Empirically Calibrated Conditional Independence Tests
This addresses reliability issues in causal discovery and feature selection for researchers and practitioners, offering an incremental improvement over existing calibration methods.
The paper tackled the problem of conditional independence tests failing to provide frequentist guarantees in practice due to small sample inaccuracies and model misspecification, proposing ECCIT which empirically calibrates p-values to achieve valid false discovery rate control with higher power across benchmarks.
Conditional independence tests (CIT) are widely used for causal discovery and feature selection. Even with false discovery rate (FDR) control procedures, they often fail to provide frequentist guarantees in practice. We highlight two common failure modes: (i) in small samples, asymptotic guarantees for many CITs can be inaccurate and even correctly specified models fail to estimate the noise levels and control the error, and (ii) when sample sizes are large but models are misspecified, unaccounted dependencies skew the test's behavior and fail to return uniform p-values under the null. We propose Empirically Calibrated Conditional Independence Tests (ECCIT), a method that measures and corrects for miscalibration. For a chosen base CIT (e.g., GCM, HRT), ECCIT optimizes an adversary that selects features and response functions to maximize a miscalibration metric. ECCIT then fits a monotone calibration map that adjusts the base-test p-values in proportion to the observed miscalibration. Across empirical benchmarks on synthetic and real data, ECCIT achieves valid FDR with higher power than existing calibration strategies while remaining test agnostic.