  Graph Neural Networks (GNNs) show promising results for graph tasks. However,
existing GNNs' generalization ability will degrade when there exist
distribution shifts between testing and training graph data. The cardinal
impetus underlying the severe degeneration is that the GNNs are architected
predicated upon the I.I.D assumptions. In such a setting, GNNs are inclined to
leverage imperceptible statistical correlations subsisting in the training set
to predict, albeit it is a spurious correlation. In this paper, we study the
problem of the generalization ability of GNNs in Out-Of-Distribution (OOD)
settings. To solve this problem, we propose the Learning to Reweight for
Generalizable Graph Neural Network (L2R-GNN) to enhance the generalization
ability for achieving satisfactory performance on unseen testing graphs that
have different distributions with training graphs. We propose a novel nonlinear
graph decorrelation method, which can substantially improve the
out-of-distribution generalization ability and compares favorably to previous
methods in restraining the over-reduced sample size. The variables of the graph
representation are clustered based on the stability of the correlation, and the
graph decorrelation method learns weights to remove correlations between the
variables of different clusters rather than any two variables. Besides, we
interpose an efficacious stochastic algorithm upon bi-level optimization for
the L2R-GNN framework, which facilitates simultaneously learning the optimal
weights and GNN parameters, and avoids the overfitting problem. Experimental
results show that L2R-GNN greatly outperforms baselines on various graph
prediction benchmarks under distribution shifts.
