  Graph is a flexible and effective tool to represent complex structures in
practice and graph neural networks (GNNs) have been shown to be effective on
various graph tasks with randomly separated training and testing data. In real
applications, however, the distribution of training graph might be different
from that of the test one (e.g., users' interactions on the user-item training
graph and their actual preference on items, i.e., testing environment, are
known to have inconsistencies in recommender systems). Moreover, the
distribution of test data is always agnostic when GNNs are trained. Hence, we
are facing the agnostic distribution shift between training and testing on
graph learning, which would lead to unstable inference of traditional GNNs
across different test environments. To address this problem, we propose a novel
stable prediction framework for GNNs, which permits both locally and globally
stable learning and prediction on graphs. In particular, since each node is
partially represented by its neighbors in GNNs, we propose to capture the
stable properties for each node (locally stable) by re-weighting the
information propagation/aggregation processes. For global stability, we propose
a stable regularizer that reduces the training losses on heterogeneous
environments and thus warping the GNNs to generalize well. We conduct extensive
experiments on several graph benchmarks and a noisy industrial recommendation
dataset that is collected from 5 consecutive days during a product promotion
festival. The results demonstrate that our method outperforms various SOTA GNNs
for stable prediction on graphs with agnostic distribution shift, including
shift caused by node labels and attributes.
