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PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data
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Proposes PAIR-CI, a nonparametric conditional independence test for causal discovery with incomplete data that pairs cross-validated full and placebo-conditioned models on the same multiply imputed conditioning set, with a unified CV-plus-multiple-imputation variance estimator.
Problem
Constraint-based causal discovery with missing values in the conditioning set: impute-then-test CI tests are miscalibrated under MNAR and misspecified imputation, producing spurious edges.
Approach
A paired classification-based CI test compares cross-validated models with and without the candidate variable (Y replaced by a conditionally permuted placebo) fed the same imputed conditioning set, so imputation error cancels in the loss difference; variance combines within-imputation CV variance with Rubin's rules.
Key results
- PAIR-CI averages 0.036 false positive rate under MNAR versus 0.282-0.447 for imputation-based baselines (Table 1).
- On 30-variable nonlinear synthetic graphs PAIR-CI reaches SHD 58 versus 68-75 for baselines (Table 2).
- On HAILFINDER (p=56, 20% missingness) PAIR-CI attains SHD 62.5-65.5 versus 103.5-128 for baselines (Table 4).
Surprising findings
- Complete-case PC achieves competitive SHD under heavy missingness only because it recovers fewer edges, with F1 of 0.000 on HAILFINDER MNAR.
- Including Z and Y in the cached imputation model is reported to improve MNAR robustness, counter to the per-query exclusion principle.
Limitations
- Lower power than well-specified parametric tests like Fisher's Z when assumptions hold; under-rejection at low signal and small n due to Barnard-Rubin adjustment.
- Assumes causal sufficiency; FCI extension not evaluated.
- Calibration under MNAR relies on imputation errors being random rather than systematic; theory relies on imputation consistency assumption (A1).
Experimental setup
Datasets: simulated linear Gaussian, post-nonlinear, latent confounder DGPs synthetic Erdos-Renyi DAGs ALARM network HAILFINDER network Sachs
Benchmarks: ALARM HAILFINDER synthetic Erdos-Renyi DAGs
Metrics: false positive rate power structural Hamming distance F1 precision recall
Baselines: FZ-single FZ-Rubin GCM KCI test-wise deletion complete-case PC FZ-vote MissDAG
Builds on: PC algorithm Rubin's rules MICE Generalized Covariance Measure FZ-Rubin
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