Optimal Inference in Contextual Stochastic Block Models
This work addresses the development of more performant GNN architectures for machine learning on graphs, though it is incremental as it builds on the established cSBM framework.
The authors tackled the problem of community detection in attributed graphs using the contextual stochastic block model (cSBM) and derived a belief-propagation-based algorithm for semi-supervised inference, showing a considerable gap in accuracy compared to existing graph-neural network (GNN) architectures.
The contextual stochastic block model (cSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine learning on graphs, the cSBM has been widely used as a synthetic dataset for evaluating the performance of graph-neural networks (GNNs) for semi-supervised node classification. We consider a probabilistic Bayes-optimal formulation of the inference problem and we derive a belief-propagation-based algorithm for the semi-supervised cSBM; we conjecture it is optimal in the considered setting and we provide its implementation. We show that there can be a considerable gap between the accuracy reached by this algorithm and the performance of the GNN architectures proposed in the literature. This suggests that the cSBM, along with the comparison to the performance of the optimal algorithm, readily accessible via our implementation, can be instrumental in the development of more performant GNN architectures.