PAIR-CI: Calibrated Conditional Independence Testing for Causal Discovery with Incomplete Data
Thomas S. Robinson, Ranjit Lall
TLDR
PAIR-CI is a new nonparametric CI test for incomplete data that restores calibration by integrating multiple imputation, significantly improving causal discovery.
Key contributions
- Introduces PAIR-CI, a nonparametric CI test for causal discovery with incomplete data.
- Restores calibration by integrating multiple imputation via a paired permutation design.
- Cancels imputation error by comparing cross-validated models with shared conditioning sets.
- Unifies cross-validation and multiple imputation for consistent variance estimation.
Why it matters
Existing causal discovery methods with incomplete data are often miscalibrated, leading to high false positive rates. PAIR-CI solves this by integrating imputation directly into the test, ensuring calibration and significantly improving accuracy. This is crucial for reliable causal inference in real-world scenarios with missing data.
Original Abstract
The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce PAIR-CI, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation -- to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28--45% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8% on 10-variable nonlinear graphs, 15% on 30-variable equivalents, and up to 44% on the 56-variable HAILFINDER network, with stable performance in all settings.
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