researcher to use linear models with a minimum number of variable factors, however, even with such a choice of the type of model, insufficient statistical significance of parameter estimates excludes the possibility of using it for reliable forecasting of changes in the explained variables. In order to expand the possibility of choosing the type of model at the specification stage and to increase the statistical significance of its parameter estimates, it is proposed to expand the volume of experimental data using a statistical model of the object of study, built on the basis of a generative adversarial neural network. When training on a small sample obtained during an experimental study of the object, the generator of a conditional generative adversarial network generates data clusters with centroids corresponding to the points of the training (experimental) sample. The results of the analysis of the data of a physical experiment are presented, confirming its main provisions.
experimental sample, linear regression model, statistical significance, regression parameter estimation, conditional generative adversarial network, statistical model, multiple correlation, Euclidean – Mahalanobis distance
1. Generative Adversarial NetWork / I. J. Goodfellow [et al.]. URL: https://arxiv.org/abs/1406.2661 (data obrascheniya 03.11.2024).
2. Grachev V. V., Fedotov M. V. Povyshenie kachestva obucheniya etalonnyh diagnosticheskih modeley slozhnyh tehnicheskih ob'ektov augmentaciey obuchayuschih dannyh // Avtomatika na transporte. 2023. T. 9, № 3. S. 258–273. DOI:https://doi.org/10.20295/2412- 9186-2023-9-03-258-273. EDN VXLQLW
3. Mehdi M., Osindero S. Conditional Generative Adversarial Nets. URL: https://arxiv.org/abs/1411.1784 (data obrascheniya 03.11.2024).
4. Ssylka na funkciyu rasstoyaniya Vasser- shteyna v Python. URL: https://question-it. com/questions/15429235/ssylka-na-funktsiju-rasstojanija- vassershtejna-v-python (data obrascheniya 03.11.2024).
5. Foster D. Generativnoe glubokoe obuchenie. Tvorcheskiy potencial neyronnyh setey. SPb.: Piter, 2020. 336 s.: il.
6. Ayvazyan S. A., Mhitaryan V. S. Prikladnaya statistika. Osnovy ekonometriki. T. 1. Teoriya veroyatnostey i prikladnaya statistika. M.: Yuniti-Dana, 2001. 656 s.
7. Ayvazyan S. A., Enyukov I. S., Meshalkin L. D. Prikladnaya statistika. Issledovanie zavisimostey // Finansy i statistika. 1985. 487 s.
8. Kremer N. Sh., Putko B. A. Ekonometrika / pod red. N. Sh. Kremera. M.: Yuniti-Dana, 2010. 328 s.
9. Chalganova A. A. Postroenie mnozhestvennoy re- gressii i ocenka kachestva modeli s ispol'zovaniem tablichnogo processora Excel. SPb.: RGGMU, 2022. 89 s.
10. Orlov A. I. O Ekonometrika: uchebnik dlya vuzov. Rostov n/D.: Feniks, 2009. 412 s.
11. Trusova A. Yu. Analiz dannyh. Mnogomernye statisticheskie metody: uchebnoe posobie. Samara: Izdatel'stvo Samarskogo universiteta, 2023. 92 s.
12. Generator sluchaynyh chisel Excel v funkciyah i analize dannyh. URL: https://exceltable.com/ unkcii-excel/ generator-sluchaynyhchisel (data obrascheniya 03.11.2024).
13. Rasstoyanie Mahalonobisa. URL: https://habr.com/ ru/articles/555144/ (data obrascheniya 03.11.2024).