Structural Conditional Independence Test via Neural Quantile Resolution

Researchers posted arXiv:2611.07165v1, introducing QRCIT, a quantile-resolution conditional independence test that compares P(X|Z) and P(X|Y,Z) through a quantile deformation learned by a shared model, backed by a lightweight residual quantile-flow model. The paper also introduces the Structural Dependency Benchmark (SDB), covering context-local, tail-only, sign-reversing, moving-ridge and mean-neutral dependence patterns, and reports that higher quantile resolution improves merged-SDB power at moderate sample sizes. QRCIT showed competitive performance and interpretable deformation patterns on Sachs, METABRIC breast cancer and CCLE/PLX4720 data.

arXiv:2611.07165v1 Announce Type: new Abstract: 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 summarizes evidence against independence but does not describe 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 a quantile deformation learned by a shared model. A lightweight residual quantile-flow model first learns the baseline conditional quantile law and then learns the additional deformation induced by Y, yielding a global predictive-gain statistic with conditional-randomization calibration and an inspectable deformation field over context and quantile level. We also introduce the Structural Dependency Benchmark SDB , which evaluates dependence structures motivated by real applications, such as context-local, tail-only, sign-reversing, moving-ridge, and mean-neutral patterns. Across synthetic post-nonlinear PNL and SDB benchmarks, QRCIT improves detection of structured alternatives, with empirical Type-I behavior evaluated across settings. Higher quantile resolution improves merged-SDB power at moderate sample sizes, while diagnostics restricted to known affected regions improve detection of localized dependence. On Sachs, METABRIC breast cancer, and CCLE/PLX4720, QRCIT provides competitive real-data performance and interpretable deformation patterns. These results support quantile-resolved conditional-law deformation as a practical framework for testing and diagnosing structured conditional dependence.