Graph Convolutional Networks against Degree-Related Biases

In recent years, Graph Convolutional Networks (GCNs) show competitive performance in different domains, such as social network analysis, recommendation, and smart city. However, training GCNs with insufficient supervision is very difficult. The performance of GCNs becomes unsatisfying with few labeled data. Although some pioneering work try to understand why GCNs work or fail, their analysis focus more on the entire model level. Profiling GCNs on different nodes is still underexplored. To address the limitations, we study GCNs with respect to the node degree distribution. We show that GCNs have a higher accuracy on nodes with larger degrees even if they are underrepresented in most graphs, with both empirical observation and theoretical proof. We then propose Self-Supervised-Learning Degree-Specific GCN (SL-DSGCN) which handles the degree-related biases of GCNs from model and data aspects. Firstly, we design a degree-specific GCN layer that models both discrepancies and similarities of nodes with different degrees, and reduces the inner model-aspect biases of GCNs caused by sharing the same parameters with all nodes. Secondly, we develop a self-supervised-learning algorithm that assigns pseudo labels with uncertainty scores on unlabeled nodes using a Bayesian neural network. Pseudo labels increase the chance of connecting to labeled neighbors for low-degree nodes, thus reducing the biases of GCNs from the data perspective. We further exploit uncertainty scores as dynamic weights on pseudo labels in the stochastic gradient descent for SL-DSGCN. We validate \ours on three benchmark datasets, and confirm SL-DSGCN not only outperforms state-of-the-art self-training/self-supervised-learning GCN methods, but also improves GCN accuracy dramatically for low-degree nodes.