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Identification of Parameters of a Linear Regression Model by Simultaneous Optimization of Two Heterogeneous Criteria.

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Title: Identification of Parameters of a Linear Regression Model by Simultaneous Optimization of Two Heterogeneous Criteria.
Authors: Noskov, S. I., Ovsyannikov, I. V.
Source: Theoretical Foundations of Chemical Engineering; Jun2024, Vol. 58 Issue 3, p905-908, 4p
Subject Terms: NONPARAMETRIC estimation, REGRESSION analysis, LINEAR programming, MATHEMATICAL statistics, MATHEMATICAL models, DECISION trees, EXPECTATION-maximization algorithms
Abstract: The article provides a brief overview of works related to the use of various criteria for the adequacy of mathematical models, each of which reflects certain characteristics in the form of a model description of the functioning of the process or object under study. In particular, the considered works deal with a finite mixed regression model, which forms sample clusters and jointly uses several mixed criteria simultaneously, ensures the selection of common functions among tasks and cluster components, allows working with anomalous tasks, and takes into account outliers in samples; the problem of constructing a heterogeneous ensemble of models, where three self-adapting genetic algorithms with different control parameters of mutation, crossing, and selection, adjusted during execution, are proposed; the problem of filling missing data in regression modeling, where 11 heterogeneous ensemble filling methods are proposed and constructed, the members of which are two, three, or four of the following single methods: K-nearest neighbors, expectation maximization, support vector regression, and decision trees; and a semiparametric modeling approach that combines parametric regression analysis and nonparametric analogical estimation. An algorithm is proposed for solving the problem of estimating unknown parameters using two criteria simultaneously: the minimum sum of the approximation error modules and the maximum consistency of behavior between the given and model-calculated values of the dependent variable in continuous form. This algorithm involves first identifying the Pareto vertices of a given polyhedron and then checking the Pareto property of the edges connecting their images in the criterion space. The computational problems that arise in this case are reduced to linear programming problems. A simple numerical example is solved. [ABSTRACT FROM AUTHOR]
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Abstract:The article provides a brief overview of works related to the use of various criteria for the adequacy of mathematical models, each of which reflects certain characteristics in the form of a model description of the functioning of the process or object under study. In particular, the considered works deal with a finite mixed regression model, which forms sample clusters and jointly uses several mixed criteria simultaneously, ensures the selection of common functions among tasks and cluster components, allows working with anomalous tasks, and takes into account outliers in samples; the problem of constructing a heterogeneous ensemble of models, where three self-adapting genetic algorithms with different control parameters of mutation, crossing, and selection, adjusted during execution, are proposed; the problem of filling missing data in regression modeling, where 11 heterogeneous ensemble filling methods are proposed and constructed, the members of which are two, three, or four of the following single methods: K-nearest neighbors, expectation maximization, support vector regression, and decision trees; and a semiparametric modeling approach that combines parametric regression analysis and nonparametric analogical estimation. An algorithm is proposed for solving the problem of estimating unknown parameters using two criteria simultaneously: the minimum sum of the approximation error modules and the maximum consistency of behavior between the given and model-calculated values of the dependent variable in continuous form. This algorithm involves first identifying the Pareto vertices of a given polyhedron and then checking the Pareto property of the edges connecting their images in the criterion space. The computational problems that arise in this case are reduced to linear programming problems. A simple numerical example is solved. [ABSTRACT FROM AUTHOR]
ISSN:00405795
DOI:10.1134/S0040579524601821