Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

2026-06-16

AI Summary

Existing fast nonparametric conditional independence tests suffer from poor calibration when nonlinear relationships exist between variables and the conditioning set, hindering their applicability in large-scale causal discovery. This work proposes BLITZ, a novel method that combines global low-order polynomial regression with local shallow tree models in a two-stage residualization procedure: first removing globally smooth dependencies on the conditioning set, then further residualizing nonlinear features. A test statistic is constructed based on the cross-covariance of the resulting residuals. This strategy substantially reduces model complexity, achieving both computational efficiency and improved calibration of the null distribution. Experiments demonstrate that BLITZ outperforms current fast methods on both synthetic and real-world single-cell flow cytometry data, offering more accurate type-I error control, reliable causal graph recovery, and competitive computational speed.

Abstract

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.

Problem

• conditional independence testing
• causal discovery
• nonparametric methods
• calibration
• constraint-based algorithms

Innovation

• conditional independence testing
• two-stage regression
• residualization
• causal discovery
• nonparametric methods