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Jewel : A Novel Method for Joint Estimation of Gaussian Graphical Models

Author

Listed:
  • Claudia Angelini

    (Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR-Napoli, 80131 Naples, Italy)

  • Daniela De Canditiis

    (Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR-Roma, 00185 Rome, Italy)

  • Anna Plaksienko

    (Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR-Napoli, 80131 Naples, Italy
    Gran Sasso Science Institute, 67100 L’Aquila, Italy)

Abstract

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel , a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.

Suggested Citation

  • Claudia Angelini & Daniela De Canditiis & Anna Plaksienko, 2021. "Jewel : A Novel Method for Joint Estimation of Gaussian Graphical Models," Mathematics, MDPI, vol. 9(17), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2105-:d:626263
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    References listed on IDEAS

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    1. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    2. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    3. Shang, Yilun, 2016. "On the likelihood of forests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 157-166.
    4. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    5. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    6. Shan, Liang & Kim, Inyoung, 2018. "Joint estimation of multiple Gaussian graphical models across unbalanced classes," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 89-103.
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    1. Claudia Angelini & Daniela De Canditiis & Anna Plaksienko, 2022. "Jewel 2.0 : An Improved Joint Estimation Method for Multiple Gaussian Graphical Models," Mathematics, MDPI, vol. 10(21), pages 1-20, October.

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