Identification of Unknown Parameters of Non-Elementary Regression Models with Integer Functions and Binary Logical Operations

Abstract

The article is devoted to the problem of constructing regression models based on a sample containing a Boolean output variable and continuous input variables. Well-known methods for constructing such models, such as logistic, logical, and pseudo-Boolean regression, are investigated. A regression model with integer functions floor and ceiling, proposed by the author earlier, is considered. The identification of this model using the least absolute deviations method is reduced to solving the problem of mixed integer linear programming. It has been shown that this model can also be used for analyzing data based on samples containing Boolean output variables. In this case, identification reduces to a mixed 0-1 integer linear programming, whose solution leads to binarization of the linear combination of explanatory variables. Based on the combination of two linear combinations of explanatory variables, binarized by the proposed method using binary logical operations, eight new specifications of regression models were introduced. For this purpose, operations such as conjunction, disjunction, exclusive OR, equivalence, implication, inverse implication, Sheffer stroke, and Pierce arrow were used. The parameters of each of these models were identified by solving mixed 0-1 linear programming problems. The correctness of the mathematical apparatus developed was proven using an example problem: studying the probability of non-repayment of a loan by a trading company. Moreover, using only one integer function floor, the accuracy of prediction of the model was 80%, higher than that of logistic regression, which had an accuracy of 72%. When using two integer functions floor, at once, six models with logical operations disjunction, exclusive OR, equivalence, implication, inverse implication, and Sheffer stroke, showed an accuracy of 96%.