Conformal Graph Prediction with Z-Gromov Wasserstein Distances

TL;DR

This paper introduces a conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances, providing distribution-free uncertainty quantification for structured graph predictions.

Contribution

It develops a novel conformal prediction method for graphs based on Z-Gromov-Wasserstein, including an adaptive prediction set technique called SCQR for complex structured outputs.

Findings

Method achieves distribution-free coverage guarantees.

Effective in synthetic graph prediction tasks.

Utilizes permutation-invariant graph comparison.

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.