Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model message passing among nodes. The messages are often deterministic. Questions naturally arise: Does there exist uncertainty in the messages? How could we propagate such uncertainty over a graph together with messages? To address these issues, we propose a Bayesian uncertainty propagation (BUP) method, which embeds GNNs in a Bayesian modeling framework, and models predictive uncertainty of node classification with Bayesian confidence of predictive probability and uncertainty of messages. Our method proposes a novel uncertainty propagation mechanism inspired by Gaussian models. Moreover, we present an uncertainty oriented loss for node classification that allows the GNNs to clearly integrate predictive uncertainty in learning procedure. Consequently, the training examples with large predictive uncertainty will be penalized. We demonstrate the BUP with respect to prediction reliability and out-of-distribution (OOD) predictions. The learned uncertainty is also analyzed in depth. The relations between uncertainty and graph topology, as well as predictive uncertainty in the OOD cases are investigated with extensive experiments. The empirical results with popular benchmark datasets demonstrate the superior performance of the proposed method.

翻译：量化神经网络预测不确定性的研究近年来日益受到关注。本文聚焦于图神经网络（GNNs）在节点分类任务中的不确定性度量问题。现有GNN大多建模节点间的消息传递机制，这些消息通常具有确定性特征。由此自然引发两个关键问题：消息传递过程中是否存在不确定性？如何在图上实现消息与不确定性的联合传播？为应对这些挑战，我们提出贝叶斯不确定性传播（BUP）方法，将GNN嵌入贝叶斯建模框架，通过预测概率的贝叶斯置信度与消息不确定性共同建模节点分类的预测不确定性。该方法创新性地提出基于高斯模型的不确定性传播机制，并针对节点分类任务设计面向不确定性的损失函数，使GNN能在学习过程中明确整合预测不确定性，从而对高不确定性训练样本施加惩罚。我们通过预测可靠性与分布外检测对BUP方法进行验证，深度剖析学习到的不确定性特性，并通过大量实验探究不确定性-图拓扑关系及分布外场景中的预测不确定性。基于主流基准数据集的实证结果表明，所提方法具有优越性能。