IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i3d10.1007_s10957-025-02660-1.html
   My bibliography  Save this article

Low-Rank Matrix Recovery Via Nonconvex Optimization Methods with Application to Errors-in-Variables Matrix Regression

Author

Listed:
  • Xin Li

    (Northwest University)

  • Dongya Wu

    (Northwest University)

Abstract

We consider the nonconvex regularized method for low-rank matrix recovery problems. Under suitable regularity conditions on the nonconvex loss function and the regularizer, we provide the recovery bound for any stationary point of the nonconvex method via separating singular values of the parameter matrix into larger and smaller ones. In this way, the established recovery bound can be much tighter than that of the convex nuclear norm regularized method when some of the singular values are larger than a threshold defined by the nonconvex regularizer. In addition, we consider the errors-in-variables matrix regression as an application of the nonconvex method. Probabilistic consequences and the advantage of the nonconvex method are demonstrated through verifying the regularity conditions for specific models with additive noise and missing data.

Suggested Citation

  • Xin Li & Dongya Wu, 2025. "Low-Rank Matrix Recovery Via Nonconvex Optimization Methods with Application to Errors-in-Variables Matrix Regression," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-27, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02660-1
    DOI: 10.1007/s10957-025-02660-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02660-1
    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/s10957-025-02660-1?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Wu, Jie & Zheng, Zemin & Li, Yang & Zhang, Yi, 2020. "Scalable interpretable learning for multi-response error-in-variables regression," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Radu-Alexandru Dragomir & Alexandre d’Aspremont & Jérôme Bolte, 2021. "Quartic First-Order Methods for Low-Rank Minimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 341-363, May.
    3. Xin Li & Dongya Wu, 2024. "Low-rank matrix estimation via nonconvex optimization methods in multi-response errors-in-variables regression," Journal of Global Optimization, Springer, vol. 88(1), pages 79-114, January.
    4. Shuvomoy Das Gupta & Bartolomeo Stellato & Bart P. G. Parys, 2024. "Exterior-Point Optimization for Sparse and Low-Rank Optimization," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 795-833, August.
    5. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    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. Xin Li & Dongya Wu, 2024. "Low-rank matrix estimation via nonconvex optimization methods in multi-response errors-in-variables regression," Journal of Global Optimization, Springer, vol. 88(1), pages 79-114, January.
    2. Li, Xin & Wu, Dongya, 2025. "Low-rank matrix estimation via nonconvex spectral regularized methods in errors-in-variables matrix regression," European Journal of Operational Research, Elsevier, vol. 323(2), pages 626-641.
    3. Hayato Maki & Sakriani Sakti & Hiroki Tanaka & Satoshi Nakamura, 2018. "Quality prediction of synthesized speech based on tensor structured EEG signals," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-13, June.
    4. Chelsey Hill & James Li & Matthew J. Schneider & Martin T. Wells, 2021. "The tensor auto‐regressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 636-652, July.
    5. Lan Liu & Wei Li & Zhihua Su & Dennis Cook & Luca Vizioli & Essa Yacoub, 2022. "Efficient estimation via envelope chain in magnetic resonance imaging‐based studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 481-501, June.
    6. Feiyang Han & Yimin Wei & Pengpeng Xie, 2024. "Regularized and Structured Tensor Total Least Squares Methods with Applications," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1101-1136, September.
    7. Kenneth W. Latimer & David J. Freedman, 2023. "Low-dimensional encoding of decisions in parietal cortex reflects long-term training history," Nature Communications, Nature, vol. 14(1), pages 1-24, December.
    8. Daniel Spencer & Rajarshi Guhaniyogi & Raquel Prado, 2020. "Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 845-869, December.
    9. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    10. Bo Wei & Limin Peng & Ying Guo & Amita Manatunga & Jennifer Stevens, 2023. "Tensor response quantile regression with neuroimaging data," Biometrics, The International Biometric Society, vol. 79(3), pages 1947-1958, September.
    11. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
    12. Vivek F. Farias & Andrew A. L, 2019. "Learning Preferences with Side Information," Management Science, INFORMS, vol. 65(7), pages 3131-3149, July.
    13. Mai Ghannam & Sévérien Nkurunziza, 2024. "Change-point detection in a tensor regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 609-630, June.
    14. Okano, Ryo & Imaizumi, Masaaki, 2024. "Distribution-on-distribution regression with Wasserstein metric: Multivariate Gaussian case," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    15. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    16. Andrea Bucci, 2025. "A Smooth Transition Autoregressive Model for Matrix-Variate Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 65(1), pages 429-458, January.
    17. Guhaniyogi, Rajarshi, 2017. "Convergence rate of Bayesian supervised tensor modeling with multiway shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 157-168.
    18. Sorin-Mihai Grad & Felipe Lara & Raúl T. Marcavillaca, 2025. "Strongly Quasiconvex Functions: What We Know (So Far)," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-41, May.
    19. Chen, Rong & Xiao, Han & Yang, Dan, 2021. "Autoregressive models for matrix-valued time series," Journal of Econometrics, Elsevier, vol. 222(1), pages 539-560.
    20. Rungang Han & Yuetian Luo & Miaoyan Wang & Anru R. Zhang, 2022. "Exact clustering in tensor block model: Statistical optimality and computational limit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1666-1698, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:205:y:2025:i:3:d:10.1007_s10957-025-02660-1. 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.