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

作     者：Noskov, S. I. Ovsyannikov, I. V. 

作者机构：Irkutsk State Transport Univ Irkutsk Russia 

出 版 物：《THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING》 (Theor. Found. Chem. Eng.)

年 卷 期：2024年第58卷第3期

页      面：905-908页

核心收录：

学科分类：0817[工学-化学工程与技术] 08[工学] 

基　　金：This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained 

主　　题：linear regression model multicriteria parameter estimation least modulus method adequacy criteria behavior consistency Pareto set linear programming 

摘      要：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.