  Graph Neural Network (GNN) has demonstrated extraordinary performance in
classifying graph properties. However, due to the selection bias of training
and testing data (e.g., training on small graphs and testing on large graphs,
or training on dense graphs and testing on sparse graphs), distribution
deviation is widespread. More importantly, we often observe \emph{hybrid
structure distribution shift} of both scale and density, despite of one-sided
biased data partition. The spurious correlations over hybrid distribution
deviation degrade the performance of previous GNN methods and show large
instability among different datasets. To alleviate this problem, we propose
\texttt{OOD-GMixup} to jointly manipulate the training distribution with
\emph{controllable data augmentation} in metric space. Specifically, we first
extract the graph rationales to eliminate the spurious correlations due to
irrelevant information. Secondly, we generate virtual samples with perturbation
on graph rationale representation domain to obtain potential OOD training
samples. Finally, we propose OOD calibration to measure the distribution
deviation of virtual samples by leveraging Extreme Value Theory, and further
actively control the training distribution by emphasizing the impact of virtual
OOD samples. Extensive studies on several real-world datasets on graph
classification demonstrate the superiority of our proposed method over
state-of-the-art baselines.
