On the Hardness of Conditional Independence Testing In Practice

Fuente: arXiv
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Autori principali: He, Zheng, Pogodin, Roman, Li, Yazhe, Deka, Namrata, Gretton, Arthur, Sutherland, Danica J.
Natura: Preprint
Pubblicazione: 2025
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author He, Zheng
Pogodin, Roman
Li, Yazhe
Deka, Namrata
Gretton, Arthur
Sutherland, Danica J.
author_facet He, Zheng
Pogodin, Roman
Li, Yazhe
Deka, Namrata
Gretton, Arthur
Sutherland, Danica J.
contents Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test - of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case - and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type-I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type-I error.
format Preprint
id arxiv_https___arxiv_org_abs_2512_14000
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the Hardness of Conditional Independence Testing In Practice
He, Zheng
Pogodin, Roman
Li, Yazhe
Deka, Namrata
Gretton, Arthur
Sutherland, Danica J.
Machine Learning
Methodology
Tests of conditional independence (CI) underpin a number of important problems in machine learning and statistics, from causal discovery to evaluation of predictor fairness and out-of-distribution robustness. Shah and Peters (2020) showed that, contrary to the unconditional case, no universally finite-sample valid test can ever achieve nontrivial power. While informative, this result (based on "hiding" dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test - of which we show the Generalized Covariance Measure underlying many recent tests is nearly a special case - and identify the major factors underlying its practical behavior. We highlight the key role of errors in the conditional mean embedding estimate for the Type-I error, while pointing out the importance of selecting an appropriate conditioning kernel (not recognized in previous work) as being necessary for good test power but also tending to inflate Type-I error.
title On the Hardness of Conditional Independence Testing In Practice
topic Machine Learning
Methodology
url https://arxiv.org/abs/2512.14000