Empirically Calibrated Conditional Independence Tests

Milleno Pan, Antoine de Mathelin, Wesley Tansey
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:5194-5202, 2026.

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. Code is available at \url{https://github.com/tansey-lab/ECCIT.}

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-pan26a, title = { Empirically Calibrated Conditional Independence Tests }, author = {Pan, Milleno and de Mathelin, Antoine and Tansey, Wesley}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {5194--5202}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/pan26a/pan26a.pdf}, url = {https://proceedings.mlr.press/v300/pan26a.html}, 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. Code is available at \url{https://github.com/tansey-lab/ECCIT.} } }
Endnote
%0 Conference Paper %T Empirically Calibrated Conditional Independence Tests %A Milleno Pan %A Antoine de Mathelin %A Wesley Tansey %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-pan26a %I PMLR %P 5194--5202 %U https://proceedings.mlr.press/v300/pan26a.html %V 300 %X 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. Code is available at \url{https://github.com/tansey-lab/ECCIT.}
APA
Pan, M., de Mathelin, A. & Tansey, W.. (2026). Empirically Calibrated Conditional Independence Tests . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:5194-5202 Available from https://proceedings.mlr.press/v300/pan26a.html.

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