There is increasing evidence suggesting neural networks' sensitivity to distribution shifts, so that research on out-of-distribution (OOD) generalization comes into the spotlight. Nonetheless, current endeavors mostly focus on Euclidean data, and its formulation for graph-structured data is not clear and remains under-explored, given the two-fold fundamental challenges: 1) the inter-connection among nodes in one graph, which induces non-IID generation of data points even under the same environment, and 2) the structural information in the input graph, which is also informative for prediction. In this paper, we formulate the OOD problem for node-level prediction on graphs and develop a new domain-invariant learning approach, named Explore-to-Extrapolate Risk Minimization, that facilitates GNNs to leverage invariant graph features for prediction. The key difference to existing invariant models is that we design multiple context explorers (specified as graph editers in our case) that are adversarially trained to maximize the variance of risks from multiple virtual environments. Such a design enables the model to extrapolate from a single observed environment which is the common case for node-level prediction. We prove the validity of our method by theoretically showing its guarantee of a valid OOD solution and further demonstrate its power on various real-world datasets for handling distribution shifts from artificial spurious features, cross-domain transfers and dynamic graph evolution.

本文提出了一种基于不变性学习和风险最小化的方法，实现图神经网络对于图结构数据上的越域通用性问题进行预测和预测不确定性的估计。

处理图上的分布偏移: 一个不变性的视角