Geometric Representations of Random Hypergraphs

• 成果类型: Article
• 署名作者: Lunagomez, Simon; Mukherjee, Sayan; Wolpert, Robert L.; Airoldi, Edoardo M.
• 署名单位: Harvard University; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1141686
• 发表日期: 2017
• 页码: 363-383
• 关键词: statistical-analysis; markov-chains; MODEL; computation; likelihood; HOMOLOGY

摘要

We introduce a novel parameterization of distributions on hypergraphs based on the geometry of points in . 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. Inference 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.