GNN Domain Adaptation using Optimal Transport

While Graph Convolutional Networks (GCNs) have recently grown in popularity due to their excellent performance on graph data, their performance under domain shift has not been studied extensively. In this work, we first explore the ability of GCNs to generalize to out-of-distribution data using contextual stochastic block models (CSBMs) on the node classification task. Our results in this area provide the first generalization criteria for GCNs on feature distribution and structure changes. Next we examine a popular Unsupervised Domain Adaptation (UDA) covariate shift assumption and demonstrate that it rarely holds for graph data. Motivated by these results, we propose addressing bias in graph models using domain adaptation with optimal transport - GDOT which features a transportation plan that minimizes the cost of the joint feature and estimated label distribution $P(X,\hat{Y})$ between source and target domains. Additionally, we demonstrate that such transportation cost metric serves as a good proxy for estimating transferability between source and target graphs, and is better as a transferability metric than other common metrics like maximum mean discrepancy (MMD). In our controlled CSBM experiments, GDOT demonstrates robustness towards distributional shift, resulting in 90\% ROC AUC (vs.\ the second-best algorithm achieving $<80$\% on feature shift). Comprehensive experiments on both semi-supervised and supervised real-world node classification problems show that our method is the only one that performs consistently better than baseline GNNs in the cross-domain adaptation setting.