Random Networks, Graphical Models, and Exchangeability

Research output: Contribution to journal › Journal article › Research › peer-review

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Random Networks, Graphical Models, and Exchangeability. / Lauritzen, Steffen L.; Rinaldo, Alessandro; Sadeghi, Kayvan.

In: Journal of The Royal Statistical Society Series B-statistical Methodology, Vol. 80, No. 3, 24.04.2018, p. 481-508.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Lauritzen, SL, Rinaldo, A & Sadeghi, K 2018, 'Random Networks, Graphical Models, and Exchangeability', Journal of The Royal Statistical Society Series B-statistical Methodology, vol. 80, no. 3, pp. 481-508. https://doi.org/10.1111/rssb.12266

APA

Lauritzen, S. L., Rinaldo, A., & Sadeghi, K. (2018). Random Networks, Graphical Models, and Exchangeability. Journal of The Royal Statistical Society Series B-statistical Methodology, 80(3), 481-508. https://doi.org/10.1111/rssb.12266

Vancouver

Lauritzen SL, Rinaldo A, Sadeghi K. Random Networks, Graphical Models, and Exchangeability. Journal of The Royal Statistical Society Series B-statistical Methodology. 2018 Apr 24;80(3):481-508. https://doi.org/10.1111/rssb.12266

Author

Lauritzen, Steffen L. ; Rinaldo, Alessandro ; Sadeghi, Kayvan. / Random Networks, Graphical Models, and Exchangeability. In: Journal of The Royal Statistical Society Series B-statistical Methodology. 2018 ; Vol. 80, No. 3. pp. 481-508.

Bibtex

@article{f46eb7f93aa045368a5517c231354ef7,
title = "Random Networks, Graphical Models, and Exchangeability",
abstract = "We study conditional independence relationships for random networks and theirinterplay with exchangeability. We show that, for finitely exchangeable network models, the em-pir ical 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 Knesergraphs. In particular, we demonstrate that the fundamental property of dissociatedness corre-sponds 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 theprobability of a networ k depends only on the degree distribution, and we identify a class of mod-els that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed onstudying consistency properties of network models under the process of forming subnetworksand we show that the only consistent systems of Markov properties correspond to the emptygraph, the bidirected line graph of the complete graph and the complete graph.",
author = "Lauritzen, {Steffen L.} and Alessandro Rinaldo and Kayvan Sadeghi",
year = "2018",
month = apr,
day = "24",
doi = "10.1111/rssb.12266",
language = "English",
volume = "80",
pages = "481--508",
journal = "Journal of the Royal Statistical Society, Series B (Statistical Methodology)",
issn = "1369-7412",
publisher = "Wiley",
number = "3",

}

RIS

TY - JOUR

T1 - Random Networks, Graphical Models, and Exchangeability

AU - Lauritzen, Steffen L.

AU - Rinaldo, Alessandro

AU - Sadeghi, Kayvan

PY - 2018/4/24

Y1 - 2018/4/24

N2 - We study conditional independence relationships for random networks and theirinterplay with exchangeability. We show that, for finitely exchangeable network models, the em-pir ical 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 Knesergraphs. In particular, we demonstrate that the fundamental property of dissociatedness corre-sponds 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 theprobability of a networ k depends only on the degree distribution, and we identify a class of mod-els that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed onstudying consistency properties of network models under the process of forming subnetworksand we show that the only consistent systems of Markov properties correspond to the emptygraph, the bidirected line graph of the complete graph and the complete graph.

AB - We study conditional independence relationships for random networks and theirinterplay with exchangeability. We show that, for finitely exchangeable network models, the em-pir ical 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 Knesergraphs. In particular, we demonstrate that the fundamental property of dissociatedness corre-sponds 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 theprobability of a networ k depends only on the degree distribution, and we identify a class of mod-els that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed onstudying consistency properties of network models under the process of forming subnetworksand we show that the only consistent systems of Markov properties correspond to the emptygraph, the bidirected line graph of the complete graph and the complete graph.

U2 - 10.1111/rssb.12266

DO - 10.1111/rssb.12266

M3 - Journal article

VL - 80

SP - 481

EP - 508

JO - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society, Series B (Statistical Methodology)

SN - 1369-7412

IS - 3

ER -

ID: 188639077