变系数模型的稳健LS-SVR估计算法及数值分析  

Robust LS-SVR Estimation Algorithm and Numerical Analysis of Varying Coefficient Model

作　　者：张辉国[1] 张孟娟 胡锡健[1] ZHANG Hui-guo;ZHANG Meng-juan;HU Xi-jian(College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《计算机仿真》2023年第4期367-372,共6页Computer Simulation

基　　金：新疆自然科学基金(2019D01C045);教育部人文社会科学研究规划基金(19YJA910007);国家自然科学基金(11961065)。

摘　　要：变系数模型的最小二乘支持向量回归估计方法(VC-LS-SVR)是最近提出的一种用于分析变量间回归关系动态变化特征的有力工具,经典非参数回归模型与机器学习方法相融合的新技术,不仅增强了变系数模型对变量间非线性关系的适应性与可计算性,同时继承了经典统计模型的可解释性。但是上述方法直接利用最小二乘支持向量回归(LS-SVR)技术拟合变系数模型,缺乏稳健性,数据中的异常值会扭曲系数函数的估计,从而引起对回归关系的误导性解释。为解决上述问题,基于VC-LS-SVR和加权思想提出了两种稳健估计方法:变系数模型的加权最小二乘支持向量回归估计方法(VC-WLS-SVR)与迭代重加权最小二乘支持向量回归估计方法(VC-IRLS-SVR)。数值实验结果表明两种方法具有稳健性,能够有效抑制异常值的影响,即使在异常数据污染率达到50%或存在极端异常值的情况下,也能获得准确和稳定的估计结果。The least squares support vector regression estimation method of varying coefficient model(VC-LSSVR)is a powerful tool recently proposed to analyze the dynamic change characteristics of regression relationship among variables.The new technique of integrating classical non-parametric regression model with machine learning method not only enhances the adaptability and computability of varying coefficient model to the nonlinear relationship of variables,but also inherits the interpretability of classical statistical model.However,this method directly uses the least squares support vector regression(LS-SVR)technology to fit the varying coefficient model,which is lack of robustness.The outliers in the data will distort the estimation of the coefficient function,resulting in misleading interpretation of the regression relationship.In order to get the robust estimation of regression coefficient,this paper proposes two robust estimation methods based on VC-LS-SVR and weighted idea:weighted least squares support vector regression estimation method of varying coefficient model(VC-WLS-SVR)and iterative reweighted least squares support vector regression estimation method of varying coefficient model(VC-IRLS-SVR).Numerical experimental results show that the two methods are robust and can effectively suppress the influence of outliers.Even when the pollution rate of abnormal data reaches 50%or extreme outliers exist,accurate and stable estimation results can be obtained.

关 键 词：变系数模型 最小二乘支持向量机 加权函数 迭代重加权 异常值 

分 类 号：N945.12[自然科学总论—系统科学] TP391.9[自动化与计算机技术—计算机应用技术]