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Graph Convolutional Networks (GCNs) have recently attracted vast interest andachieved state-of-the-art performance on graphs, but its success couldtypically hinge on careful training with amounts of expensive andtime-consuming labeled data. To alleviate labeled data scarcity, self-trainingmethods have been widely adopted on graphs by labeling high-confidenceunlabeled nodes and then adding them to the training step. In this line, weempirically make a thorough study for current self-training methods on graphs.Surprisingly, we find that high-confidence unlabeled nodes are not alwaysuseful, and even introduce the distribution shift issue between the originallabeled dataset and the augmented dataset by self-training, severely hinderingthe capability of self-training on graphs. To this end, in this paper, wepropose a novel Distribution Recovered Graph Self-Training framework (DR-GST),which could recover the distribution of the original labeled dataset.Specifically, we first prove the equality of loss function in self-trainingframework under the distribution shift case and the population distribution ifeach pseudo-labeled node is weighted by a proper coefficient. Considering theintractability of the coefficient, we then propose to replace the coefficientwith the information gain after observing the same changing trend between them,where information gain is respectively estimated via both dropout variationalinference and dropedge variational inference in DR-GST. However, such aweighted loss function will enlarge the impact of incorrect pseudo labels. As aresult, we apply the loss correction method to improve the quality of pseudolabels. Both our theoretical analysis and extensive experiments on fivebenchmark datasets demonstrate the effectiveness of the proposed DR-GST, aswell as each well-designed component in DR-GST.

Confidence May Cheat: Self-Training on Graph Neural Networks under Distribution Shift