{"id":1153586,"date":"2025-10-27T15:05:21","date_gmt":"2025-10-27T22:05:21","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=1153586"},"modified":"2025-10-27T15:05:21","modified_gmt":"2025-10-27T22:05:21","slug":"on-the-hardness-of-conditional-independence-testing-in-practice","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/on-the-hardness-of-conditional-independence-testing-in-practice\/","title":{"rendered":"On the Hardness of Conditional Independence Testing In Practice"},"content":{"rendered":"<p>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 \u201chiding\u201d dependence) does not seem to explain the frequent practical failures observed with popular CI tests. We investigate the Kernel-based Conditional Independence (KCI) test \u2013 of which we show the Generalized Covariance Measure underlying many recent tests is\u00a0<em>nearly<\/em>\u00a0a special case \u2013 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.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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. 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