Lasso正则化参数选择的修正AIC方法研究
A Modified AIC Method for the Selection of Lasso Regularization Parameters
DOI: 10.12677/AAM.2023.123106, PDF,    科研立项经费支持
作者: 赵哲宇, 王少春, 尚美晨, 王延新*：宁波工程学院理学院，浙江 宁波
关键词: Lasso；变量选择；正则化方法；MAIC准则；高维数据；Lasso； Variable Selection； Regularization Parameter； MAIC； High-Dimensional Data
摘要: Lasso正则化方法是常用的变量选择方法。但Lasso正则化方法的优劣取决于能否选取出最优的正则化参数。本文在AIC准则的基础上，提出适用于Lasso正则化参数选择的修正的AIC (MAIC)准则。数据模拟及实例分析表明，Lasso方法在MAIC准则下能够以更高的概率选择正确的模型，MAIC准则明显优于其它参数选择方法。
Abstract: Lasso regularization method is a commonly used variable selection method. However, the merits of Lasso regularization method depend on whether the optimal regularization parameters can be se-lected. Based on the AIC criterion, a modified AIC (MAIC) criterion is proposed for the selection of Lasso regularization parameter selection. Through data simulation and practical application, Lasso method can select the correct model with higher probability under MAIC criterion, and MAIC crite-rion is obviously superior to other parameter selection methods.
文章引用：赵哲宇, 王少春, 尚美晨, 王延新. Lasso正则化参数选择的修正AIC方法研究[J]. 应用数学进展, 2023, 12(3): 1045-1053. https://doi.org/10.12677/AAM.2023.123106

参考文献

[1] Akaike, H. (1973) Information Theory and an Extension of the Maximum Likelihood Principle. In: Petrov, B.N. and Csaki, F., Eds., Second International Symposium on Information Theory, Akademiai Kiado, Budapest, 267-281.
[2] Schwarz, G. (1978) Estimating the Dimension of a Model. The Annals of Statistics, 6, 461-464. [Google Scholar] [CrossRef] 
[3] Craven, P. and Wahba, G. (1979) Smoothing Noisy Data with Spline Functions: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation. Numerische Mathematik, 31, 377-403. [Google Scholar] [CrossRef] 
[4] Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58, 267-288. [Google Scholar] [CrossRef] 
[5] Fan, J. and Li, R. (2001) Variable Selection via Noncon-cave Penalized Likelihood and Its Oracle Properties. Journal of the American Statistical Association, 96, 1348-1360. [Google Scholar] [CrossRef] 
[6] Zhang, C.-H. (2010) Nearly Unbiased Variable Selection under Minimax Concave Penalty. The Annals of Statistics, 38, 894-942. [Google Scholar] [CrossRef] 
[7] Zou, H. and Hastie, T. (2005) Regularization and Variable Selection via the Elastic Net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 301-320. [Google Scholar] [CrossRef] 
[8] Zou, H. (2006) The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association, 101, 1418-1429. [Google Scholar] [CrossRef] 
[9] Lim, C. and Yu, B. (2016) Estimation Stability with Cross-Validation (ESCV). Journal of Computational and Graphical Statistics, 25, 464-492. [Google Scholar] [CrossRef] 
[10] Wang, H., Li, R. and Tsai, C.L. (2007) Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method. Biometrika, 94, 553-568. [Google Scholar] [CrossRef] [PubMed]
[11] Akaike, H. (1977) On Entropy Maximization Principle. Application of Statistics, 543, 27-41.
[12] Wang, H. and Leng, C. (2007) Unified Lasso Estimation by Least Squares Approximation. Journal of the American Statistical Association, 102, 1039-1048. [Google Scholar] [CrossRef] 
[13] Wang, H., Li, B. and Leng, C. (2009) Shrinkage Tuning Pa-rameter Selection with a Diverging Number of Parameters. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71, 671-683. [Google Scholar] [CrossRef] 
[14] Chen, J. and Chen, Z. (2008) Extended Bayesian Infor-mation Criteria for Model Selection with Large Model Spaces. Biometrika, 95, 759-771. [Google Scholar] [CrossRef] 
[15] Wang, T. and Zhu, L. (2011) Consistent Tuning Parameter Selection in High Dimensional Sparse Linear Regression. Journal of Multivariate Analysis, 102, 1141-1151. [Google Scholar] [CrossRef] 
[16] Fan, Y. and Tang, C.Y. (2013) Tuning Parameter Selection in High Dimensional Penalized Likelihood. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75, 531-552. [Google Scholar] [CrossRef] 
[17] Hui, F.K., Warton, D.I. and Foster, S.D. (2015) Tuning Parame-ter Selection for the Adaptive Lasso Using ERIC. Journal of the American Statistical Association, 110, 262-269. [Google Scholar] [CrossRef] 
[18] Chichignoud, M., Johannes, L. and Wainwright, M. (2016) A Practical Scheme and Fast Algorithm to Tune the Lasso with Optimality Guarantees. Journal of Machine Learning Re-search, 17, 1-20.
[19] Li, W. and Lederer, J. (2019) Tuning Parameter Calibration in High-Dimensional Logistic Re-gression with Theoretical Guarantees. Journal of Statistical Planning and Inference, 202, 80-98. [Google Scholar] [CrossRef] 
[20] Wu, Y. and Wang, L. (2020) A Survey of Tuning Parameter Selec-tion for High-Dimensional Regression. Annual Review of Statistics and Its Application, 7, 209-226. [Google Scholar] [CrossRef] 
[21] Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004) Least Angle Regression. The Annals of Statistics, 32, 407-451. [Google Scholar] [CrossRef] 
[22] Zou, H., Hastie, T. and Tibshirani, R. (2007) On the “Degrees of Freedom” of the Lasso. The Annals of Statistics, 35, 2173-2192. [Google Scholar] [CrossRef] 
[23] Zhu, Y.Z. (2017) An Augmented ADMM Algorithm with Ap-plication to the Generalized Lasso Problem. Journal of Computational and Graphical Statistics, 26, 195-204. [Google Scholar] [CrossRef] 

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