Research map / Probabilistic and scientific modeling / Causal discovery
Interventional Causal Discovery in a Mixture of DAGs
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Studies interventional causal discovery for a mixture of DAGs, proving matching necessary and sufficient intervention sizes for identifying true edges and proposing the CADIM algorithm that uses O(n^2) interventions with a cyclic-complexity optimality gap.
Problem
Learning causal interactions among variables governed by a mixture of multiple co-existing DAGs, where observational data cannot separate true edges from emergent (inseparable but nonadjacent) pairs and cycles can arise across components.
Approach
Uses hard interventions to identify mixture parents: establishes that intervention size one more than the number of mixture parents is necessary and sufficient, and designs an adaptive algorithm that breaks cycles among mixture ancestors via a breaking set, then processes topological layers, with the gap to optimal bounded by the cyclic complexity number.
Key results
- Recovery of true edges on synthetic mixtures of K=3 DAGs with n in [5,30] nodes using 5000 samples per DAG maintains strong precision and recall, including at n=30.
- Average cyclic complexity remains small, approximately 1.5 for K=3 DAGs with n=10 nodes.
- Observational-only CI tests fail to recover true edges even in undirected form, while interventions are needed.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CADIM's adaptive interventions to identify mixture parents | Mixture of DAGs · Mixture of DAGs | number of interventions: \mcO(n^2) interventions | Helped |
| Use interventions of size at most |mixture parents|+1 when ancestors are cycle-free | CADIM · Mixture of DAGs with cycle-free ancestors | maximum intervention size: |\pam(i)|+1 | Helped |
| Break cycles among mixture ancestors using a breaking set | CADIM · Mixture of DAGs with cyclic ancestors | maximum intervention size: |\pam(i)|+\tau_i+1; \tau_i larger than |\pam(i)|+1 | Mixed |
| Use interventions of size at most K+1 | Mixtures of directed trees · Mixture of directed trees | intervention size sufficient for identifying a true edge: K+1 | Helped |
| Use interventions of size at most |mixture parents| | Any method using CI tests on interventional mixture distributions · Worst-case mixture of DAGs | identifiability of a true edge: |\pam(i)| | Hurt |
| Use interventions of size at most K | Any method using CI tests on interventional mixture distributions · Worst-case mixture of directed trees | identifiability of a true edge: K | Hurt |
| Use single-node interventions to identify mixture ancestors | CADIM · Mixture of DAGs | mixture-ancestor identification: n single-node interventions | Helped |
| Use interventions rather than observational data alone to recover true edges | Causal discovery in a mixture of K=2 DAGs · Synthetic mixture of DAGs | true-edge recovery | Helped |
| Increase the number of nodes up to n=30 | CADIM · Synthetic mixture of K=3 DAGs | average precision and recall | No clear effect |
| Increase the number of mixture components | CADIM · Synthetic mixtures of DAGs | average cyclic complexity: approximately 1.5 for K=3 and n=10 | Hurt |
| Estimate cyclic complexity with CADIM | CADIM · Synthetic mixtures of DAGs | cyclic complexity estimation | No clear effect |
Surprising findings
- Learning the skeleton of a mixture of DAGs is impossible from observational data alone, unlike single DAGs where the skeleton is identifiable via CI tests.
Limitations
- Optimality gap of tau_i (cyclic complexity) in the presence of cycles among mixture ancestors.
- Component DAGs are not identifiable without further assumptions; only true edges are learned.
- Experiments are limited to synthetic linear Gaussian SEMs with partial-correlation tests.
Experimental setup
Datasets: synthetic linear Gaussian SEM mixtures of DAGs
Benchmarks: synthetic mixtures of DAGs
Metrics: precision recall average cyclic complexity
Baselines: observational-only inseparable pair CI-test learning
Builds on: mixture DAG emergent edges intervention design for single DAG
Closest papers by meaning
- Learning Mixtures of Unknown Causal Interventions (NeurIPS 2024 · similarity 0.91)
- Sample Efficient Bayesian Learning of Causal Graphs from Interventions (NeurIPS 2024 · similarity 0.91)
- Adaptive Online Experimental Design for Causal Discovery (ICML 2024 · similarity 0.90)
- Coarsening Linear Non-Gaussian Causal Models with Cycles (NeurIPS 2026 · similarity 0.90)
- Differentiable Cyclic Causal Discovery Under Unmeasured Confounders (NeurIPS 2025 · similarity 0.89)
- Causal Discovery with Fewer Conditional Independence Tests (ICML 2024 · similarity 0.89)
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