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Fast and adaptive sparse precision matrix estimation in high dimensions

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  • Liu, Weidong
  • Luo, Xi

Abstract

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.

Suggested Citation

  • Liu, Weidong & Luo, Xi, 2015. "Fast and adaptive sparse precision matrix estimation in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 153-162.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:153-162
    DOI: 10.1016/j.jmva.2014.11.005
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    References listed on IDEAS

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    5. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    6. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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    Cited by:

    1. Zheng, Zemin & Li, Liwan & Zhou, Jia & Kong, Yinfei, 2020. "Innovated scalable dynamic learning for time-varying graphical models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. Yang, Yihe & Dai, Hongsheng & Pan, Jianxin, 2023. "Block-diagonal precision matrix regularization for ultra-high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    3. 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.
    4. 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.
    5. 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.
    6. Dong, Wei & Xu, Chen & Xie, Jinhan & Tang, Niansheng, 2024. "Tuning-free sparse clustering via alternating hard-thresholding," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    7. Qin, Xing & Hu, Jianhua & Ma, Shuangge & Wu, Mengyun, 2024. "Estimation of multiple networks with common structures in heterogeneous subgroups," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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