提出快速校准的非参数条件独立性检验方法,提升因果发现效率与可靠性。
Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

- 先用多项式回归消除全局平滑依赖,再用浅层树残差化特征
- 在1秒内完成测试,模拟中零假设校准优于现有快速方法
- 适合需要数千次测试的约束型因果发现算法,尤其处理非线性关系
基于约束的因果发现依赖重复的条件独立性检验,但快速的非参数检验常牺牲校准精度,尤其在变量通过非线性关系依赖于条件集时。我们提出BLITZ(Broad-to-Local Independence Testing via residualiZation),一种可在1秒内运行的非参数条件独立性检验方法,兼顾准确性与速度,满足约束型因果发现算法所需的上千次查询。BLITZ首先使用低阶多项式回归去除对条件集的广泛平滑依赖,再通过小规模非线性特征映射并用浅层树回归进行残差化。最终统计量检验残差交叉协方差,并采用矩匹配的卡方近似估计零分布。理论分析表明,两阶段设计降低了树模型需应对的有效复杂度,使浅层树既能控制残差条件均值偏差,又避免过拟合。仿真结果显示,BLITZ在零假设校准上优于快速核、随机特征和回归基线方法,同时保持测试速度领先。在合成图和流式细胞数据上的因果发现实验中,BLITZ能更可靠地确定保留邻接关系的定向结果,并实现具有竞争力的结构恢复。这些结果表明,广域到局部残差化是一种实用的、可扩展的非参数条件独立性检验路径,适用于因果发现。
原文摘要 · Abstract (English)
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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