| Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation | |
| Chang, Xiangyu1; Zhong, Yan2; Wang Y(王尧)1,3; Lin SB(林绍波)3,4 | |
| Department | 机器人学研究室 |
| Source Publication | IEEE Transactions on Neural Networks and Learning Systems
 |
| ISSN | 2162-237X |
| 2019 | |
| Volume | 30Issue:2Pages:474-485 |
| Indexed By | SCI ; EI |
| EI Accession number | 20182705408718 |
| WOS ID | WOS:000457114600012 |
| Contribution Rank | 3 |
| Keyword | Degrees of freedom low-rank matrix estimate multivariate linear regression multivariate quantile regression (QR) |
| Abstract | 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. |
| Language | 英语 |
| WOS Subject | Computer Science, Artificial Intelligence ; Computer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic |
| WOS Keyword | REGRESSION ; ALGORITHM ; DIMENSION |
| WOS Research Area | Computer Science ; Engineering |
| Funding Project | Major Program of National Natural Science Foundation of China[71742005] ; Major Program of National Natural Science Foundation of China[71731009] ; National Natural Science Foundation of China[91546119] ; National Natural Science Foundation of China[61502342] ; National Natural Science Foundation of China[11771012] ; Key Research Program of Hunan Province, China[2017GK2273] ; China Postdoctoral Science Foundation[2017M610628] ; National Natural Science Foundation of China[11501440] ; National Natural Science Foundation of China[11501440] ; China Postdoctoral Science Foundation[2017M610628] ; Key Research Program of Hunan Province, China[2017GK2273] ; National Natural Science Foundation of China[11771012] ; 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] |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.sia.cn/handle/173321/22146 |
| Collection | 机器人学研究室 |
| Corresponding Author | Wang Y(王尧) |
| Affiliation | 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 |
| 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 SB.(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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| File Name/Size | DocType | Version | Access | License | ||
| Unified Low-Rank Mat（1882KB） | 期刊论文 | 作者接受稿 | 开放获取 | CC BY-NC-SA | View Download | |
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