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A joint convex penalty for inverse covariance matrix estimation

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  • Maurya, Ashwini

Abstract

The paper proposes a joint convex penalty for estimating the Gaussian inverse covariance matrix. A proximal gradient method is developed to solve the resulting optimization problem with more than one penalty constraints. The analysis shows that imposing a single constraint is not enough and the estimator can be improved by a trade-off between two convex penalties. The developed framework can be extended to solve wide arrays of constrained convex optimization problems. A simulation study is carried out to compare the performance of the proposed method to graphical lasso and the SPICE estimate of the inverse covariance matrix.

Suggested Citation

  • Maurya, Ashwini, 2014. "A joint convex penalty for inverse covariance matrix estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 15-27.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:15-27
    DOI: 10.1016/j.csda.2014.01.015
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    References listed on IDEAS

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    1. Sheena Yo & Gupta Arjun K., 2003. "Estimation of the multivariate normal covariance matrix under some restrictions," Statistics & Risk Modeling, De Gruyter, vol. 21(4), pages 327-342, April.
    2. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
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    2. Avagyan, Vahe & 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.
    3. Cui, Ying & Leng, Chenlei & Sun, Defeng, 2016. "Sparse estimation of high-dimensional correlation matrices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 390-403.
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    5. Vahe Avagyan & Andrés M. Alonso & Francisco J. Nogales, 2018. "D-trace estimation of a precision matrix using adaptive Lasso penalties," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 425-447, June.

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