Random Networks, Graphical Models, and Exchangeability

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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.
Original languageEnglish
JournalJournal of The Royal Statistical Society Series B-statistical Methodology
Volume80
Issue number3
Pages (from-to)481-508
ISSN1369-7412
DOIs
Publication statusPublished - 24 Apr 2018

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