IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i1d10.1007_s00180-022-01224-5.html
   My bibliography  Save this article

An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso

Author

Listed:
  • Seunghwan Lee

    (Inha University)

  • Sang Cheol Kim

    (Korea Centers for Disease Control and Prevention)

  • Donghyeon Yu

    (Inha University)

Abstract

The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many methods have been proposed, and their theoretical properties are given as well. Among these, the sparse precision matrix estimation via scaled lasso (SPMESL) has an attractive feature in which the penalty level is automatically set to achieve the optimal convergence rate under the sparsity and invertibility conditions. Conversely, other methods need to be used in searching for the optimal tuning parameter. Despite such an advantage, the SPMESL has not been widely used due to its expensive computational cost. In this paper, we develop a GPU-parallel coordinate descent (CD) algorithm for the SPMESL and numerically show that the proposed algorithm is much faster than the least angle regression (LARS) tailored to the SPMESL. Several comprehensive numerical studies are conducted to investigate the scalability of the proposed algorithm and the estimation performance of the SPMESL. The results show that the SPMESL has the lowest false discovery rate for all cases and the best performance in the case where the level of the sparsity of the columns is high.

Suggested Citation

  • Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01224-5
    DOI: 10.1007/s00180-022-01224-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01224-5
    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/s00180-022-01224-5?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. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Kshitij Khare & Sang-Yun Oh & Bala Rajaratnam, 2015. "A convex pseudolikelihood framework for high dimensional partial correlation estimation with convergence guarantees," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 803-825, September.
    3. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    4. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    5. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    6. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    7. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    8. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    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. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    2. Sung, Bongjung & Lee, Jaeyong, 2023. "Covariance structure estimation with Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    3. Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
    4. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    5. Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    6. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.
    7. Chen, Shuo & Kang, Jian & Xing, Yishi & Zhao, Yunpeng & Milton, Donald K., 2018. "Estimating large covariance matrix with network topology for high-dimensional biomedical data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 82-95.
    8. Fan, Xinyan & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2021. "Conditional score matching for high-dimensional partial graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    9. Young-Geun Choi & Seunghwan Lee & Donghyeon Yu, 2022. "An efficient parallel block coordinate descent algorithm for large-scale precision matrix estimation using graphics processing units," Computational Statistics, Springer, vol. 37(1), pages 419-443, March.
    10. Choi, Young-Geun & Lim, Johan & Roy, Anindya & Park, Junyong, 2019. "Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 234-249.
    11. Avagyan, Vahe & Alonso Fernández, Andrés Modesto & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Bar, Haim & Wells, Martin T., 2023. "On graphical models and convex geometry," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    13. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    14. Huang, Na & Fryzlewicz, Piotr, 2018. "NOVELIST estimator of large correlation and covariance matrices and their inverses," LSE Research Online Documents on Economics 89055, London School of Economics and Political Science, LSE Library.
    15. Arnab Chakrabarti & Rituparna Sen, 2018. "Some Statistical Problems with High Dimensional Financial data," Papers 1808.02953, arXiv.org.
    16. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.
    17. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.
    18. Pan, Yuqing & Mai, Qing, 2020. "Efficient computation for differential network analysis with applications to quadratic discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    19. Ikeda, Yuki & Kubokawa, Tatsuya & Srivastava, Muni S., 2016. "Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 95-108.
    20. Ziqi Chen & Chenlei Leng, 2016. "Dynamic Covariance Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1196-1207, July.

    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:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01224-5. 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.