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
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Accepted author manuscript
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -