Hierarchical graph sampling based minibatch learning with chain preservation and variance reduction

Graph sampling based Graph Convolutional Networks (GCNs) decouple the sampling from the forward and backward propagation during minibatch training, which exhibit good scalability in terms of layer depth and graph size. We propose HIS_GCNs, a hierarchical importance graph sampling based learning method. By constructing minibatches using sampled subgraphs, HIS_GCNs gives attention to the importance of both core and periphery nodes/edges. Specifically, it preserves the centrum of the core to most minibatches, which maintains connectivity between periphery nodes, and samples periphery edges without core node interference, in order to keep more long chains composed entirely of low-degree nodes in the same minibatch. In addition, we verify the effectiveness of HIS_GCNs in reducing node embedding variance and chain information loss. Experiments on GCNs and other Graph Neural Networks (GNNs) with node classification tasks on five large-scale graphs confirm superior performance of the proposed hierarchical importance sampling method in both accuracy and training time.

@article{hu2025_2503.00860,
  title={ Hierarchical graph sampling based minibatch learning with chain preservation and variance reduction },
  author={ Qia Hu and Bo Jiao },
  journal={arXiv preprint arXiv:2503.00860},
  year={ 2025 }
}