Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Oliver E. Richardson, Spencer Peters, Joseph Y. Halpern
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 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, compatibility has deep connections to information theory. Applying compatibility to cyclic structures helps to clarify a longstanding conceptual issue in information theory.