Synthesis of Logisitic Regression, Based on Self-Organisation Principles of Models

Настенко, Євген; Boyko, Anna Dmitrievna; Nosovets, O.; Teplyakov, K.; Pavlov, V. N.

doi:10.15407/kvt182.02.086

Cited by 2 publications

(4 citation statements)

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“…Вісник Національного технічного університету «ХПІ». Серія: Системний аналіз, управління та інформаційні технології, № 1 (9)' 2023 7…”

Section: A Modified Group Methods Of Data Handling (Mgmdh)unclassified

“…With the appropriate selection of the values of the virtual scalar variable z , expression (10) significantly simplifies the preliminary analysis and the input data formation for the main active experiment to obtain, with acceptable accuracy, estimates of the coefficients for nonlinear terms of the UPR and, as will be shown later, an MPR. Such a requirement is for n r  max a compromise between the number of tests n of the main experiment and the value of variances of the estimates of the coefficients for nonlinear members of the virtual UPR (9). As a result of the analysis of the conducted experiments, the following compromise solution is proposed for…”

Section: Estimation With Acceptable Accuracy Of the Coefficients For ...mentioning

confidence: 99%

“…, for a UPR (1). The expressions were obtained from the results of estimation by a virtual UPR (9). This makes it possible to determine, depending on the values of…”

Section: Justification Of Conditions For Obtaining Estimates For Nonl...mentioning

confidence: 99%

“…Introduction. Multivariate linear and non-linear regressions, constructed based on the results of active or passive experiments, are widely used in modern diagnostic information systems, in particular, medical ones, and in information management systems with a wide range of applications [1][2][3][4][5][6][7][8][9][10]. Universal methods for multivariate regressions construction vary from classical statistical methods to heuristics, such as the group method of data handling (GMDH) or genetic algorithms.…”

mentioning

confidence: 99%

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Efficiency Substantiation for a Synthetical Method of Constructing a Multivariate Polynomial Regression Given by a Redundant Representation

Pavlov¹,

Holovchenko²,

Drozd³

2023

SACIT

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In recent years, the authors in their publications have developed two different approaches to the construction of a multivariate polynomial (in particular, linear) regressions given by a redundant representation. The first approach allowed us to reduce estimation of coefficients for nonlinear terms of a multivariate polynomial regression to construction of a sequence of univariate polynomial regressions and solution of corresponding nondegenerate systems of linear equations. The second approach was implemented using an example of a multivariate linear regression given by a redundant representation and led to the creation of a method the authors called a modified group method of data handling (GMDH), as it is a modification of the well-known heuristic self-organization method of GMDH (the author of GMDH is an Academician of the National Academy of Sciences of Ukraine O. G. Ivakhnenko). The modification takes into account that giving a multivariate linear regression by redundant representation allows for construction of a set of partial representations, one of which has the structure of the desired regression, to use not a multilevel selection algorithm, but an efficient algorithm for splitting the coefficients of the multivariate linear regression into two classes. As in the classic GMDH, the solution is found using a test sequence of data. This method is easily extended to the case of a multivariate polynomial regression since the unknown coefficients appear in the multivariate polynomial regression in a linear way. Each of the two approaches has its advantages and disadvantages. The obvious next step is to combine both approaches into one. This has led to the creation of a synthetic method that implements the advantages of both approaches, partially compensating for their disadvantages. This paper presents the aggregated algorithmic structure of the synthetic method, the theoretical properties of partial cases and, as a result, the justification of its overall efficiency.

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Section: A Modified Group Methods Of Data Handling (Mgmdh)unclassified

Section: Estimation With Acceptable Accuracy Of the Coefficients For ...mentioning

confidence: 99%

“…, for a UPR (1). The expressions were obtained from the results of estimation by a virtual UPR (9). This makes it possible to determine, depending on the values of…”

Section: Justification Of Conditions For Obtaining Estimates For Nonl...mentioning

confidence: 99%