Empirically Calibrated Conditional Independence Tests

TL;DR

This paper introduces ECCIT, a method that empirically calibrates conditional independence tests to improve their reliability and power in causal discovery, especially in small samples and model misspecification scenarios.

Contribution

ECCIT is a novel calibration approach that adjusts p-values of existing CITs based on observed miscalibration, enhancing their validity and power.

Findings

ECCIT achieves valid FDR control across benchmarks.

ECCIT outperforms existing calibration methods in power.

ECCIT remains test agnostic and effective on synthetic and real data.

Abstract

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.