Information-theoretic signatures of causality in Bayesian networks and hypergraphs

2025-12-23

AI Summary

Existing partial information decomposition (PID) lacks a rigorous theoretical connection to causal structures, particularly within causal graph models such as Bayesian networks and directed hypergraphs. The semantic interpretation of PID components—unique, redundant, and synergistic information—remains disconnected from formal causal semantics. Method: This work establishes the first principled mapping between PID components and causal graph primitives: unique information corresponds to direct causal neighbors; redundant information arises from shared ancestors; and synergistic information is attributed to collider structures—including higher-order colliders induced by multi-tailed hyperedges. Contribution/Results: We introduce “localist causal discovery,” a novel paradigm enabling variable-level causal structure reconstruction without global graph search. We design systematic, model-agnostic algorithms for higher-order causal analysis, bridging information-theoretic measures with causal inference. This framework provides a foundational basis for information-theoretic causal reasoning and advances the theoretical integration of PID with structural causal models.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined, and thus requires tools that capture interactions beyond pairwise relations. Higher-order information theory provides such tools. 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 higher-order systems, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a higher-order collider effect unique to multi-tail hyperedges. We also present procedures by which our results can be used to characterize systematically the causal structure of Bayesian networks and hypergraphs. 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.

Problem

• Establishes correspondence between PID components and causal structure.
• Shows unique information identifies direct causal neighbors in Bayesian networks.
• Proves PID signatures differentiate causal roles in Bayesian hypergraphs.

Innovation

• PID components map to causal structures in Bayesian networks
• Localist paradigm recovers structure from immediate informational footprint
• PID signatures differentiate higher-order relationships in hypergraphs