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High-dimensional grouped folded concave penalized estimation via the LLA algorithm
Guo X(郭骁)1; Wang Y(王尧)2,3; Zhang H(张海)1,4
Department机器人学研究室
Source PublicationJournal of the Korean Statistical Society
2019
Volume48Issue:1Pages:84-96
Indexed BySCI
WOS IDWOS:000460719100007
Contribution Rank2
Funding OrganizationNational Natural Science Foundation of China ; China Postdoctoral Science Foundation ; Key Research Program of Hunan Province, China
KeywordGrouped variable selection High-dimensional linear models Folded concave penalty Local linear approximation Oracle estimator
AbstractThe group folded concave penalization problems have been shown to process the satisfactory oracle property theoretically. However, it remains unknown whether the optimization algorithm for solving the resulting nonconvex problem can find such oracle solution among multiple local solutions. In this paper, we extend the well-known local linear approximation (LLA) algorithm to solve the group folded concave penalization problem for the linear models. We prove that, with the group LASSO estimator as the initial value, the two-step LLA solution converges to the oracle estimator with overwhelming probability, and thus closing the theoretical gap. The results are high-dimensional which allow the group number to grow exponentially, the true relevant groups and the true maximum group size to grow polynomially. Numerical studies are also conducted to show the merits of the LLA procedure.
Language英语
WOS SubjectStatistics & Probability
WOS KeywordGROUP SELECTION ; REGRESSION ; LIKELIHOOD ; LASSO
WOS Research AreaMathematics
Funding ProjectKey Research Program of Hunan Province, China[2017GK2273] ; China Postdoctoral Science Foundation[2018T111031] ; China Postdoctoral Science Foundation[2017M610628] ; National Natural Science Foundation of China[11571011] ; National Natural Science Foundation of China[11571011] ; China Postdoctoral Science Foundation[2017M610628] ; China Postdoctoral Science Foundation[2018T111031] ; Key Research Program of Hunan Province, China[2017GK2273]
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Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/24153
Collection机器人学研究室
Corresponding AuthorZhang H(张海)
Affiliation1.School of Mathematics, Northwest University, Xi’an, 710069, China
2.School of Management, Xi’an Jiaotong University, Xi’an 710049, China
3.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Science, Shenyang 110016, China
4.Faculty of Information Technology, Macau University of Science and Technology, Macau, China
Recommended Citation
GB/T 7714
Guo X,Wang Y,Zhang H. High-dimensional grouped folded concave penalized estimation via the LLA algorithm[J]. Journal of the Korean Statistical Society,2019,48(1):84-96.
APA Guo X,Wang Y,&Zhang H.(2019).High-dimensional grouped folded concave penalized estimation via the LLA algorithm.Journal of the Korean Statistical Society,48(1),84-96.
MLA Guo X,et al."High-dimensional grouped folded concave penalized estimation via the LLA algorithm".Journal of the Korean Statistical Society 48.1(2019):84-96.
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