沿节点直线下降和单纯形算法:基于最小绝对偏差法的回归分析的两种变体

O. A. Golovanov, A. N. Tyrsin
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引用次数: 0

摘要

使用最小绝对偏差法对估计线性回归方程的精确算法的计算复杂性进行了比较分析。研究的目的是比较沿节点线下降的精确算法和基于求解线性规划问题的算法的计算效率。为此,考虑了沿节点线梯度下降的算法和使用单纯形法求解等效原始和对偶线性规划问题的算法。估算了在解决直接和对偶线性规划问题时实施最小模块法的算法的计算复杂度。使用蒙特卡洛统计实验方法,对使用原始线性规划问题和对偶线性规划问题确定回归系数的平均时间与沿节点线梯度下降的平均时间进行了比较。结果表明,无论从算法的计算复杂度还是从计算时间来看,这两种方案都明显不如沿节点线梯度下降法,而且这种优势随着样本量的增加而增加,达到百倍或更多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Descent along nodal straight lines and simplex algorithm: two variants of regression analysis based on the least absolute deviation method
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.
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