Qualitative Mechanism Independence
Keywords: causality, information theory, directed hypergraphs, qualitative structures
TL;DR: a definition of compatibility between a distribution and a directed hypergraph, with implications for causality and information theory
Abstract: We define what it means for a joint probability distribution to be compatible with aset of independent causal mechanisms, at a qualitative level—or, more precisely with a directed hypergraph $\mathcal A$, which is the qualitative structure of a probabilistic dependency graph (PDG). When A represents a qualitative Bayesian network, QIM-compatibility with $\mathcal A$ 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, compatibility has deep connections to information theory. Applying compatibility to cyclic structures helps to clarify a longstanding conceptual issue in information theory.
Primary Area: Causal inference
Submission Number: 12944
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