揭示条件独立性检验在实践中失败的根源，指出核方法误差与核选择的关键影响。
On the Hardness of Conditional Independence Testing In Practice
- 分析核方法中的条件均值嵌入误差对假阳性率的影响
- 发现选择不当的条件核会显著降低检验功效并增加误报风险
- 解释主流检验在实际中表现不佳的根本原因，适合因果推断研究者阅读
条件独立性（CI）检验是机器学习与统计学中许多重要问题的基础，如因果发现、预测公平性评估及分布外鲁棒性检验。Shah 和 Peters（2020）指出，与无条件情况不同，不存在能实现非平凡检验力的通用有限样本有效检验。尽管具有启发性，该结论基于“隐藏依赖”机制，并未充分解释实际中常见测试失败现象。本文研究基于核的条件独立性（KCI）检验，发现其背后的广义协方差测度是近年多数检验的特例。我们识别出导致其实用行为的主要因素：条件均值嵌入估计误差显著影响第一类错误；同时，合适的条件核对提升检验功效至关重要，但不当选择反而会放大第一类错误。这些发现揭示了现有方法的实际局限性。
原文摘要 · Abstract (English)
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.
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