提出更抗估计误差的序列条件独立性检验方法。
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
- 基于自适应优化的核条件独立统计量，结合赌法测试
- 在高维合成与真实公平性任务中保持高检测力且误报率低
- 适合需要稳健性的真实场景，如数据隐私与公平性分析
条件独立性检验基础但困难：无额外假设下通常无法控制第一类错误。Model-X范式通过假设已知相关条件分布来应对此问题。尽管经典单次检验对假设微小偏差有一定容忍度，现有序列检验通常要求Model-X条件分布精确已知，导致估计误差时表现脆弱。本文提出新方法，显著提升对估计误差的鲁棒性。该方法将赌法测试应用于自适应优化的核条件独立统计量，配合归一化与截断-平移校准策略，在高维合成基准和真实世界公平性任务中有效抑制第一类错误膨胀，同时保持高检测力，优于现有序列Model-X方法。代码已开源：https://github.com/he-zh/SKCI。
原文摘要 · Abstract (English)
Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The "Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at https://github.com/he-zh/SKCI.
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