Conformal Graph Prediction with Z-Gromov Wasserstein Distances

2026-03-02

AI Summary

This work addresses the lack of reliable uncertainty quantification in supervised prediction tasks with graph-structured outputs by extending conformal prediction to graph output spaces for the first time. The authors propose a novel nonconformity measure based on the Z-Gromov–Wasserstein distance, which is permutation-invariant and well-suited for comparing complex graph structures. Integrated within the Score Conformalized Quantile Regression (SCQR) framework, this approach constructs adaptive prediction sets that offer finite-sample coverage guarantees without requiring distributional assumptions. Empirical evaluations on synthetic benchmarks and real-world molecular recognition tasks demonstrate the method’s effectiveness, achieving theoretically grounded uncertainty quantification for graph predictions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• conformal prediction
• graph-valued outputs
• uncertainty quantification
• structured output spaces
• coverage guarantees

Innovation

• Conformal Prediction
• Z-Gromov-Wasserstein Distance
• Graph-Valued Regression
• Fused Gromov-Wasserstein
• Score Conformalized Quantile Regression