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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
作者部门机器人学研究室
关键词Degrees of freedom low-rank matrix estimate multivariate linear regression multivariate quantile regression (QR)
发表期刊IEEE Transactions on Neural Networks and Learning Systems
ISSN2162-237X
2018
页码1-12
收录类别EI
EI收录号20182705408718
产权排序3
资助机构National Natural Science Foundation of China under Grant 11771012, Grant 11501440, Grant 61502342, and Grant 91546119, in part by the Major Program of National Natural Science Foundation of China under Project 71731009 and Project 71742005, in part by the China Postdoctoral Science Foundation under Grant 2017M610628, and in part by the Key Research Program of Hunan Province, China under Grant 2017GK2273
摘要Low-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.
语种英语
文献类型期刊论文
条目标识符http://ir.sia.cn/handle/173321/22146
专题机器人学研究室
通讯作者Wang Y(王尧)
作者单位1.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
推荐引用方式
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,2018:1-12.
APA Chang, Xiangyu,Zhong, Yan,Wang Y,&Lin, Shaobo.(2018).Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation.IEEE Transactions on Neural Networks and Learning Systems,1-12.
MLA Chang, Xiangyu,et al."Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation".IEEE Transactions on Neural Networks and Learning Systems (2018):1-12.
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