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Characterization and Learning of Causal Graphs from Hard Interventions
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Characterizes interventional Markov equivalence of causal graphs with latents under hard interventions via generalized do-calculus constraints, and proposes a sound FCI-style algorithm that learns augmented-graph tuples from multiple hard-interventional datasets.
Problem
Causal discovery with latent variables from multiple experimental datasets generated by hard interventions (plus optional observational data), where existing I-Markov equivalence characterizations were developed for soft interventions and cannot exploit the extra do-invariances hard interventions pr
Approach
Generalizes do-calculus rules to arbitrary pairs of hard-intervention sets, encodes them via augmented pair graphs with F-nodes and twin augmented MAGs, compresses them into I-augmented MAG tuples, and learns these with an FCI-variant that adds new orientation rules (Rules 8-11).
Key results
- For 4-node ADMGs, mean I-MEC size under hard interventions is 677 vs 1219 under soft (random graphs), ratio about 0.56.
- For 5-node complete DAGs with 0.5 bidirected density, estimated hard/soft ratio is 0.459 ± 0.028 (sampling-based estimate).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use hard instead of soft interventions | I-MEC size on enumerated ADMGs · Random and complete ADMGs, n=2–4 | mean I-MEC size: 2.03 \pm 0.15 vs 2.93 \pm 0.29; 721.37 \pm 276.36 vs 1529.57 \pm 368.68 | Helped |
| Use hard instead of soft interventions | I-MEC size estimated by sampling complete DAGs · n=2–6 | estimated equivalent-ADMG probability: 0.417 \pm 0.010 vs 0.584 \pm 0.010; 0.015 \pm 0.010 vs 0.036 \pm 0.012 | Helped |
| Use hard instead of soft interventions | I-MEC size estimated on dense ADMGs · n=3–6, approximately 0.9 bidirected-edge density | estimated equivalent-ADMG probability: 0.151 \pm 0.011 vs 0.264 \pm 0.015; 0.019 \pm 0.010 vs 0.059 \pm 0.012 | Helped |
| Use hard instead of soft interventions | I-MEC size estimated across bidirected-edge densities · Complete DAGs, n=5, densities 0.1–0.9 | estimated equivalent-ADMG probability: 0.020 \pm 0.011 vs 0.024 \pm 0.011; 0.034 \pm 0.010 vs 0.093 \pm 0.011 | Mixed |
Surprising findings
- Hard interventions shrink the I-MEC more as bidirected-edge density increases, with the hard/soft ratio falling from 0.80 at density 0.1 to 0.37 at density 0.9 for 5-node graphs.
Limitations
- Assumes no selection bias and h-faithfulness of the interventional distributions.
- Enumeration-based experiments are only feasible for small numbers of nodes; larger settings require sampling.
Experimental setup
Metrics: I-MEC size ratio of hard to soft I-MEC size
Baselines: soft-intervention I-MEC characterization
Builds on: do-calculus FCI F-node augmented graphs Markov equivalence characterization for interventions
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- Interventional Causal Discovery in a Mixture of DAGs (NeurIPS 2024 · similarity 0.89)
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