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

doi:10.1007/s10898-022-01220-5

	Sparse estimation via lower-order penalty optimization methods in high-dimensional linear regression
	Li, Xin 1; Hu, Yaohua 2; Li, Chong3 ; Yang, Xiaoqi 4; Jiang, Tianzi5
发表期刊	JOURNAL OF GLOBAL OPTIMIZATION
ISSN	0925-5001
	2022-09-06
页码	35
通讯作者	Hu, Yaohua(mayhhu@szu.edu.cn)
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.
关键词	Sparse optimization Lower-order penalty methods Restricted eigenvalue condition Recovery bound
DOI	10.1007/s10898-022-01220-5
关键词[WOS]	UNCERTAINTY PRINCIPLES ; LAGRANGIAN APPROACH ; VARIABLE SELECTION ; ALGORITHMIC THEORY ; SIGNAL RECOVERY ; RECONSTRUCTION ; REGULARIZATION ; LASSO ; MINIMIZATION ; LIKELIHOOD
收录类别	SCI
语种	英语
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]
项目资助者	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
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000849996100001
出版者	SPRINGER
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/50036
专题	脑图谱与类脑智能实验室_脑网络组研究
通讯作者	Hu, Yaohua
作者单位	1.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
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.