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.

翻译：监督式图预测处理输出为结构化图的回归问题。尽管已有多种图值预测方法，但原则性的不确定性量化仍存在局限。我们提出了一种适用于图值输出的共形预测框架，在结构化输出空间中提供无分布假设的覆盖保证。该方法通过Z-Gromov-Wasserstein距离定义非符合性度量，在实际中利用融合Gromov-Wasserstein距离（FGW）实现，从而支持预测图与候选图之间的置换不变比较。为了获得自适应预测集，我们引入了分数共形分位数回归（SCQR），这是对共形分位数回归（CQR）的扩展，旨在处理图值输出等复杂输出空间。我们在合成任务上对所提方法进行了评估。