试验设计及参数优化的LS-SVR显著性因子筛选  

Significant factors screening of LS-SVR for experimental design and parameters optimization

作　　者：崔庆安 崔楠[2] CUI Qing-an;CUI Nan(School of Economics and Management,Shanghai Maritime University,Shanghai 201306,China;Economics and Management School,Wuhan University,Wuhan 430072,China)

机构地区：[1]上海海事大学经济管理学院,上海201306 [2]武汉大学经济与管理学院,武汉430072

出　　处：《管理科学学报》2023年第12期42-61,共20页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(71571168,U1904211,72172110);国家科技部创新方法专项资助项目(2019IM020200);河南省高校科技创新人才人文社科类支持计划项目(2019cx007)。

摘　　要：针对最小二乘支持向量回归机(LS-SVR)应用于试验设计建模及参数优化而产生的可解释性差、难以识别显著性影响因子等不足,提出一种适用于LS-SVR的拟合不足检验及显著性因子筛选方法.首先在重复性试验设计条件下,将LS-SVR拟合模型的“残差平方和”分解为“拟合不足平方和”与“纯误差平方和”;进而给出了“拟合不足均方”与“纯误差均方”比值的近似非中心F-分布,构造出拟合不足检验的方差分析表;在此基础上,提出一种两阶段的显著性因子筛选方法,通过考察某个因子(组合)移除后模型拟合不足显著性的变化,来推断该因子(组合)显著性.仿真研究与实证表明,所提方法不仅能够增强LS-SVR的统计可解释性,有效识别出显著性因子;而且可以得到预测性能更优的简化模型;有助于提升试验设计建模及参数优化效率,降低质量改进成本.The least squares support vector regression(LS-SVR)in experimental design modeling and parameters optimization is accompanied by poor interpretability and difficulties in significant factors screening.This paper proposes an under-fitting-test-based significant factors screening approach for the LS-SVR model.Firstly,the“residual sum of squares”is decomposed into the sum squares of“lack-of-fit”and“pure error”.Then the nearly non-central F-distribution of the ratio between the mean square of“lack-of-fit”and“pure error”is given.Consequently,a two-stage factor screening method is developed,which infers the significance of a certain factor(or combination)by investigating the change of the significance of model’s under-fitting after factor removing.The simulation and case studies show that the proposed approach can enhance the statistical inference interpretability of LS-SVR,screen the significant factors effectively and obtain a reduced LS-SVR model with lower complexity and higher predictive performance.Furthermore,the proposed approach is conductive to increase the efficiency of experimental design and parameters optimization,and to reduce the cost of quality improvement.

关 键 词：因子筛选 参数优化 试验设计 拟合不足检验 最小二乘支持向量回归机 

分 类 号：F406.2[经济管理—产业经济]