Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation
文献类型：期刊论文
| 作者 | Chang, Xiangyu4; Zhong, Yan3; Lin SB(林绍波)1,2; Wang Y(王尧)2,4 |
| 刊名 | IEEE Transactions on Neural Networks and Learning Systems
 |
| 出版日期 | 2019 |
| 卷号 | 30期号:2页码:474-485 |
| 关键词 | Degrees of freedom low-rank matrix estimate multivariate linear regression multivariate quantile regression (QR) |
| ISSN号 | 2162-237X |
| 产权排序 | 3 |
| 英文摘要 | 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. |
| WOS关键词 | REGRESSION ; ALGORITHM ; DIMENSION |
| 资助项目 | 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] |
| WOS研究方向 | Computer Science ; Engineering |
| 语种 | 英语 |
| WOS记录号 | WOS:000457114600012 |
| 源URL | [http://119.78.100.139/handle/173321/22146]  |
| 专题 | 沈阳自动化研究所_机器人学研究室 |
| 通讯作者 | Wang Y(王尧) |
| 作者单位 | 1.Department of Mathematics, Wenzhou University, Wenzhou 325035, China110016, China 2.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China 3.Department of Statistics, Texas AM University, College Station, TX 77843 USA. 4.Center of Data Science and Information Quality, School of Management, Xi'an Jiaotong University, Xi'an 710049, China. |
| 推荐引用方式 GB/T 7714 | Chang, Xiangyu,Zhong, Yan,Lin SB,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,Lin SB,&Wang Y.(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. |
入库方式： OAI收割
来源：沈阳自动化研究所
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