Explainable machine learning (XML) pipelines applied to composite mental health outcomes can produce apparently-robust, cross-population-stable risk hierarchies that are largely artefacts of how the outcome was constructed. We demonstrate this using an ElasticNet pipeline applied to 886 medical students at the University of Lausanne (primary cohort, 2022), validated across 2,580 longitudinal observations at three time points and 701 non-medical students from eight faculties; all three datasets share identical instruments. The pipeline produces a hierarchy in which trait anxiety and health satisfaction dominate wherever the outcome is measured, with Kendall $τ= 1.0$ for the top-two positions across all five evaluation sets and consistent transfer performance ($R^2$: 0.41-0.49). Two residualization experiments, which isolate shared variance between correlated variables via regression, reveal the mechanism: when trait anxiety (STAI-T) is residualized against the co-included depression subscale (CES-D, $r = 0.72$), model $R^2$ drops from 0.41 to 0.16 and STAI-T falls from rank 1 to rank 6; when burnout subscales are residualized against CES-D, $R^2$ collapses to 0.016. Prediction intervals average 35.4 units on a 0-100 scale (2.4 outcome standard deviations), independently ruling out individual-level deployment. The residualization protocol is the paper's transferable contribution: any XAI study combining correlated predictor and outcome constructs should apply this check before interpreting apparent stability as a finding.
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.