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

TL;DR

CalPro addresses calibrated uncertainty for protein-structure predictions under distribution shift by integrating a geometric evidential head with a differentiable conformal layer and domain priors. The method outputs a Normal–Inverse–Gamma predictive family and uses a smooth conformal surrogate to achieve finite-sample coverage, with PAC-Bayesian structure-aware guarantees under ambiguity sets around the calibration distribution. Empirically, CalPro yields near-nominal coverage across modality shifts, sharper intervals in informative regions, and tangible gains in docking and active learning, with demonstrated transfer to non-biological structured regression. This combination of theory and practice provides a scalable, principled approach to uncertainty quantification in structured scientific domains where priors encode local reliability. The framework is broadly applicable to other structured regression problems beyond proteins while delivering practically meaningful improvements in decision-making under uncertainty.

Abstract

Deep protein structure predictors such as AlphaFold provide confidence estimates (e.g., pLDDT) that are often miscalibrated and degrade under distribution shifts across experimental modalities, temporal changes, and intrinsically disordered regions. We introduce CalPro, a prior-aware evidential-conformal framework for shift-robust uncertainty quantification. CalPro combines (i) a geometric evidential head that outputs Normal-Inverse-Gamma predictive distributions via a graph-based architecture; (ii) a differentiable conformal layer that enables end-to-end training with finite-sample coverage guarantees; and (iii) domain priors (disorder, flexibility) encoded as soft constraints. We derive structure-aware coverage guarantees under distribution shift using PAC-Bayesian bounds over ambiguity sets, and show that CalPro maintains near-nominal coverage while producing tighter intervals than standard conformal methods in regions where priors are informative. Empirically, CalPro exhibits at most 5% coverage degradation across modalities (vs. 15-25% for baselines), reduces calibration error by 30-50%, and improves downstream ligand-docking success by 25%. Beyond proteins, CalPro applies to structured regression tasks in which priors encode local reliability, validated on non-biological benchmarks.

Figures (6)

• Figure 1: Empirical coverage vs. PAC-Bayesian bound from Corollary \ref{['cor:coverage']} under increasing shift magnitude $\epsilon$ for modality shift (left) and synthetic perturbations (right). The curves show that the bound is conservative but tracks the empirical degradation closely.
• Figure 2: Group-wise coverage and ECE for CalPro and baselines across ordered/disordered and secondary-structure partitions.
• Figure 3: Calibration curves showing predicted versus empirical frequencies for CalPro and baseline methods at 90% nominal coverage.
• Figure 4: Scatter plots of predicted uncertainty versus true error for different perturbation types.
• Figure 5: Docking success rate versus uncertainty threshold for CalPro and pLDDT filtering strategies.

Theorems & Definitions (3)

• Theorem 4.2: PAC-Bayesian coverage control under shift
• Corollary 4.3: Worst-case coverage under shift
• Theorem 4.4: Prior-aware efficiency improvement