СОВЕРШЕНСТВОВАНИЕ АЛГОРИТМА ТОЧНОГО ОЦЕНИВАНИЯ МОДУЛЬНЫХ ЛИНЕЙНЫХ РЕГРЕССИЙ С ПОМОЩЬЮ МЕТОДА НАИМЕНЬШИХ МОДУЛЕЙ

Abstract

This article is devoted to the study of the algorithm for exact estimation of modular linear regression models using the least absolute deviations. Such models contain a mathematical operation module and are linear in factors, but nonlinear in parameters, regressions. Previously, a special algorithm was developed to exact estimate them using the least absolute deviations. Its essence is that by manually going through all possible combinations of absolute values signs and solving a mixed integer 0-1 linear programming problem for each case, the best model in terms of the sum of absolute residuals is selected. To implement this algorithm, the MODULIR-1 software package was previously developed. The disadvantage of the algorithm is that, in total, quite a lot of time is spent on its implementation. This paper proposes a new and improved algorithm for exact estimation of modular regressions. In it, instead of solving a series of mixed integer 0-1 linear programming problems, you only need to solve one single problem. The developed algorithm is implemented in the new version of the MODULIR-1 program. To compare the effectiveness of the old and new algorithms using the example of chemical data processing, computational experiments were carried out. In six out of seven cases, the new algorithm turned out to be more effective than the existing one. When constructing the most computationally complex modular regression, the estimation time decreased by 74.3%. The modular regression constructed as a result of the experiments based on the sum of absolute residuals turned out to be approximately 2.3 times better than the classical linear regression. At the same time, the number of zero residues in modular regression also turned out to be greater.