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Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation
Chang, Xiangyu1; Zhong, Yan2; Wang Y(王尧)1,3; Lin, Shaobo3,4
Department机器人学研究室
Source PublicationIEEE Transactions on Neural Networks and Learning Systems
ISSN2162-237X
2019
Volume30Issue:2Pages:474-485
Indexed BySCI ; EI
EI Accession number20182705408718
WOS IDWOS:000457114600012
Contribution Rank3
Funding OrganizationNational Natural Science Foundation of China ; Major Program of National Natural Science Foundation of China ; China Postdoctoral Science Foundation ; Key Research Program of Hunan Province, China
KeywordDegrees of freedom low-rank matrix estimate multivariate linear regression multivariate quantile regression (QR)
AbstractLow-rank matrix estimation arises in a number of statistical and machine learning tasks. In particular, the coefficient matrix is considered to have a low-rank structure in multivariate linear regression and multivariate quantile regression. In this paper, we propose a method called penalized matrix least squares approximation (PMLSA) toward a unified yet simple low-rank matrix estimate. Specifically, PMLSA can transform many different types of low-rank matrix estimation problems into their asymptotically equivalent least-squares forms, which can be efficiently solved by a popular matrix fast iterative shrinkage-thresholding algorithm. Furthermore, we derive analytic degrees of freedom for PMLSA, with which a Bayesian information criterion (BIC)-type criterion is developed to select the tuning parameters. The estimated rank based on the BIC-type criterion is verified to be asymptotically consistent with the true rank under mild conditions. Extensive experimental studies are performed to confirm our assertion.
Language英语
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic
WOS KeywordREGRESSION ; ALGORITHM ; DIMENSION
WOS Research AreaComputer Science ; Engineering
Funding ProjectNational Natural Science Foundation of China[11771012] ; National Natural Science Foundation of China[11501440] ; National Natural Science Foundation of China[61502342] ; National Natural Science Foundation of China[91546119] ; Major Program of National Natural Science Foundation of China[71731009] ; Major Program of National Natural Science Foundation of China[71742005] ; China Postdoctoral Science Foundation[2017M610628] ; Key Research Program of Hunan Province, China[2017GK2273]
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Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.sia.cn/handle/173321/22146
Collection机器人学研究室
Corresponding AuthorWang Y(王尧)
Affiliation1.Center of Data Science and Information Quality, School of Management, Xi'an Jiaotong University, Xi'an 710049, China.
2.Department of Statistics, Texas AM University, College Station, TX 77843 USA.
3.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
4.Department of Mathematics, Wenzhou University, Wenzhou 325035, China110016, China
Recommended Citation
GB/T 7714
Chang, Xiangyu,Zhong, Yan,Wang Y,et al. Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation[J]. IEEE Transactions on Neural Networks and Learning Systems,2019,30(2):474-485.
APA Chang, Xiangyu,Zhong, Yan,Wang Y,&Lin, Shaobo.(2019).Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation.IEEE Transactions on Neural Networks and Learning Systems,30(2),474-485.
MLA Chang, Xiangyu,et al."Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation".IEEE Transactions on Neural Networks and Learning Systems 30.2(2019):474-485.
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