# On a hypergraph probabilistic graphical model

arXiv: https://arxiv.org/abs/1811.08372 · HTML: https://mlsanity.com/paper/1811.08372/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2018.

## Built on by (most cited first, 5 of 5)

- [Low-Rank Constraints for Fast Inference in Structured Models](https://mlsanity.com/paper/2201.02715/) (2022)
- [Accelerating Recursive Partition-Based Causal Structure Learning](https://mlsanity.com/paper/2102.11545/) (2021)
- [Higher-Order Causal Structure Learning with Additive Models](https://mlsanity.com/paper/2511.03831/) (2025)
- [Higher order definition of causality by optimally conditioned transfer entropy](https://mlsanity.com/paper/2409.08295/) (2024)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)

## Abstract (arXiv)

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 define a projection operator, called shadow, that maps Bayesian hypergraphs to chain graphs, and show that the Markov properties of a Bayesian hypergraph are equivalent to those of its corresponding chain graph. We extend the causal interpretation of LWF chain graphs to Bayesian hypergraphs and provide corresponding formulas and a graphical criterion for intervention.