Research map / Probabilistic and scientific modeling / Causal discovery
Causal discovery with endogenous context variables
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Proposes an adaptive PC-based constraint-based discovery algorithm that recovers context-specific causal skeletons when the context variable is endogenous, avoiding selection bias from masking and inflated test counts.
Problem
Constraint-based causal discovery of context-specific causal graphs when the context indicator is endogenous (can be influenced by system variables), where masking induces selection bias and pooling loses context-specific information.
Approach
Adapt the PC skeleton phase so that a conditional independence test conditions on the context value (on context-specific data) only when the context variable is in the separating set, and otherwise tests on pooled data; a single test per separating set is chosen by this rule, avoiding inflated test counts. Theory connects output to SCM-defined physical/descriptive graphs under sufficiency assumpti
Key results
- PC-AC has the best TPR and FPR on union and context-specific graphs when context-child links are known, and performs best among methods on context-specific graph TPR without link assumptions.
- Without prior knowledge of context adjacencies, the parametric CIT inflates FPR for PC-B and PC-AC; a non-parametric CIT significantly lowers FPR for all methods.
- On union graphs, the method slightly outperforms CD-NOD and has higher TPR than FCI, though FCI has lower FPR.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PC-AC instead of PC-M (masking) | Context-specific causal discovery · Simulated context-specific graphs, no cycles | false positive rate | Helped |
| Use PC-AC instead of PC-B | Context-specific causal discovery · Simulated context-specific graphs | true positive rate | Helped |
| Use PC-AC instead of PC-B | Context-specific causal discovery · Simulated graphs | finite-sample performance | Helped |
| Use PC-AC instead of CD-NOD | Union-graph discovery · Simulated union graphs | overall performance | Helped |
| Use PC-AC instead of FCI | Union-graph discovery · Simulated union graphs | true positive rate | Helped |
| Use PC-AC instead of FCI | Union-graph discovery · Simulated union graphs | false positive rate | Hurt |
| Use PC-M with fully known context-system links instead of PC-AC | Context-specific causal discovery · Simulated graphs with fully known context-system links | true positive rate | Helped |
| Use PC-M with fully known context-system links instead of PC-AC | Context-specific causal discovery · Simulated graphs with fully known context-system links | false positive rate | Hurt |
| Use a non-parametric CIT instead of a parametric CIT (ablation) | PC-AC and comparison methods · Simulated graphs without cycles, no link assumptions | false positive rate | Helped |
| Add enforced cycles to the union graph (ablation) | PC-AC and comparison methods · Simulated graphs with enforced cycles | false positive rate | Hurt |
| Use PC-P instead of PC-AC on cyclic union graphs | Union-graph discovery · Simulated cyclic union graphs | false positive rate | Hurt |
| Use PC-AC with context-child link assumptions rather than no link assumptions (ablation) | PC-AC · Simulated graphs without cycles | false positive rate | Helped |
Surprising findings
- Naive masking (PC-M) and the baseline PC-B suffer higher false positive rates from selection bias, and the proposed method has difficulty significantly outperforming pooled methods without link assumptions due to conditional independence test issues.
Limitations
- Requires an observed and appropriately chosen context indicator; assumes causal sufficiency (no hidden confounders).
- Cannot reliably handle large union cycles; relies on cycles of length at most 2.
- Without known context adjacencies, performance suffers due to conditional independence testing difficulties with non-linear context relations.
Experimental setup
Datasets: synthetic linear-nonlinear SCM data (D+1=8 nodes)
Benchmarks: synthetic SCM simulations
Metrics: true positive rate false positive rate edge mark precision edge mark recall
Baselines: PC-M (masking) PC-P (pooled) PC-B (baseline intersection) CD-NOD FCI-JCI0
Builds on: PC algorithm Joint Causal Inference Labeled DAGs CD-NOD FCI
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