KREDIT: High-Dimensional Conditional Independence Testing via Kernel-Residualized Distances

Conditional independence testing underpins graphical model learning and causal discovery, yet high-dimensional inference with estimated conditional distance features remains challenging. To this end, we introduce KREDIT (Kernel-Residualized Distance Testing), a nonparametric framework combining two-sided distance residualization, independent conditional-mean fitting, and off-diagonal joint studentization. An exact pair-kernel analysis separates sampling variation from directional regression error. Under explicit moment, spectral, and prediction conditions, we prove feasible Gaussian limits, finite-sample approximation bounds, and dimension-dependent convergence rates. We further establish shrinking-signal power guarantees, empirical-variance inference under nondegenerate alternatives, and testing and estimation lower bounds in a rectangular Gaussian subexperiment. A specified nonlinear family remains detectable despite zero linear covariances. Simulation studies verify linear and nonlinear settings under which stratum-calibrated KREDIT has higher empirical power than the benchmark methods, with size near the nominal level. Wine chemistry and rolling gold–inflation analyses further illustrate its practical utility.