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）被广泛用于节点和图表示学习任务，但在分布偏移下GNN不确定性估计的可靠性仍相对未被充分探索。实际上，虽然事后校准策略可用于改善分布内校准，但它们未必能同时提升分布偏移下的校准效果。然而，能够产生具有更优内在不确定性估计的GNN的技术尤为宝贵，因为它们可随时与事后策略结合使用。因此，本文提出G-$\Delta$UQ，一种旨在改进GNN内在不确定性估计的新型训练框架。该框架通过新颖的图锚定策略将随机数据中心化原理适配至图数据，并支持部分随机化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，采样假设时由锚定策略诱导的函数多样性消除了这一需求，使得我们能够在预训练模型上支持G-$\Delta$UQ。事实上，通过在协变量、概念和图规模偏移下的广泛评估，我们表明G-$\Delta$UQ能为节点和图分类任务带来校准更优的GNN。此外，它还能提升基于不确定性的任务（如分布外检测与泛化差距估计）的性能。总体而言，本研究为GNN不确定性估计提供了见解，并展示了G-$\Delta$UQ在获取可靠估计中的效用。