EviCD: Structured Evidential Uncertainty for Causal Discovery

When causal graphs support downstream decisions, knowing which predicted relations warrant commitment can be as important as the graph itself. Existing methods typically return a point estimate or an edge confidence, which does not by itself reveal whether uncertainty reflects weak commitment or incompatible relation-specific assessments. We propose EviCD, a graph neural network that predicts per-pair Dempster–Shafer mass functions over four modeled relations: $X_i\to X_j$, $X_j\to X_i$, latent confounding without a direct edge, and no modeled relation. A restricted-focal architecture yields two complementary model-level diagnostics: vacuity $m(\Omega )$, measuring support left uncommitted, and conflict $K$, measuring incompatibility among channel-level assessments. These quantities support selective prediction, allowing EviCD to abstain on high-vacuity pairs under a retained-accuracy guarantee conditional on calibration. EviCD does not resolve observational non-identifiability; its outputs are simulator-relative assessments. On the main synthetic benchmark, EviCD attains the highest aggregate selective-prediction score among methods with an available selective confidence, while maintaining competitive structural accuracy and providing an explicit continuous confounding score. Controlled perturbations further show that increasing latent-confounder strength primarily changes $K$, whereas changes in noise, sample size, and signal strength primarily affect $m(\Omega )$.