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.

翻译：监督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，但原理性的不确定性量化仍然有限。我们提出了一种针对图值输出的保形预测框架，为结构化输出空间提供无分布覆盖保证。该方法通过Z-Gromov-Wasserstein距离定义非保形性度量，实践中通过融合Gromov-Wasserstein（FGW）距离实现，从而支持预测图与候选图之间的置换不变比较。为获得自适应预测集，我们提出了分数保形分位数回归（SCQR），这是将保形分位数回归（CQR）扩展到处理复杂输出空间（如图值输出）的推广方法。我们在合成任务和分子识别的实际问题上评估了所提方法。