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Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression
Li, Xin1; Hu, Yaohua2; Li, Chong3; Yang, Xiaoqi4; Jiang, Tianzi5
Source PublicationJOURNAL OF GLOBAL OPTIMIZATION
ISSN0925-5001
2022-09-06
Pages35
Corresponding AuthorHu, Yaohua(mayhhu@szu.edu.cn)
AbstractThe lower-order penalty optimization methods, including the l(q) minimization method and the l(q) regularization method (0 < q <= 1), have been widely applied to find sparse solutions of linear regression problems and gained successful applications in various mathematics and applied science fields. In this paper, we aim to investigate statistical properties of the l(q) penalty optimization methods with randomly noisy observations and a deterministic/random design. For this purpose, we introduce a general q-Restricted Eigenvalue Condition (REC) and provide its sufficient conditions in terms of several widely-used regularity conditions such as sparse eigenvalue condition, restricted isometry property, and mutual incoherence property. By virtue of the q-REC, we exhibit the l(2) recovery bounds of order O( epsilon(2)) and O(lambda 2/2-q s) for the l(q) minimization method and the l(q) regularization method, respectively, with high probability for either deterministic or random designs. The results in this paper are nonasymptotic and only assume the weak q-REC. The preliminary numerical results verify the established statistical properties and demonstrate the advantages of the l(q) penalty optimization methods over existing sparse optimization methods.
KeywordSparse optimization Lower-order penalty methods Restricted eigenvalue condition Recovery bound
DOI10.1007/s10898-022-01220-5
WOS KeywordUNCERTAINTY PRINCIPLES ; LAGRANGIAN APPROACH ; VARIABLE SELECTION ; ALGORITHMIC THEORY ; SIGNAL RECOVERY ; RECONSTRUCTION ; REGULARIZATION ; LASSO ; MINIMIZATION ; LIKELIHOOD
Indexed BySCI
Language英语
Funding ProjectNatural Science Foundation of Shaanxi Province of China[2022JQ-045] ; National Natural Science Foundation of China[11971429] ; National Natural Science Foundation of China[12071306] ; National Natural Science Foundation of China[32170655] ; National Natural Science Foundation of China[11871347] ; Natural Science Foundation of Guangdong Province of China[2019A1515011917] ; Natural Science Foundation of Guangdong Province of China[2020B1515310008] ; Project of Educational Commission of Guangdong Province of China[2021KTSCX103] ; Project of Educational Commission of Guangdong Province of China[2019KZDZX1007] ; Natural Science Foundation of Shenzhen[JCYJ20190808173603590] ; Zhejiang Provincial Natural Science Foundation of China[LY18A010004] ; Research Grants Council of Hong Kong[PolyU 15212817] ; Science and Technology Innovation 2030 - Brain Science and Brain-Inspired Intelligence Project of China[2021ZD0200200]
Funding OrganizationNatural Science Foundation of Shaanxi Province of China ; National Natural Science Foundation of China ; Natural Science Foundation of Guangdong Province of China ; Project of Educational Commission of Guangdong Province of China ; Natural Science Foundation of Shenzhen ; Zhejiang Provincial Natural Science Foundation of China ; Research Grants Council of Hong Kong ; Science and Technology Innovation 2030 - Brain Science and Brain-Inspired Intelligence Project of China
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000849996100001
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/50036
Collection脑网络组研究
Corresponding AuthorHu, Yaohua
Affiliation1.Northwest Univ, Sch Math, Xian 710069, Peoples R China
2.Shenzhen Univ, Guangdong Key Lab Intelligent Informat Proc, Coll Math & Stat, Shenzhen Key Lab Adv Machine Learning & Applicat, Shenzhen 518060, Peoples R China
3.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China
4.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
5.Chinese Acad Sci, Inst Automat, Brainnetome Ctr, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Li, Xin,Hu, Yaohua,Li, Chong,et al. Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression[J]. JOURNAL OF GLOBAL OPTIMIZATION,2022:35.
APA Li, Xin,Hu, Yaohua,Li, Chong,Yang, Xiaoqi,&Jiang, Tianzi.(2022).Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression.JOURNAL OF GLOBAL OPTIMIZATION,35.
MLA Li, Xin,et al."Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression".JOURNAL OF GLOBAL OPTIMIZATION (2022):35.
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