Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation

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	Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation
	Wang Y(王尧)1,3; Chang, Xiangyu 1; Zhong, Yan 4; Lin, Shaobo 2,3; Sun P(孙鹏); Wang HG(王洪光); Pan XA(潘新安); Hu MW(胡明伟); Ling L(凌烈); Jing FR(景凤仁)
刊名	IEEE Transactions on Neural Networks and Learning Systems
	2018
页码	1-12
关键词	Degrees of freedom low-rank matrix estimate multivariate linear regression multivariate quantile regression (QR)
ISSN号	2162-237X
通讯作者	Wang Y(王尧)
产权排序	3
中文摘要	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.
收录类别	EI
语种	英语
内容类型	期刊论文
源URL	[http://ir.sia.cn/handle/173321/22204]
专题	沈阳自动化研究所_空间自动化技术研究室
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 Mathematics, Wenzhou University, Wenzhou 325035, China110016, China 3.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China 4.Department of Statistics, Texas AM University, College Station, TX 77843 USA.
推荐引用方式 GB/T 7714	Wang Y,Chang, Xiangyu,Zhong, Yan,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	Wang Y.,Chang, Xiangyu.,Zhong, Yan.,Lin, Shaobo.,孙鹏.,...&田勇.(2018).Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation.IEEE Transactions on Neural Networks and Learning Systems,1-12.
MLA	Wang Y,et al."Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation".IEEE Transactions on Neural Networks and Learning Systems (2018):1-12.