高维混料模型的LASSO变量选择
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摘要
变量选择是统计建模中重要的问题。当试验数据维数很高时,传统变量选择方法的应用受到了很多制约。本文以高维混料试验为基础,比较了AIC准则和LASSO在变量选择问题上的优良性。通过实例验证,LASSO可以快速且准确地对高维混料模型中的变量进行筛选,从而得出最优模型,达到降低成本、提高利益的目的。
Variable selection is an important issue in Statistical Modeling. Traditional variable selection method is difficult in dealing with the increasing dimension of experimental data. In this paper, based on the high-dimensional mixture experimental design, the optimality of the AIC criterion and LASSO on variable selection are compared. As showed by examples, LASSO can quickly and accurately filter the variables for the high-dimensional mixture model selection process. The optimal model got by the process are powerful in reducing cost and increasing benefit.
Variable selection is an important issue in Statistical Modeling. Traditional variable selection method is difficult in dealing with the increasing dimension of experimental data. In this paper, based on the high-dimensional mixture experimental design, the optimality of the AIC criterion and LASSO on variable selection are compared. As showed by examples, LASSO can quickly and accurately filter the variables for the high-dimensional mixture model selection process. The optimal model got by the process are powerful in reducing cost and increasing benefit.
引文
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[9]闫湛,张崇岐.混料试验设计的变量选择[J].数理统计与管理,2016, 35(5):786-793.
[10]张崇岐,闫湛.混料试验设计变量选择AIC准则研究[J].广州大学学报(自然科学版),2016, 15(2):21-24.
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[17]李光辉,张崇岐.混料试验的拟分量变换设计[J].应用数学学报,2017, 40(5):734-751.
[2] AKAIKE H. Information theory and an extension of the maximum likelihood principle[A]. 2nd International Symposium on Information Theory[C]. Akademiai Kiado, 1973:267-281.
[3] Schwarz G. Estimating the dimension of a model[J]. The annals of statistics, 1978, 6(2):461-464.
[4]王大荣,张忠占.线性回归模型中变量选择方法综述[J].数理统计与管理,2010, 29(4):615-627.
[5]李根,邹国华,张新雨.高维模型选择方法综述[J].数理统计与管理,2012, 31(4):640-658.
[6] Tibshirani R. Regression shrinkage and selection via the lasso[J]. Journal of the Royal Statistical Society(Series B):Methodological,1996:267-288.
[7] Zou H, Hastie T. Regularization and variable selection via the elastic net[J]. Journal of the Royal Statistical Society(Series B):Statistical Methodology, 2005, 67(2):301-320.
[8] Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journal of the American statistical Association, 2001, 96(456):1348-1360.
[9]闫湛,张崇岐.混料试验设计的变量选择[J].数理统计与管理,2016, 35(5):786-793.
[10]张崇岐,闫湛.混料试验设计变量选择AIC准则研究[J].广州大学学报(自然科学版),2016, 15(2):21-24.
[11] Breiman L. Better subset regression using the nonnegative garrote[J]. Technometrics, 1995, 37(4):373-384.
[12] Breiman L. Heuristics of instability and stabilization in model selection[J]. The annals of statistics,1996, 24(6):2350-2383.
[13] Scheffe H. Experiments with mixtures[J]. Journal of the Royal Statistical Society(Series B):Methodological, 1958:344-360.
[14] Cornell J A. Experiments with Mixture Designs[M]. New York:John Wiley, 1981.
[15]关颖男.混料试验设计[M].上海:上海科技出版社,1990.
[16]李光辉,张崇岐.具有复杂约束混料试验的渐近D-最优设计[J].应用概率统计,2017, 33(2):203-220.
[17]李光辉,张崇岐.混料试验的拟分量变换设计[J].应用数学学报,2017, 40(5):734-751.