  Graph neural networks (GNNs) have been demonstrated to perform well in graph
representation learning, but always lacking in generalization capability when
tackling out-of-distribution (OOD) data. Graph invariant learning methods,
backed by the invariance principle among defined multiple environments, have
shown effectiveness in dealing with this issue. However, existing methods
heavily rely on well-predefined or accurately generated environment partitions,
which are hard to be obtained in practice, leading to sub-optimal OOD
generalization performances. In this paper, we propose a novel graph invariant
learning method based on invariant and variant patterns co-mixup strategy,
which is capable of jointly generating mixed multiple environments and
capturing invariant patterns from the mixed graph data. Specifically, we first
adopt a subgraph extractor to identify invariant subgraphs. Subsequently, we
design one novel co-mixup strategy, i.e., jointly conducting environment Mixup
and invariant Mixup. For the environment Mixup, we mix the variant
environment-related subgraphs so as to generate sufficiently diverse multiple
environments, which is important to guarantee the quality of the graph
invariant learning. For the invariant Mixup, we mix the invariant subgraphs,
further encouraging to capture invariant patterns behind graphs while getting
rid of spurious correlations for OOD generalization. We demonstrate that the
proposed environment Mixup and invariant Mixup can mutually promote each other.
Extensive experiments on both synthetic and real-world datasets demonstrate
that our method significantly outperforms state-of-the-art under various
distribution shifts.
