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Volume 39, Issue 5
A Greedy Algorithm for Sparse Precision Matrix Approximation

Didi Lv & Xiaoqun Zhang

DOI: 10.4208/jcm.2005-m2019-0151

J. Comp. Math., 39 (2021), pp. 693-707.

Published online: 2021-09

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  • Abstract

Precision matrix estimation is an important problem in statistical data analysis. This paper proposes a sparse precision matrix estimation approach, based on CLIME estimator and an efficient algorithm GISS$^{{\rho}}$ that was originally proposed for $l_1$ sparse signal recovery in compressed sensing. The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISS$^{{\rho}}$ algorithm. Finally, numerical comparison of GISS$^{\rho}$ with other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.

  • Keywords

Precision matrix estimation, CLIME estimator, Sparse recovery, Inverse scale space method, Greedy methods.

  • AMS Subject Headings

49J52, 65K05, 62H12.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Eric2014_Lv@sjtu.edu.cn (Didi Lv)

xqzhang@sjtu.edu.cn (Xiaoqun Zhang)

  • BibTex
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  • TXT
@Article{JCM-39-693, author = {Lv , Didi and Zhang , Xiaoqun}, title = {A Greedy Algorithm for Sparse Precision Matrix Approximation}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {5}, pages = {693--707}, abstract = {

Precision matrix estimation is an important problem in statistical data analysis. This paper proposes a sparse precision matrix estimation approach, based on CLIME estimator and an efficient algorithm GISS$^{{\rho}}$ that was originally proposed for $l_1$ sparse signal recovery in compressed sensing. The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISS$^{{\rho}}$ algorithm. Finally, numerical comparison of GISS$^{\rho}$ with other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2005-m2019-0151}, url = {http://global-sci.org/intro/article_detail/jcm/19520.html} }
TY - JOUR T1 - A Greedy Algorithm for Sparse Precision Matrix Approximation AU - Lv , Didi AU - Zhang , Xiaoqun JO - Journal of Computational Mathematics VL - 5 SP - 693 EP - 707 PY - 2021 DA - 2021/09 SN - 39 DO - http://doi.org/10.4208/jcm.2005-m2019-0151 UR - https://global-sci.org/intro/article_detail/jcm/19520.html KW - Precision matrix estimation, CLIME estimator, Sparse recovery, Inverse scale space method, Greedy methods. AB -

Precision matrix estimation is an important problem in statistical data analysis. This paper proposes a sparse precision matrix estimation approach, based on CLIME estimator and an efficient algorithm GISS$^{{\rho}}$ that was originally proposed for $l_1$ sparse signal recovery in compressed sensing. The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISS$^{{\rho}}$ algorithm. Finally, numerical comparison of GISS$^{\rho}$ with other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.

Didi Lv & Xiaoqun Zhang. (2021). A Greedy Algorithm for Sparse Precision Matrix Approximation. Journal of Computational Mathematics. 39 (5). 693-707. doi:10.4208/jcm.2005-m2019-0151
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