CalPro: Prior-Aware Evidential Conformal Prediction with Structure-Aware Sensitivity Bounds for Protein Structures

Deep protein structure predictors such as AlphaFold provide confidence estimates (e.g., pLDDT) that are not calibrated and degrade under distribution shifts across experimental modalities, temporal changes, and disordered regions. We introduce CalPro, a prior-aware evidential conformal framework for shift-robust uncertainty quantification. CalPro combines three components: (i) a geometric evidential head outputting Normal Inverse Gamma distributions via graph neural networks; (ii) a differentiable calibration surrogate that shapes representations during training, followed by split-conformal calibration for finite-sample coverage; and (iii) domain priors (disorder, flexibility) encoded as soft constraints on predicted uncertainty. Theoretically, we derive structure-aware sensitivity bounds for coverage degradation under distribution shift using PAC-Bayesian control over ambiguity sets, quantifying how miscoverage increases with model complexity and shift magnitude. Empirically, CalPro achieves at most 5 percentage points coverage degradation across modalities compared to 15 to 25 points for baselines, reduces calibration error by 30\% to 50\%, and improves downstream docking success from 52\% to 75\% when filtering by uncertainty. The framework extends beyond proteins to structured regression tasks where priors encode local reliability.