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

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  • 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
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    Citations

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    Cited by:

    1. 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).
    2. 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.
    3. 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).
    4. 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.
    5. Wei Dong & Hongzhen Liu, 2024. "Distributed Sparse Precision Matrix Estimation via Alternating Block-Based Gradient Descent," Mathematics, MDPI, vol. 12(5), pages 1-15, February.

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