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Random networks, graphical models and exchangeability

Author

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  • Steffen Lauritzen
  • Alessandro Rinaldo
  • Kayvan Sadeghi

Abstract

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network depends only on the degree distribution, and we identify a class of models that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph and the complete graph.

Suggested Citation

  • Steffen Lauritzen & Alessandro Rinaldo & Kayvan Sadeghi, 2018. "Random networks, graphical models and exchangeability," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 481-508, June.
  • Handle: RePEc:bla:jorssb:v:80:y:2018:i:3:p:481-508
    DOI: 10.1111/rssb.12266
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    Cited by:

    1. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Aug 2024.
    2. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Michael Schweinberger, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 253-260, June.
    4. Kayvan Sadeghi & Alessandro Rinaldo, 2020. "Hierarchical models for independence structures of networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 439-457, August.
    5. Kei, Yik Lun & Chen, Yanzhen & Madrid Padilla, Oscar Hernan, 2023. "A partially separable model for dynamic valued networks," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

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