Out-of-distribution (OOD) generalization on graphs is drawing widespread attention. However, existing efforts mainly focus on the OOD issue of correlation shift. While another type, covariate shift, remains largely unexplored but is the focus of this work. From a data generation view, causal features are stable substructures in data, which play key roles in OOD generalization. While their complementary parts, environments, are unstable features that often lead to various distribution shifts. Correlation shift establishes spurious statistical correlations between environments and labels. In contrast, covariate shift means that there exist unseen environmental features in test data. Existing strategies of graph invariant learning and data augmentation suffer from limited environments or unstable causal features, which greatly limits their generalization ability on covariate shift. In view of that, we propose a novel graph augmentation strategy: Adversarial Causal Augmentation (AdvCA), to alleviate the covariate shift. Specifically, it adversarially augments the data to explore diverse distributions of the environments. Meanwhile, it keeps the causal features invariant across diverse environments. It maintains the environmental diversity while ensuring the invariance of the causal features, thereby effectively alleviating the covariate shift. Extensive experimental results with in-depth analyses demonstrate that AdvCA can outperform 14 baselines on synthetic and real-world datasets with various covariate shifts.
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