Individual and Structural Graph Information Bottlenecks for
  Out-of-Distribution Generalization
Ling Yang Jiayi Zheng Heyuan Wang Zhongyi Liu Zhilin Huang Shenda Hong Wentao Zhang Bin Cui
Out-of-distribution (OOD) graph generalization are critical for many
real-world applications. Existing methods neglect to discard spurious or noisy
features of inputs, which are irrelevant to the label. Besides, they mainly
conduct instance-level class-invariant graph learning and fail to utilize the
structural class relationships between graph instances. In this work, we
endeavor to address these issues in a unified framework, dubbed Individual and
Structural Graph Information Bottlenecks (IS-GIB). To remove class spurious
feature caused by distribution shifts, we propose Individual Graph Information
Bottleneck (I-GIB) which discards irrelevant information by minimizing the
mutual information between the input graph and its embeddings. To leverage the
structural intra- and inter-domain correlations, we propose Structural Graph
Information Bottleneck (S-GIB). Specifically for a batch of graphs with
multiple domains, S-GIB first computes the pair-wise input-input,
embedding-embedding, and label-label correlations. Then it minimizes the mutual
information between input graph and embedding pairs while maximizing the mutual
information between embedding and label pairs. The critical insight of S-GIB is
to simultaneously discard spurious features and learn invariant features from a
high-order perspective by maintaining class relationships under multiple
distributional shifts. Notably, we unify the proposed I-GIB and S-GIB to form
our complementary framework IS-GIB. Extensive experiments conducted on both
node- and graph-level tasks consistently demonstrate the superior
generalization ability of IS-GIB. The code is available at
https://github.com/YangLing0818/GraphOOD.