通过两阶段回归的快速非参数条件独立性检验
Fast Nonparametric Conditional Independence Testing via Two-Stage Regression
AI总结：
提出BLITZ方法，通过两阶段回归（低阶多项式+浅层树）快速消除条件集影响，实现校准良好的非参数条件独立性检验，适用于因果发现。
摘要：
基于约束的因果发现依赖于重复的条件独立性检验，但快速非参数检验往往牺牲校准性，尤其是当变量通过非线性关系依赖于条件集时。我们提出了BLITZ（Broad-to-Local Independence Testing via residualiZation），一种非参数条件独立性检验，旨在在一秒内运行良好，同时保持约束因果发现算法执行数千次查询所需的准确性。BLITZ首先使用低阶多项式回归消除对条件集的广泛平滑依赖，然后应用一个小型非线性特征映射，并通过浅层树回归对这些特征进行残差化。得到的统计量检验残差互协方差，并采用矩匹配卡方近似于零分布。我们从理论上证明，两阶段设计降低了树残差化器面临的有效复杂度，使得浅层树能够控制残差条件均值偏差，同时避免过度过拟合。在模拟中，BLITZ提供了比快速核、随机特征和基于回归的竞争者更好的零校准，同时保持所测试方法中最快的速度之一。在合成图和流式细胞术数据的因果发现实验中，BLITZ在保留的邻接中产生了更可靠的端点方向，并具有竞争力的结构恢复。这些结果表明，从宽到局部残差化是实现因果发现中校准、可扩展的非参数条件独立性检验的实用途径。
英文摘要：
Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.
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