Structural Conditional Independence Test via Neural Quantile Resolution

Khoa Nguyen, Bao Duong, Thin Nguyen

Conditional independence testing is difficult when dependence is weak, localized, or expressed through distributional changes rather than a global mean shift. Existing tests usually return a scalar statistic or p-value, which can detect rejection but gives limited resolution about where the conditional law changes. We propose QRCIT, a quantile-resolution conditional independence test that compares P(X | Z) and P(X | Y, Z) through an amortized quantile deformation. A lightweight residual quantile-flow model first learns the baseline conditional quantile law and then learns the additional deformation induced by Y, yielding both a calibrated global test statistic and an inspectable deformation field over context and quantile level. We also introduce the Structural Dependency Benchmark (SDB), which evaluates real-world-inspired dependence structures, such as context-local, tail-only, sign-reversing, moving-ridge, and mean-neutral patterns. Across synthetic PNL and SDB benchmarks, QRCIT improves detection of structured alternatives while maintaining empirical Type-I control. Increasing quantile resolution consistently improves merged-SDB power, and the local-rescue strategy sharpens…