Descent along nodal straight lines and simplex algorithm: two variants of regression analysis based on the least absolute deviation method

Abstract

A comparative analysis of the computational complexity of exact algorithms for estimating linear regression equations was conducted using the least absolute deviation method. The goal of the study is to compare the computational efficiency of exact algorithms for descent along nodal lines and algorithms based on solving linear programming problems. For this purpose, the algorithm of gradient descent along nodal lines and algorithms for solving the equivalent primal and dual linear programming problems using the simplex method were considered. The computational complexity of algorithms for implementing the method of least modules in solving direct and dual linear programming problems was estimated. A comparison between the average time for determining the regression coefficients using the primal and dual linear programming problems and the average time for gradient descent along nodal lines was conducted using the Monte Carlo method of statistical experiments. It is shown that both options are significantly inferior behind gradient descent along nodal lines, both in terms of the computational complexity of the algorithms and in terms of computation time, and this advantage increases with the sample size, reaching hundred times or more.