为图结构输出提供无需假设的不确定性量化方法，提升预测可靠性。
Conformal Graph Prediction with Z-Gromov-Wasserstein Distances
- 用Z-Gromov-Wasserstein距离衡量图的不匹配程度，支持图间排列不变比较
- 在分子识别任务中实现95%覆盖率且预测集更紧凑
- 适用于需要可信图预测的化学、生物等领域的研究者
监督图预测解决输出为结构化图的回归问题。尽管已有多种图值预测方法，但合理的不确定性量化仍受限。本文提出一种针对图值输出的合取预测框架，在结构化输出空间中提供分布无关的覆盖率保证。方法通过Z-Gromov-Wasserstein距离定义非一致性度量，并在实践中采用融合型格罗莫夫-沃瑟斯坦（FGW）实现，可对预测图与候选图进行排列不变比较。为获得自适应预测集，引入评分合取分位数回归（SCQR），扩展了合取分位数回归（CQR）以处理复杂输出空间如图值输出。我们在一个合成任务和真实的分子识别问题上评估该方法。
原文摘要 · Abstract (English)
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.
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