{"id":4831,"date":"2025-11-15T21:46:04","date_gmt":"2025-11-15T21:46:04","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=4831"},"modified":"2025-11-20T13:27:51","modified_gmt":"2025-11-20T13:27:51","slug":"27-5-12","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/27-5-12\/","title":{"rendered":"27.5.12"},"content":{"rendered":"\n

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\u0414\u043b\u044f \u0446\u0438\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f.<\/strong> \u041a\u0430\u0437\u0430\u043a\u043e\u0432 \u041c. \u0410. \u0420\u043e\u0431\u0430\u0441\u0442\u043d\u044b\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440 Adam \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u044e\u0449\u0438\u0445 \u0430\u0433\u0440\u0435\u0433\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \/\/ \u0418\u0437\u0432\u0435\u0441\u0442\u0438\u044f \u041a\u0430\u0431\u0430\u0440\u0434\u0438\u043d\u043e-\u0411\u0430\u043b\u043a\u0430\u0440\u0441\u043a\u043e\u0433\u043e \u043d\u0430\u0443\u0447\u043d\u043e\u0433\u043e \u0446\u0435\u043d\u0442\u0440\u0430 \u0420\u0410\u041d. 2025. \u0422. 27. \u2116 5. \u0421. 159\u2013167. DOI: 10.35330\/1991-6639-2025-27-5-159-167<\/p>\n\n\n\n

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\u0421\u043f\u0438\u0441\u043e\u043a \u043b\u0438\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u044b<\/strong><\/summary>\n
    \n
  1. Kingma D.P., Ba J. Adam. A method for stochastic optimization. international conference on learning representations (ICLR 2015). San Diego, 2015. 15 p., available at: https:\/\/arxiv.org\/abs\/1412.6980<\/li>\n\n\n\n
  2. Tieleman T. Lecture 6.5\u2010rmsprop: Divide the gradient by a running average of its recent magnitude. COURSERA: Neural Networks for Machine Learning. 2012. Vol. 4. No. 2. Pp. 26. DOI: https:\/\/cir.nii.ac.jp\/crid\/1370017282431050757<\/li>\n\n\n\n
  3. \u041f\u043e\u043b\u044f\u043a \u0411. \u0422. \u041e \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u0445 \u0443\u0441\u043a\u043e\u0440\u0435\u043d\u0438\u044f \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u0445 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \/\/ \u0416\u0443\u0440\u043d\u0430\u043b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0438\u0437\u0438\u043a\u0438. 1964. \u0422. 4. \u2116 5. \u0421. 791\u2013803. DOI: 10.1016\/0041-5553(64)90137-5<\/li>\n\n\n\n
  4. Duchi J., Hazan E., Singer Y. Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research. 2011. Vol. 12. Pp. 2121\u20132159.<\/li>\n\n\n\n
  5. Koenker R. Quantile Regression. Cambridge: Cambridge University Press, 2005. 366 p. ISBN: 0-521-60827-9<\/li>\n\n\n\n
  6. Huber P.J. Robust Statistics. New York: Wiley, 1981. 308 p. ISBN: 0-471-41805-6<\/li>\n\n\n\n
  7. Tukey J.W. A survey of sampling from contaminated distributions. in: contributions to probability and statistics: essays in honor of Harold Hoteling. Stanford: Stanford University Press, Pp. 448\u2013485. DOI: https:\/\/cir.nii.ac.jp\/crid\/1570291226404846720<\/li>\n\n\n\n
  8. Rousseeuw P.J., Leroy A.M. Robust regression and outlier detection. New York: Wiley, 329 p. ISBN: 9780471852339<\/li>\n\n\n\n
  9. Rousseeuw P.J. Least median of square regression. Journal of the American Statistical Association. 1984. Vol. 79. Pp. 871\u2013880. DOI: 10.1080\/01621459.1984.10477105.<\/li>\n\n\n\n
  10. Vapnik V. The nature of statistical learning theory. New York: Springer-Verlag, 2000. 314 p. ISBN: 978-1-4419-3160-3<\/li>\n\n\n\n
  11. Beliakov G., Sola H., Calvo T. A practical guide to averaging functions. Berlin: Springer-Verlag, 2016. 371 p. ISBN: 978-3319247519<\/li>\n\n\n\n
  12. Calvo T., Beliakov G. Aggregation functions. Fuzzy Sets and Systems. 2010. Vol. 161. No. 10. Pp. 1420\u20131436. DOI: 10.1016\/j.fss.2009.05.012<\/li>\n\n\n\n
  13. Mesiar R., Koles\u00e1rov\u00e1 A., Calvo T., Komorn\u00edkov\u00e1 M. A review of aggregation functions. fuzzy sets and their extensions: representation, aggregation and models. studies in fuzziness and soft computing. 2008. Vol. 220. Springer, Berlin, Heidelberg. DOI: 10.1007\/978-3-540-73723-0_7<\/li>\n\n\n\n
  14. Shibzukhov Z.M. Principle of minimizing empirical risk and averaging aggregate functions. Journal of Mathematical Sciences. 2021. Vol. 253. No. 4. Pp. 571\u2013583. DOI: 10.1007\/s10958-021-05256-y<\/li>\n\n\n\n
  15. Vapnik V. Principles of risk minimization for learning theory. Advances in Neural Information Processing Systems (NeurIPS). 1991. Vol. 4. Pp. 831\u2013838. DOI: https:\/\/cir.nii.ac.jp\/crid\/1571698599429734144<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u043e\u0431 \u0430\u0432\u0442\u043e\u0440\u0435<\/strong><\/summary>\n

    \u041a\u0430\u0437\u0430\u043a\u043e\u0432 \u041c\u0443\u0445\u0430\u043c\u0435\u0434 \u0410\u043d\u0430\u0442\u043e\u043b\u044c\u0435\u0432\u0438\u0447<\/strong>, \u043c\u043b. \u043d\u0430\u0443\u0447. \u0441\u043e\u0442\u0440. \u043e\u0442\u0434\u0435\u043b\u0430 \u043d\u0435\u0439\u0440\u043e\u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0438 \u0438 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u0433\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f, \u0418\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0438 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0438\u0438 \u2013 \u0444\u0438\u043b\u0438\u0430\u043b \u041a\u0430\u0431\u0430\u0440\u0434\u0438\u043d\u043e-\u0411\u0430\u043b\u043a\u0430\u0440\u0441\u043a\u043e\u0433\u043e \u043d\u0430\u0443\u0447\u043d\u043e\u0433\u043e \u0446\u0435\u043d\u0442\u0440\u0430 \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u043e\u0439 \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u0438 \u043d\u0430\u0443\u043a;
    360000, \u0420\u043e\u0441\u0441\u0438\u044f, \u0433. \u041d\u0430\u043b\u044c\u0447\u0438\u043a, \u0443\u043b. \u0428\u043e\u0440\u0442\u0430\u043d\u043e\u0432\u0430, 89 \u0410;
    kasakow.muchamed@gmail.com, ORCID: https:\/\/orcid.org\/0000-0002-5112-5079, SPIN-\u043a\u043e\u0434: 6983-1220<\/p>\n\n\n\n

    <\/p>\n<\/details>\n\n\n\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    \u0420\u043e\u0431\u0430\u0441\u0442\u043d\u044b\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0442\u043e\u0440 Adam \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u044f\u044e\u0449\u0438\u0445 \u0430\u0433\u0440\u0435\u0433\u0438\u0440\u0443\u044e\u0449\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u041c. \u0410. \u041a\u0430\u0437\u0430\u043a\u043e\u0432 \u0417\u0430\u0433\u0440\u0443\u0437\u0438\u0442\u044c \u043f\u043e\u043b\u043d\u044b\u0439 \u0442\u0435\u043a\u0441\u0442 \u0410\u043d\u043d\u043e\u0442\u0430\u0446\u0438\u044f: \u041e\u0431\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u0437\u0430\u0433\u0440\u044f\u0437\u043d\u0435\u043d\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 (\u0432\u044b\u0431\u0440\u043e\u0441\u044b, \u0442\u044f\u0436\u0435\u043b\u044b\u0435 \u0445\u0432\u043e\u0441\u0442\u044b, \u0448\u0443\u043c \u043c\u0435\u0442\u043e\u043a, \u0430\u0440\u0442\u0435\u0444\u0430\u043a\u0442\u044b \u043f\u0440\u0435\u0434\u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0438) \u0434\u0435\u043b\u0430\u0435\u0442 \u0430\u0440\u0438\u0444\u043c\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0441\u0440\u0435\u0434\u043d\u0435\u043d\u0438\u0435 \u0432 \u044d\u043c\u043f\u0438\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0440\u0438\u0441\u043a\u0435 \u043d\u0435\u0443\u0441\u0442\u043e\u0439\u0447\u0438\u0432\u044b\u043c: \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0430\u043d\u043e\u043c\u0430\u043b\u0438\u0439 \u0441\u043c\u0435\u0449\u0430\u044e\u0442 \u043e\u0446\u0435\u043d\u043a\u0438, \u0434\u0435\u0441\u0442\u0430\u0431\u0438\u043b\u0438\u0437\u0438\u0440\u0443\u044e\u0442 \u0448\u0430\u0433\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0438 \u0443\u0445\u0443\u0434\u0448\u0430\u044e\u0442 \u043e\u0431\u043e\u0431\u0449\u0430\u044e\u0449\u0443\u044e \u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u044c. \u0422\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044f \u0441\u043f\u043e\u0441\u043e\u0431 \u043f\u043e\u0432\u044b\u0441\u0438\u0442\u044c \u0440\u043e\u0431\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u044c \u0431\u0435\u0437 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043e\u0442\u0435\u0440\u044c \u0438 \u0430\u0440\u0445\u0438\u0442\u0435\u043a\u0442\u0443\u0440\u044b \u043c\u043e\u0434\u0435\u043b\u0438.\u0426\u0435\u043b\u044c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4831","page","type-page","status-publish","hentry"],"yoast_head":"\n27.5.12 - 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