While graph neural networks (GNNs) are widely used for node and graph representation learning tasks, the reliability of GNN uncertainty estimates under distribution shifts remains relatively under-explored. Indeed, while post-hoc calibration strategies can be used to improve in-distribution calibration, they need not also improve calibration under distribution shift. However, techniques which produce GNNs with better intrinsic uncertainty estimates are particularly valuable, as they can always be combined with post-hoc strategies later. Therefore, in this work, we propose G-$\Delta$UQ, a novel training framework designed to improve intrinsic GNN uncertainty estimates. Our framework adapts the principle of stochastic data centering to graph data through novel graph anchoring strategies, and is able to support partially stochastic GNNs. While, the prevalent wisdom is that fully stochastic networks are necessary to obtain reliable estimates, we find that the functional diversity induced by our anchoring strategies when sampling hypotheses renders this unnecessary and allows us to support G-$\Delta$UQ on pretrained models. Indeed, through extensive evaluation under covariate, concept and graph size shifts, we show that G-$\Delta$UQ leads to better calibrated GNNs for node and graph classification. Further, it also improves performance on the uncertainty-based tasks of out-of-distribution detection and generalization gap estimation. Overall, our work provides insights into uncertainty estimation for GNNs, and demonstrates the utility of G-$\Delta$UQ in obtaining reliable estimates.

翻译：尽管图神经网络（GNN）已广泛用于节点与图表示学习任务，其在分布偏移下不确定性估计的可靠性仍相对缺乏深入探索。事实上，虽然事后校准策略可用于改善分布内校准效果，但这些策略未必能同时提升分布偏移下的校准性能。然而，能够产生具备更优内在不确定性估计的GNN技术具有特殊价值，因为它们始终可与事后策略结合使用。为此，本研究提出G-$\Delta$UQ——一种旨在提升图神经网络内在不确定性估计的新型训练框架。该框架通过创新的图锚定策略，将随机数据中心化原理适配至图数据，并能支持部分随机化的GNN。尽管普遍观点认为完全随机化网络是获得可靠估计的必要条件，但我们发现通过假设采样时锚定策略所诱导的函数多样性使得这一条件不再必需，从而允许我们在预训练模型上实现G-$\Delta$UQ。通过在协变量偏移、概念偏移和图规模偏移场景下的广泛评估，我们证明G-$\Delta$UQ能为节点分类与图分类任务带来校准效果更优的GNN。此外，该方法还能提升基于不确定性的任务表现，包括分布外检测与泛化间隙估计。总体而言，本研究为图神经网络的不确定性估计提供了新见解，并验证了G-$\Delta$UQ在获取可靠估计方面的实用价值。