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Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression

文献类型：期刊论文

作者Li, Xin1; Hu, Yaohua5; Li, Chong4; Yang, Xiaoqi3; Jiang, Tianzi2
刊名JOURNAL OF GLOBAL OPTIMIZATION
出版日期2022-09-06
页码35
关键词Sparse optimization Lower-order penalty methods Restricted eigenvalue condition Recovery bound
ISSN号0925-5001
DOI10.1007/s10898-022-01220-5
通讯作者Hu, Yaohua(mayhhu@szu.edu.cn)
英文摘要The 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.
WOS关键词UNCERTAINTY PRINCIPLES ; LAGRANGIAN APPROACH ; VARIABLE SELECTION ; ALGORITHMIC THEORY ; SIGNAL RECOVERY ; RECONSTRUCTION ; REGULARIZATION ; LASSO ; MINIMIZATION ; LIKELIHOOD
资助项目Natural 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]
WOS研究方向Operations Research & Management Science ; Mathematics
语种英语
WOS记录号WOS:000849996100001
出版者SPRINGER
资助机构Natural 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
源URL[http://ir.ia.ac.cn/handle/173211/50035]  
专题自动化研究所_脑网络组研究中心
通讯作者Hu, Yaohua
作者单位1.Northwest Univ, Sch Math, Xian 710069, Peoples R China
2.Chinese Acad Sci, Inst Automat, Brainnetome Ctr, Beijing 100190, Peoples R China
3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
4.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China
5.Shenzhen Univ, Guangdong Key Lab Intelligent Informat Proc, Coll Math & Stat, Shenzhen Key Lab Adv Machine Learning & Applicat, Shenzhen 518060, Peoples R China
推荐引用方式
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.

入库方式： OAI收割

来源：自动化研究所

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