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Robust sparse Gaussian graphical modeling

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  • Hirose, Kei
  • Fujisawa, Hironori
  • Sese, Jun

Abstract

Gaussian graphical modeling is popular as a means of exploring network structures, such as gene regulatory networks and social networks. An L1 penalized maximum likelihood approach is often used to learn high-dimensional graphical models. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the γ-divergence. The proposed method has a redescending property, which is a desirable feature in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies show that our procedure performs much better than the existing methods, in particular, when the contamination ratio is large. Two real data analyses are used for illustration purposes.

Suggested Citation

  • Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:172-190
    DOI: 10.1016/j.jmva.2017.07.012
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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. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    3. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    4. Fellinghauer, Bernd & Bühlmann, Peter & Ryffel, Martin & von Rhein, Michael & Reinhardt, Jan D., 2013. "Stable graphical model estimation with Random Forests for discrete, continuous, and mixed variables," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 132-152.
    5. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    6. 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.
    7. Hokeun Sun & Hongzhe Li, 2012. "Robust Gaussian Graphical Modeling Via l 1 Penalization," Biometrics, The International Biometric Society, vol. 68(4), pages 1197-1206, December.
    8. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
    9. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    10. Jeremiah J Faith & Boris Hayete & Joshua T Thaden & Ilaria Mogno & Jamey Wierzbowski & Guillaume Cottarel & Simon Kasif & James J Collins & Timothy S Gardner, 2007. "Large-Scale Mapping and Validation of Escherichia coli Transcriptional Regulation from a Compendium of Expression Profiles," PLOS Biology, Public Library of Science, vol. 5(1), pages 1-13, January.
    11. Arend Voorman & Ali Shojaie & Daniela Witten, 2014. "Graph estimation with joint additive models," Biometrika, Biometrika Trust, vol. 101(1), pages 85-101.
    12. Vinciotti, Veronica & Hashem, Hussein, 2013. "Robust methods for inferring sparse network structures," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 84-94.
    13. Miyamura, Masashi & Kano, Yutaka, 2006. "Robust Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1525-1550, August.
    14. Takafumi Kanamori & Hironori Fujisawa, 2015. "Robust estimation under heavy contamination using unnormalized models," Biometrika, Biometrika Trust, vol. 102(3), pages 559-572.
    15. 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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