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Influence measures and stability for graphical models

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  • Bar-Hen, Avner
  • Poggi, Jean-Michel

Abstract

Graphical models allow to represent a set of random variables together with their probabilistic conditional dependencies. Various algorithms have been proposed to estimate such models from data. The focus of this paper is on individual observations diagnosis issues. The use of an influence measure is a classical diagnostic method to measure the perturbation induced by a single element, in other terms we consider stability issue through jackknife. For a given graphical model, we provide tools to perform diagnosis on observations. In a second step we propose a filtering of the dataset to obtain a stable network. All along the paper an application to a gene expression dataset illustrates the proposals.

Suggested Citation

  • Bar-Hen, Avner & Poggi, Jean-Michel, 2016. "Influence measures and stability for graphical models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 145-154.
    • Handle: RePEc:eee:jmvana:v:147:y:2016:i:c:p:145-154
    DOI: 10.1016/j.jmva.2016.01.006
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    References listed on IDEAS

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    1. 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.
    2. Croux, Christophe, 1998. "Limit behavior of the empirical influence function of the median," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 331-340, March.
    3. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
    4. D. Vogel & D. E. Tyler, 2014. "Robust estimators for nondecomposable elliptical graphical models," Biometrika, Biometrika Trust, vol. 101(4), pages 865-882.
    5. Giraud Christophe & Huet Sylvie & Verzelen Nicolas, 2012. "Graph Selection with GGMselect," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-52, February.
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