Fast Nonparametric Conditional Independence Testing via Two-Stage Regression
通过两阶段回归快速进行非参数条件独立检验AI 解读 ↓
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通过两阶段回归快速进行非参数条件独立检验
- 研究问题
- 基于约束的因果发现需要大量条件独立检验，如何在非线性条件依赖下兼顾计算速度与零假设校准？
- 方法与思路
- 作者提出 BLITZ，先用低阶多项式去除宽尺度依赖，再以浅树残差化非线性特征，检验交叉协方差并近似零分布。
- 材料陈述的贡献
- 摘要称，两阶段结构降低浅树面对的有效复杂度；模拟中校准较好且运行较快，因果发现实验也展示了结构恢复表现。
- 阅读关注点
- 应核对残差条件均值偏误的控制条件、矩匹配卡方近似的有效性，以及维度、样本规模和非线性强度下的速度与校准。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出完整理论条件，快速检验不能单独保证因果图正确恢复。
原文摘要
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.