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  • 0912.3648

    Rights statement: 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: http://www.tandfonline.com/10.1080/01621459.2016.1141686

    Accepted author manuscript, 1.42 MB, PDF document

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Geometric Representations of Random Hypergraphs

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Geometric Representations of Random Hypergraphs. / Lunagomez Coria, Simon; Mukherjee, Sayan ; Wolpert, Robert et al.
In: Journal of the American Statistical Association, Vol. 112, No. 517, 2017, p. 363-383.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Lunagomez Coria, S, Mukherjee, S, Wolpert, R & Airoldi, E 2017, 'Geometric Representations of Random Hypergraphs', Journal of the American Statistical Association, vol. 112, no. 517, pp. 363-383. https://doi.org/10.1080/01621459.2016.1141686

APA

Lunagomez Coria, S., Mukherjee, S., Wolpert, R., & Airoldi, E. (2017). Geometric Representations of Random Hypergraphs. Journal of the American Statistical Association, 112(517), 363-383. https://doi.org/10.1080/01621459.2016.1141686

Vancouver

Lunagomez Coria S, Mukherjee S, Wolpert R, Airoldi E. Geometric Representations of Random Hypergraphs. Journal of the American Statistical Association. 2017;112(517):363-383. Epub 2017 May 3. doi: 10.1080/01621459.2016.1141686

Author

Lunagomez Coria, Simon ; Mukherjee, Sayan ; Wolpert, Robert et al. / Geometric Representations of Random Hypergraphs. In: Journal of the American Statistical Association. 2017 ; Vol. 112, No. 517. pp. 363-383.

Bibtex

@article{b400248ef2014cfd9e2a503f76f1e182,
title = "Geometric Representations of Random Hypergraphs",
abstract = "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.",
keywords = "Graphical models, Computational Geometry, Bayesian inference",
author = "{Lunagomez Coria}, Simon and Sayan Mukherjee and Robert Wolpert and Edoardo Airoldi",
note = "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: http://www.tandfonline.com/10.1080/01621459.2016.1141686",
year = "2017",
doi = "10.1080/01621459.2016.1141686",
language = "English",
volume = "112",
pages = "363--383",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "517",

}

RIS

TY - JOUR

T1 - Geometric Representations of Random Hypergraphs

AU - Lunagomez Coria, Simon

AU - Mukherjee, Sayan

AU - Wolpert, Robert

AU - Airoldi, Edoardo

N1 - 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: http://www.tandfonline.com/10.1080/01621459.2016.1141686

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Graphical models

KW - Computational Geometry

KW - Bayesian inference

U2 - 10.1080/01621459.2016.1141686

DO - 10.1080/01621459.2016.1141686

M3 - Journal article

VL - 112

SP - 363

EP - 383

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 517

ER -