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On a hypergraph probabilistic graphical model

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Abstract

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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Acknowledgments

This work is primarily supported by Office on Naval Research grant ONR N00014-17-1-2842. The causal interpretation of Bayesian hypergraphs described in Section 6 was presented at the AAAI Spring Symposium “Beyond Curve Fitting: Causation, Counterfactuals, and Imagination-based AI (AAAI-WHY 2019),” Palo Alto. CA, March 25-27, 2019. Comments by reviewers and symposium participants are gratefully acknowledged.

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  1. University of South Carolina, 29208, Columbia, SC, USA

    Mohammad Ali Javidian, Zhiyu Wang, Linyuan Lu & Marco Valtorta

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  1. Mohammad Ali Javidian
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  2. Zhiyu Wang
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  3. Linyuan Lu
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  4. Marco Valtorta
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Correspondence to Mohammad Ali Javidian.

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Linyuan Lu was supported in part by NSF grant DMS-1600811 and ONR grant N00014-17-1-2842.

Marco Valtorta was supported in part by ONR grant N00014-17-1-2842.

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Javidian, M.A., Wang, Z., Lu, L. et al. On a hypergraph probabilistic graphical model. Ann Math Artif Intell 88, 1003–1033 (2020). https://doi.org/10.1007/s10472-020-09701-7

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