IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v189y2021i3d10.1007_s10957-021-01852-9.html
   My bibliography  Save this article

Regularization Parameter Selection for the Low Rank Matrix Recovery

Author

Listed:
  • Pan Shang

    (Beijing Jiaotong University)

  • Lingchen Kong

    (Beijing Jiaotong University)

Abstract

A popular approach to recover low rank matrices is the nuclear norm regularized minimization (NRM) for which the selection of the regularization parameter is inevitable. In this paper, we build up a novel rule to choose the regularization parameter for NRM, with the help of the duality theory. Our result provides a safe set for the regularization parameter when the rank of the solution has an upper bound. Furthermore, we apply this idea to NRM with quadratic and Huber functions, and establish simple formulae for the regularization parameters. Finally, we report numerical results on some signal shapes by embedding our rule into the cross validation, which state that our rule can reduce the computational time for the selection of the regularization parameter. To the best of our knowledge, this is the first attempt to select the regularization parameter for the low rank matrix recovery.

Suggested Citation

  • Pan Shang & Lingchen Kong, 2021. "Regularization Parameter Selection for the Low Rank Matrix Recovery," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 772-792, June.
  • Handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01852-9
    DOI: 10.1007/s10957-021-01852-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01852-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-021-01852-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    2. Hua Zhou & Lexin Li, 2014. "Regularized matrix regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 463-483, March.
    3. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    4. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    2. Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    3. Han, Dongxiao & Huang, Jian & Lin, Yuanyuan & Shen, Guohao, 2022. "Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 230(2), pages 416-431.
    4. Goh, Gyuhyeong & Dey, Dipak K. & Chen, Kun, 2017. "Bayesian sparse reduced rank multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 14-28.
    5. Chen, Huangyue & Kong, Lingchen & Shang, Pan & Pan, Shanshan, 2020. "Safe feature screening rules for the regularized Huber regression," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Li, Mei & Kong, Lingchen, 2019. "Double fused Lasso penalized LAD for matrix regression," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 119-138.
    7. Joaquim Fernando Pinto da Costa & Manuel Cabral, 2022. "Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    8. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    9. Sauvenier, Mathieu & Van Bellegem, Sébastien, 2023. "Direction Identification and Minimax Estimation by Generalized Eigenvalue Problem in High Dimensional Sparse Regression," LIDAM Discussion Papers CORE 2023005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Ahmed Ismaïl & Hartikainen Anna-Liisa & Järvelin Marjo-Riitta & Richardson Sylvia, 2011. "False Discovery Rate Estimation for Stability Selection: Application to Genome-Wide Association Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-20, November.
    11. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    12. Shi Chen & Wolfgang Karl Hardle & Brenda L'opez Cabrera, 2020. "Regularization Approach for Network Modeling of German Power Derivative Market," Papers 2009.09739, arXiv.org.
    13. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    14. Laurent Ferrara & Anna Simoni, 2023. "When are Google Data Useful to Nowcast GDP? An Approach via Preselection and Shrinkage," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1188-1202, October.
    15. Caroline Jardet & Baptiste Meunier, 2022. "Nowcasting world GDP growth with high‐frequency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(6), pages 1181-1200, September.
    16. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    17. Sangjin Kim & Jong-Min Kim, 2019. "Two-Stage Classification with SIS Using a New Filter Ranking Method in High Throughput Data," Mathematics, MDPI, vol. 7(6), pages 1-16, May.
    18. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    19. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    20. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:189:y:2021:i:3:d:10.1007_s10957-021-01852-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.