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This research introduces a novel conformal prediction framework for supervised graph-valued outputs that ensures distribution-free coverage guarantees using Z-Gromov-Wasserstein distances. By extending Conformalized Quantile Regression to handle complex structured spaces like graphs, the method enables robust uncertainty quantification in tasks such as molecule identification without requiring specific data distributions. The approach represents a significant advancement in statistical learning for scenarios where output structures are non-Euclidean and permutation-invariant comparisons are essential.
Conformal Graph Prediction with Z-Gromov-Wasserstein Distances
arXiv:2603.02460v5 Announce Type: replace-cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2603.02460 [stat.ML]
(or arXiv:2603.02460v5 [stat.ML] for this version)
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