IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v142y2020ics0167947319301574.html
   My bibliography  Save this article

An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss

Author

Listed:
  • Wang, Cheng
  • Jiang, Binyan

Abstract

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension p, many state-of-the-art methods do not scale well to solve problems with a very large p. In this paper, we propose a very efficient algorithm for precision matrix estimation via penalized quadratic loss functions. Under the high dimension low sample size setting, the computation complexity of our algorithm is linear in both the sample size and the number of parameters. Such a computation complexity is in some sense optimal, as it is the same as the complexity needed for computing the sample covariance matrix. Numerical studies show that our algorithm is much more efficient than other state-of-the-art methods when the dimension p is very large.

Suggested Citation

  • Wang, Cheng & Jiang, Binyan, 2020. "An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301574
    DOI: 10.1016/j.csda.2019.106812
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319301574
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.106812?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pun, Chi Seng & Hadimaja, Matthew Zakharia, 2021. "A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    2. Vahe Avagyan, 2022. "Precision matrix estimation using penalized Generalized Sylvester matrix equation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 950-967, December.
    3. Le, Khuyen T. & Chaux, Caroline & Richard, Frédéric J.P. & Guedj, Eric, 2020. "An adapted linear discriminant analysis with variable selection for the classification in high-dimension, and an application to medical data," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    4. 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.

    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:eee:csdana:v:142:y:2020:i:c:s0167947319301574. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.