We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call Bayesian hypergraphs. The space of directed acyclic hypergraphs is much larger than the space of chain graphs. Hence Bayesian hypergraphs can model much finer factorizations than Bayesian networks or LWF chain graphs and provide simpler and more computationally efficient procedures for factorizations and interventions. Bayesian hypergraphs also allow a modeler to represent causal patterns of interaction such as Noisy-OR graphically (without additional annotations). We introduce global, local and pairwise Markov properties of Bayesian hypergraphs and prove under which conditions they are equivalent. We also extend the causal interpretation of LWF chain graphs to Bayesian hypergraphs and provide corresponding formulas and a graphical criterion for intervention.

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关于超图概率图模型

我们为概率图模型提出了一个有向无环超图框架，我们称之为贝叶斯超图。有向无环超图的空间远大于链图的空间。因此，贝叶斯超图可以对比贝叶斯网络或 LWF 链图更精细的分解建模，并为分解和干预提供更简单、计算效率更高的程序。贝叶斯超图还允许建模者以图形方式表示交互的因果模式，例如 Noisy-OR（无附加注释）。我们介绍了贝叶斯超图的全局、局部和成对马尔可夫特性，并证明它们在哪些条件下是等价的。