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Abstract: We prove identifiability of parameters for a broad class of random graphmixture models. These models are characterized by a partition of the set ofgraph nodes into latent unobservable groups. The connectivities between nodesare independent random variables when conditioned on the groups of the nodesbeing connected. In the binary random graph case, in which edges are eitherpresent or absent, these models are known as stochastic blockmodels and havebeen widely used in the social sciences and, more recently, in biology. Theirgeneralizations to weighted random graphs, either in parametric ornon-parametric form, are also of interest in many areas. Despite a broad rangeof applications, the parameter identifiability issue for such models isinvolved, and previously has only been touched upon in the literature. We givehere a thorough investigation of this problem. Our work also has consequencesfor parameter estimation. In particular, the estimation procedure proposed byFrank and Harary for binary affiliation models is revisited in this article.



Author: Elizabeth S. Allman, Catherine Matias, John A. Rhodes

Source: https://arxiv.org/







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