Research map / Probabilistic and scientific modeling / Causal discovery
Qualitative Mechanism Independence
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Defines qualitative independent-mechanism (QIM) compatibility between a distribution and a directed hypergraph, shows it reduces to BN independencies for DAGs, captures functional dependence and cyclic causal structure, and connects it to causal models and information theory.
Problem
What it means for a joint probability distribution to be qualitatively compatible with a set of independent causal mechanisms represented by a directed hypergraph (the qualitative structure of a PDG), including functional dependencies and cyclic structures.
Approach
Define compatibility via the existence of a witness extended distribution in which each hyperarc's targets are a function of its sources and an independent noise variable; this yields a semantics for hypergraphs that generalizes BN independencies, captures functional dependence via parallel hyperarcs, and corresponds to generalized randomized structural equation models.
Key results
- QIM-compatibility with a DAG hypergraph coincides exactly with the conditional independencies of the corresponding Bayesian network (Theorem bns).
- Adding two parallel hyperarcs from X to Y ensures functional dependence X->Y, with n=2 sufficient when a hyperarc has no sources targeting X (Theorem func).
- Compatibility with a hypergraph is equivalent to arising from a generalized randomized PSEM with that structure (Proposition gen-sim-compat-means-arise).
Surprising findings
- Conditioning on the do-event over noise variables has the effect of intervention, linking conditioning and intervention for witnesses.
- Compatibility with undirected graphs does not coincide with standard Markov properties, a consequence of capturing causality.
Limitations
- Only partial characterization of distributions compatible with general (cyclic, non-partitional) dependency structures.
- Compatibility with undirected graphs does not match standard Markov properties.
- Several open problems on distributional implications of cyclic structures remain unsolved.
Experimental setup
Builds on: probabilistic dependency graphs structural equations models Bayesian networks d-separation
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