Geometric Representations of Random Hypergraphs

Understand

A parametrization of hypergraphs based on the geometry of points in $\mathbf{R}^d$ is developed.

• Informative prior distributions on hypergraphs are induced through this parametrization by priors on point configurations via spatial processes.
• This prior specification is used to infer conditional independence models or Markov structure of multivariate distributions.
• Specifically, we can recover both the junction tree factorization as well as the hyper Markov law.