# Information-theoretic signatures of causality in Bayesian networks and hypergraphs

arXiv: https://arxiv.org/abs/2512.20552 · HTML: https://mlsanity.com/paper/2512.20552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Foundations and Trends in Multimodal Machine Learning: Principles, Challenges, and Open Questions](https://mlsanity.com/paper/2209.03430/) (2022)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information](https://mlsanity.com/paper/1902.11239/) (2019)
- [The why, how, and when of representations for complex systems](https://mlsanity.com/paper/2006.02870/) (2020)
- [Unveiling the higher-order organization of multivariate time series](https://mlsanity.com/paper/2203.10702/) (2022)
- [Gaussian Partial Information Decomposition: Bias Correction and Application to High-dimensional Data](https://mlsanity.com/paper/2307.10515/) (2023)
- [Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems](https://mlsanity.com/paper/1411.2832/) (2014)
- [A Weaker Faithfulness Assumption based on Triple Interactions](https://mlsanity.com/paper/2010.14265/) (2020)
- [Partial entropy decomposition reveals higher-order structures in human brain activity](https://mlsanity.com/paper/2301.05307/) (2023)
- [A General Framework for Interpretable Neural Learning based on Local Information-Theoretic Goal Functions](https://mlsanity.com/paper/2306.02149/) (2023)
- [We Are Not Your Real Parents: Telling Causal from Confounded using MDL](https://mlsanity.com/paper/1901.06950/) (2019)
- [On a hypergraph probabilistic graphical model](https://mlsanity.com/paper/1811.08372/) (2018)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [Higher-Order Causal Structure Learning with Additive Models](https://mlsanity.com/paper/2511.03831/) (2025)

## Abstract (arXiv)

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined. Traditional causal discovery frameworks are capable of multivariate reasoning but their intrinsic pairwise graph topology restricts them to do so only indirectly by integrating multivariate information across pairwise edges. Higher-order information theory provides direct tools that can explicitly model higher-order interactions. In particular, Partial Information Decomposition (PID) allows the decomposition of the information that a set of sources provides about a target into redundant, unique, and synergistic components. Yet the mathematical connection between such higher-order information-theoretic measures and causal structure remains undeveloped. Here we establish the first theoretical correspondence between PID components and causal structure in both Bayesian networks and hypergraphs. We first show that in Bayesian networks unique information precisely characterizes direct causal neighbors, while synergy identifies collider relationships. This establishes a localist causal discovery paradigm in which the structure surrounding each variable can be recovered from its immediate informational footprint, eliminating the need for global search over graph space. Extending these results to more expressive causal representation, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a novel collider effect unique to multi-tail hyperedges. Our results position PID as a rigorous, model-agnostic foundation for inferring both pairwise and higher-order causal structure, and introduce a fundamentally local information-theoretic viewpoint on causal discovery.