  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.
