Causal Discovery from Quantile Separation

Causal discovery exploits asymmetries in uncertainty measures such as variance. However, many uncertainty-based methods rely on additive-noise assumptions. We extend this principle to structural causal models beyond additive noise using the Pairwise Average Separation Score (PASS), which measures uncertainty through quantile separation. Under a quantile-separation condition, our algorithm uses the same nodewise PASS score for both topological ordering and parent recovery. Under stated conditions, we establish graph-recovery consistency for a growing tensor-spline estimator. The criterion accommodates heavy-tailed distributions, including those with infinite variance, under suitable fractional-moment conditions. Experiments demonstrate robust graph recovery across additive-noise, heteroskedastic-noise, and heavy-tailed settings, with evaluations on three real-data benchmarks.