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Searching for a source of difference in graphical models

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  • Djordjilović, Vera
  • Chiogna, Monica

Abstract

We look at a two-sample problem within the framework of decomposable graphical models. When the global hypothesis of equality of two distributions is rejected, the interest is usually in localizing the source of difference. Motivated by the idea that diseases can be seen as system perturbations, and by the need to distinguish between the origin of perturbation and components affected by the perturbation, we introduce the concept of a minimal seed set, and its graphical counterpart a graphical seed set. They intuitively consist of variables driving the difference between the two conditions. We propose a simple testing procedure, linear in the number of nodes, to estimate the graphical seed set from data. We illustrate our approach in the context of gene set analysis, where we show that is possible to zoom in on the origin of perturbation in a gene network.

Suggested Citation

  • Djordjilović, Vera & Chiogna, Monica, 2022. "Searching for a source of difference in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000185
    DOI: 10.1016/j.jmva.2022.104973
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    References listed on IDEAS

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    1. Yin Xia & Tianxi Cai & T. Tony Cai, 2015. "Testing differential networks with applications to the detection of gene-gene interactions," Biometrika, Biometrika Trust, vol. 102(2), pages 247-266.
    2. James M. Robins, 2003. "Uniform consistency in causal inference," Biometrika, Biometrika Trust, vol. 90(3), pages 491-515, September.
    3. Dethlefsen, Claus & Højsgaard, Søren, 2005. "A Common Platform for Graphical Models in R: The gRbase Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i17).
    4. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    5. Sihai Dave Zhao & T. Tony Cai & Hongzhe Li, 2014. "Direct estimation of differential networks," Biometrika, Biometrika Trust, vol. 101(2), pages 253-268.
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    1. Banzato, Erika & Chiogna, Monica & Djordjilović, Vera & Risso, Davide, 2023. "A Bartlett-type correction for likelihood ratio tests with application to testing equality of Gaussian graphical models," Statistics & Probability Letters, Elsevier, vol. 193(C).

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