Geometric Representations of Random Hypergraphs

Lunagomez Coria, Simon and Mukherjee, Sayan and Wolpert, Robert and Airoldi, Edoardo (2017) Geometric Representations of Random Hypergraphs. Journal of the American Statistical Association, 112 (517). pp. 363-383. ISSN 0162-1459

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We introduce a novel parameterization of distributions on hypergraphs based on the geometry of points in Rd. The idea is to induce distributions on hypergraphs by placing priors on point configurations via spatial processes. This specification is then used to infer conditional independence models, or Markov structure, for multivariate distributions. This approach results in a broader class of conditional independence models beyond standard graphical models. Factorizations that cannot be retrieved via a graph are possible. Infer- ence of nondecomposable graphical models is possible without requiring decomposability, or the need of Gaussian assumptions. This approach leads to new Metropolis-Hastings Markov chain Monte Carlo algorithms with both local and global moves in graph space, generally offers greater control on the distribution of graph features than currently possible, and naturally extends to hypergraphs. We provide a comparative performance evaluation against state-of-the-art approaches, and illustrate the utility of this approach on simulated and real data.

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Journal Article
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Journal of the American Statistical Association
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This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 03/05/2017, available online:
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26 Apr 2018 14:08
Last Modified:
22 Nov 2022 05:48