Geometric Representations of Random Hypergraphs (original) (raw)

We introduce a novel parametrization of distributions on hypergraphs based on the geometry of points in R d . The idea is to induce distributions on hypergraphs by placing priors on point configurations via spatial processes. This prior specification is then used to infer conditional independence models or Markov structure for multivariate distributions. This approach supports inference of factorizations that cannot be retrieved by a graph alone, leads to new Metropolis-Hastings Markov chain Monte Carlo algorithms with both local and global moves in graph space, and generally offers greater control on the distribution of graph features than currently possible. We provide a comparative performance evaluation against state-of-the-art, and we illustrate the utility of this approach on simulated and real data.