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Joint estimation of multiple Gaussian graphical models across unbalanced classes

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  • Shan, Liang
  • Kim, Inyoung

Abstract

The problem of jointly estimating unbalanced multi-class Gaussian graphical models is considered. Most existing methods require equal or similar sample sizes among classes. However, many real applications do not have similar sample sizes. Hence, the joint adaptive graphical lasso, a weighted l1 penalized approach is proposed for unbalanced multi-class problems. The joint adaptive graphical lasso approach combines information across classes so that their common characteristics can be shared during the estimation process. Regularization is also introduced into the adaptive term. Simulation studies show that the new approach performs better than existing methods in terms of false positive rate, accuracy, Mathews correlation coefficient, and false discovery rate. The advantages of the new approach are also demonstrated using a liver cancer data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:89-103
    DOI: 10.1016/j.csda.2017.11.009
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    3. 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.
    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. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Yan Zhou & Peter X.-K. Song, 2016. "Regression analysis of networked data," Biometrika, Biometrika Trust, vol. 103(2), pages 287-301.
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    Cited by:

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    2. 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.

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