Research map / Probabilistic and scientific modeling / Causal discovery
Counterfactual Graphical Models: Constraints and Inference
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Introduces Ancestral Multi-World Networks, a sound and complete d-separation-based graphical test for counterfactual independences, and the counterfactual calculus (three rules) that is sound and complete for counterfactual identification.
Problem
Reading counterfactual independences from causal diagrams efficiently and transforming counterfactual quantities into observational/interventional expressions, generalizing do-calculus to counterfactual reasoning.
Approach
Constructs a graph (AMWN) over ancestral counterfactual variables with latent nodes for shared exogenous units so that d-separation is complete for counterfactual independences, and derives three counterfactual calculus rules (consistency, independence, exclusion) that subsume do-calculus.
Key results
- Proves soundness and completeness of counterfactual d-separation on the Ancestral Multi-World Network, with O(z(n+m)) construction and check time.
- Shows the ctf-calculus is sound and complete for counterfactual identification from observational and interventional distributions (Theorem 3.2).
- Shows ctf-calculus subsumes do-calculus (Lemma 3.3) and derives ETT and natural direct effect expressions as examples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AMWN to test counterfactual independence with d-separation | Counterfactual independence queries · Causal diagrams | d-separation completeness | Helped |
| Use AMWN instead of Twin Networks | Counterfactual independence queries · Causal diagrams | d-separation completeness | Helped |
| Use AMWN instead of k-plet Networks | Counterfactual independence queries · Causal diagrams | time complexity: O(zn(n + m)) -> O(z(n + m)) | Helped |
| Use AMWN instead of Multi-Networks | Counterfactual independence queries · Causal diagrams | time complexity: O(dn(n + m)) -> O(z(n + m)) | Helped |
| Apply counterfactual calculus rules with probability axioms | Counterfactual identification · Observational and experimental distributions | identifiability completeness | Helped |
Limitations
- Assumes finite variable domains and positive distributions.
- Assumes the underlying SCM is recursive (no cyclic dependencies).
Experimental setup
Baselines: Twin Network SWIG Multi-Networks k-plet Network po-calculus
Builds on: do-calculus Twin Networks Single World Intervention Graphs Potential Outcome Calculus
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