Bayesian multidimensional-matrix polynomial empirical regression

• Autorzy: Mukha Vladimir S.
• Języki publikacji: EN

Abstrakty

EN

The problem of parameter estimation for the polynomial in the input variables regression function is formulated and solved. The input and output variables of the regression function are multidimensional matrices. The parameters of the regression function are assumed to be random independent multidimensional matrices with Gaussian distribution and known mean value and variance matrices. The solution to this problem is a multidimensional-matrix system of the linear algebraic equations in multidimensional-matrix unknown regression function parameters. We consider the particular cases of constant, affine and quadratic regression function, for which we have obtained formulas for parameter calculation. Computer simulation of the quadratic regression function is performed for the two-dimensional matrix input and output variables.

Słowa kluczowe

EN

regression function; parameter estimation; maximum likelihood estimation; Bayesian estimation; multidimensional matrice

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2020
• Tom: Vol. 49, No. 3
• Strony: 291--314
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Mukha Vladimir S.

• Belarusian State University of Informatics and Radioelectronics, P. Brovki str. 6, Minsk, 220013, Republic of Belarus

Bibliografia

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• Mukha, V. S. and Sergeev, E. V. (1974) Bayesian estimations of the parameters of the regression objects. Proceedings of LETI, 149, 26–29. In Russian.
• Mukha, V. S. and Sergeev E. V. (1976) Dual control of regression objects. Proceedings of LETI, 202, 58–65. In Russian.
• Mukha, V. S. (2004) Analysis of multidimensional data. Minsk, Technoprint. In Russian.
• Mukha, V. S. (2005) Vector Multiconnected Markov Chains. Journal of Automation and Information Sciences, 37, 63–69.
• Mukha, V. S. (2006) Multidimensional Matrix Approach in Parallel Factor Analysis. Journal of Automation and Information Sciences, 38, 21–29.
• Mukha, V. S. (2007a) The Best Polynomial Multidimensional-matrix Regression. Cybernetics and Systems Analysis, 43, 3, 427–432.
• Mukha, V. S. (2007b) Multidimensional-matrix polynomial regression analysis. Parameters estimations. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 1, 45–51. In Russian.
• Mukha, V. S. (2008) PARAFAC-regression Analysis for Determining the Concentration of Substances in Solutions. Journal of Automation and Information Sciences, 40, 25–40.
• Mukha, V. S. (2011) Minimum average risk and efficiency of optimal polynomial multidimensional-matrix predictors. Cybernetics and Systems Analysis, 47, 2, 277–285.
• Mukha, V. S. (2012) Educational Timetable Problem: Formulation and Solving. Journal of Automation and Information Sciences, 44, 12, 55–67.
• Mukha, V.S. (2017) On Statistical Forecasting of the Atmospheric Temperature for Month. American Journal of Environmental Engineering and Science, 4, 6, 71–77.
• Mukha, V. S. (2020) On the Bayesian multidimensional-matrix polynomial empirical regression / Vladimir S. Mukha, Irina G. Malikova // Scientific research of the SCO countries: synergy and integration: Materials of the International Conference, Beijing, May 14, 2020. China, 2020, 159–165. DOI: https://doi.org/10.34660/INF.2020.28.63870.
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• Sokolov, N. P. (1960) Spatial matrices and their applications. Moscow, Fizmatgiz. In Russian.
• Sokolov, N. P. (1972) Introduction to the theory of multidimensional matrices. Kiev, Naukova dumka. In Russian.
• Wakefield, J. (2013) Bayesian and Frequentist Regression Methods. Springer.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).