Improving Graph Out-of-distribution Generalization Beyond Causality

Existing methods for graph out-of-distribution (OOD) generalization primarily rely on empirical studies on synthetic datasets. Such approaches tend to overemphasize the causal relationships between invariant sub-graphs and labels, thereby neglecting the non-negligible role of environment in real-world scenarios. In contrast to previous studies that impose rigid independence assumptions on environments and invariant sub-graphs, this paper presents the theorems of environment-label dependency and mutable rationale invariance, where the former characterizes the usefulness of environments in determining graph labels while the latter refers to the mutable importance of graph rationales. Based on analytic investigations, a novel variational inference based method named ``Probability Dependency on Environments and Rationales for OOD Graphs on Real-world Data'' (DEROG) is introduced. To alleviate the adverse effect of unknown prior knowledge on environments and rationales, DEROG utilizes generalized Bayesian inference. Further, DEROG employs an EM-based algorithm for optimization. Finally, extensive experiments on real-world datasets under different distribution shifts are conducted to show the superiority of DEROG. Our code is publicly available at https://github.com/LEOXC1571/DEROG.