IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i7d10.1007_s00362-024-01570-0.html
   My bibliography  Save this article

The statistical rate for support matrix machines under low rankness and row (column) sparsity

Author

Listed:
  • Ling Peng

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Xiaohui Liu

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Xiangyong Tan

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

  • Yiweng Zhou

    (Jiangxi University of Finance and Economics
    Wuhan University)

  • Shihua Luo

    (Jiangxi University of Finance and Economics
    Jiangxi University of Finance and Economics)

Abstract

This paper proposes a novel estimator for support vector machines with matrix-valued covariates in a high-dimensional setting. We assume that the underlying parameter matrix lies in a low-dimensional subspace that is simultaneously low-rank and row (column) sparse. We formulate the problem as a regularized hinge loss minimization problem using the nuclear and group lasso norms as penalties to exploit the low-dimensional structure. Our primary focus is deriving the statistical convergence rate of the regularized estimator for the unknown parameter matrix. To validate our theoretical findings, we conducted numerical experiments on both simulated and real-world datasets, demonstrating the efficacy of the regularized support matrix machines framework.

Suggested Citation

  • Ling Peng & Xiaohui Liu & Xiangyong Tan & Yiweng Zhou & Shihua Luo, 2024. "The statistical rate for support matrix machines under low rankness and row (column) sparsity," Statistical Papers, Springer, vol. 65(7), pages 4567-4598, September.
  • Handle: RePEc:spr:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01570-0
    DOI: 10.1007/s00362-024-01570-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-024-01570-0
    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/s00362-024-01570-0?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. Jianhui Chen & Jieping Ye, 2014. "Sparse trace norm regularization," Computational Statistics, Springer, vol. 29(3), pages 623-639, June.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Lin, Yi, 2004. "A note on margin-based loss functions in classification," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 73-82, June.
    4. Zhao, Junlong & Niu, Lu & Zhan, Shushi, 2017. "Trace regression model with simultaneously low rank and row(column) sparse parameter," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 1-18.
    5. Qiao, Xingye & Zhang, Hao Helen & Liu, Yufeng & Todd, Michael J. & Marron, J. S., 2010. "Weighted Distance Weighted Discrimination and Its Asymptotic Properties," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 401-414.
    6. Yiyuan She, 2017. "Selective factor extraction in high dimensions," Biometrika, Biometrika Trust, vol. 104(1), pages 97-110.
    7. Fan, Jianqing & Gong, Wenyan & Zhu, Ziwei, 2019. "Generalized high-dimensional trace regression via nuclear norm regularization," Journal of Econometrics, Elsevier, vol. 212(1), pages 177-202.
    8. Wang, Lifeng & Shen, Xiaotong, 2007. "On L1-Norm Multiclass Support Vector Machines: Methodology and Theory," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 583-594, June.
    9. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    10. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    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. Wan, Runzhe & Li, Yingying & Lu, Wenbin & Song, Rui, 2024. "Mining the factor zoo: Estimation of latent factor models with sufficient proxies," Journal of Econometrics, Elsevier, vol. 239(2).
    2. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    3. 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.
    4. Qianyun Li & Runmin Shi & Faming Liang, 2019. "Drug sensitivity prediction with high-dimensional mixture regression," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-18, February.
    5. Soave, David & Lawless, Jerald F., 2023. "Regularized regression for two phase failure time studies," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    6. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    7. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    8. Zichen Zhang & Ye Eun Bae & Jonathan R. Bradley & Lang Wu & Chong Wu, 2022. "SUMMIT: An integrative approach for better transcriptomic data imputation improves causal gene identification," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    9. 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.
    10. Bartosz Uniejewski, 2024. "Regularization for electricity price forecasting," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(3), pages 267-286.
    11. 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.
    12. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    13. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    14. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    15. Zeyu Bian & Erica E. M. Moodie & Susan M. Shortreed & Sahir Bhatnagar, 2023. "Variable selection in regression‐based estimation of dynamic treatment regimes," Biometrics, The International Biometric Society, vol. 79(2), pages 988-999, June.
    16. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    17. Ian W. McKeague & Min Qian, 2015. "An Adaptive Resampling Test for Detecting the Presence of Significant Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1422-1433, December.
    18. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    20. Yongjin Li & Qingzhao Zhang & Qihua Wang, 2017. "Penalized estimation equation for an extended single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 169-187, February.

    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:stpapr:v:65:y:2024:i:7:d:10.1007_s00362-024-01570-0. 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.