2025/01/26 by Oliver E Richardson, Oliver Richardson, Richardson, Oliver E +5 · 1 voice · 1 citation
Computer Science · #FOS: Computer and information sciences #Information Theory (cs.IT) #Semantic Web and Ontologies #cs.IT
paper · pdf · doi:10.48550/arxiv.2501.15488
openalex publication_date 2025/01/26 · arxiv published 2025/01/26 · arxiv updated 2025/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We define what it means for a joint probability distribution to be compatible with a set of independent causal mechanisms, at a qualitative level -- or, more precisely, with a directed hypergraph A, which is the qualitative structure of a probabilistic dependency graph (PDG). When A represents a qualitative Bayesian network, QIM-compatibility with A reduces to satisfying the appropriate conditional independencies. But giving semantics to hypergraphs using QIM-compatibility lets us do much more. For one thing, we can capture functional dependencies. For another, we can capture important aspects of causality using compatibility: we can use compatibility to understand cyclic causal graphs, and to demonstrate structural compatibility, we must essentially produce a causal model. Finally, QIM-compatibility has deep connections to information theory. Applying our notion to cyclic structures helps to clarify a longstanding conceptual issue in information theory.