Conformal Graph Prediction with Z-Gromov Wasserstein Distances

Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the {Z-Gromov}–{Wasserstein} distance, instantiated in practice through Fused Gromov–{Wasserstein} (FGW), enabling permutation-invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) to handle complex output spaces such as graph-valued outputs. We evaluate the proposed approach on a synthetic task and a real problem of molecule identification.