Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks

Graph convolutional networks (GCNs) have recently received wide attentions, due to their successful applications in different graph tasks and different domains. Training GCNs for a large graph, however, is still a challenge. Original full-batch GCN training requires calculating the representation of all the nodes in the graph per GCN layer, which brings in high computation and memory costs. To alleviate this issue, several sampling-based methods are proposed to train GCNs on a subset of nodes. Among them, the node-wise neighbor-sampling method recursively samples a fixed number of neighbor nodes, and thus its computation cost suffers from exponential growing neighbor size across layers; while the layer-wise importance-sampling method discards the neighbor-dependent constraints, and thus the nodes sampled across layer suffer from sparse connection problem. To deal with the above two problems, we propose a new effective sampling algorithm called LAyer-Dependent ImportancE Sampling (LADIES). Based on the sampled nodes in the upper layer, LADIES selects nodes that are in the neighborhood of these nodes and uses the constructed bipartite graph to compute the importance probability. Then, it samples a fixed number of nodes according to the probability for the whole layer, and recursively conducts such procedure per layer to construct the whole computation graph. We prove theoretically and experimentally, that our proposed sampling algorithm outperforms the previous sampling methods regarding both time and memory. Furthermore, LADIES is shown to have better generalization accuracy than original full-batch GCN, due to its stochastic nature.