Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice, and achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22% higher coverage and 50% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.

翻译：不确定性量化在图中神经网络高风险领域中至关重要，但仍是重大挑战。在图场景中，消息传递常依赖可交换性等强假设，这些假设在实践中鲜少成立，且实现可靠的不确定性量化通常需要昂贵的重采样或事后校准。为解决这些问题，我们提出无分位数预测区间图神经网络，该框架基于分位数回归，通过直接优化覆盖率和区间宽度实现图神经网络的不确定性量化，无需分位数输入或后处理。无分位数预测区间图神经网络采用双头架构解耦预测与不确定性，并通过无分位数联合损失函数仅使用标签监督进行训练。这种设计支持高效训练并生成稳健的预测区间，在温和假设下具有渐近覆盖率和近最优宽度的理论保证。在19个合成与真实世界基准测试上的实验表明，无分位数预测区间图神经网络相比基线方法平均覆盖率提高22%，区间宽度缩小50%，同时保持对噪声和结构偏移的鲁棒性与效率。