Research map / Probabilistic and scientific modeling / Causal discovery
Sample Efficient Bayesian Learning of Causal Graphs from Interventions
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Proposes a Bayesian causal discovery algorithm that uses random interventions on a separating system of target sets, tracking posteriors over cut configurations (with DAG sampling from the MEC) to learn the causal graph from limited interventional samples.
Problem
Learning the complete causal graph from a limited number of interventional samples (rather than infinite interventional data), under causal sufficiency and faithfulness with infinite observational data.
Approach
Enumerate all cut configurations of each separating-system target set, weight them with MEC-size priors, and update Bayesian posteriors from finite interventional samples via uniform DAG sampling in polynomial time; combine the highest-posterior configurations greedily into an anytime DAG, with a non-parametric guarantee of recovering the true DAG given enough samples.
Key results
- Proposed Bayesian algorithm reaches low SHD with substantially fewer interventional samples than Random Intervention, DCT and adaptivity-sensitive baselines on complete and sparse chordal graphs.
- Sample requirement of the proposed method grows little with graph order and density, whereas baselines need many more samples on denser graphs.
- Case study shows estimated causal effect of a non-intervenable variable converges to ground truth (KL and TVD) as interventional samples increase.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Bayesian Causal Discovery instead of Random Intervention, DCT, or adaptivity-sensitive search | Causal graph discovery · Random complete graphs (n=5, 6, 7) and random sparse chordal graphs (n=10) | SHD | Helped |
| Use Bayesian Causal Discovery across graph orders and densities | Causal graph discovery · Random complete and sparse chordal graphs | SHD | Helped |
| Increase the number of interventional samples | Bayesian causal-effect estimation using DAG sampling · Simulated causal graphs (n=5, 6, 7; ρ=0.3) | KL divergence and TVD | Helped |
Limitations
- Tracking posteriors of all cut configurations is exponential in target-set size and density, intractable for large dense graphs.
- Requires causal sufficiency, faithfulness, and infinite observational data, plus a positivity-type bounded log-likelihood-ratio assumption.
Experimental setup
Datasets: simulated random chordal DAGs (n=5,6,7,10,20) with random CPTs
Benchmarks: simulated random complete graphs (n=5,6,7) simulated sparse chordal graphs (n=10, density 0.1-0.2) causal effect estimation on random graphs (n=5,6,7)
Metrics: structural Hamming distance KL divergence total variation distance
Baselines: Random Intervention Directed Clique Trees (DCTs) active structure learning adaptivity-sensitive search (clique tree based)
Builds on: separating system based intervention design Meek rules MEC counting uniform DAG sampling
Closest papers by meaning
- Adaptive Online Experimental Design for Causal Discovery (ICML 2024 · similarity 0.93)
- Learning Mixtures of Unknown Causal Interventions (NeurIPS 2024 · similarity 0.91)
- Interventional Causal Discovery in a Mixture of DAGs (NeurIPS 2024 · similarity 0.91)
- Characterization and Learning of Causal Graphs from Hard Interventions (NeurIPS 2025 · similarity 0.90)
- Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning (NeurIPS 2025 · similarity 0.90)
- Causal Discovery via Bayesian Optimization (ICLR 2025 · similarity 0.90)
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