ADVERSARIAL CAUSAL AUGMENTATION FOR GRAPH COVARIATE SHIFT Anonymous

Abstract

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 stable 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.



Covariate shift is in stark contrast to correlation shift w.r.t. causal and environmental features of datafoot_0 . Specifically, from a data generation view, causal featuresfoot_1 are the substructures of the entire graphs that truly reflect the predictive property of data, while their complementary parts are the environmental features that are noncausal to the predictions. Following prior studies (Arjovsky et al., 2019; Wu et al., 2022b) , we assume causal features are stable across distributions, in contrast to the environmental features. Correlation shift denotes that environments and labels establish inconsistent statistical correlations in training and test data; whereas, covariate shift We provide detailed discussions of these two distribution shifts in Appendix C. We provide a formal definition in Assumption 1.1



Figure 1: P train and P test denote the training and test distributions. P drop and P ours represent the distributions of augmented data via DropEdge and AdvCA. AdvCA establishes a smaller covariate shift (↔) with test distribution than DropEdge (↔).

