Optimal Inference in Contextual Stochastic Block Models

TL;DR

This paper introduces a belief-propagation-based algorithm for the semi-supervised contextual stochastic block model, providing a benchmark for GNN performance and highlighting potential improvements in graph neural network architectures.

Contribution

It develops a Bayes-optimal inference algorithm for cSBM and demonstrates its utility as a benchmark to improve GNNs for community detection.

Findings

The belief-propagation algorithm achieves high accuracy in cSBM inference.

There is a significant gap between the algorithm's performance and existing GNNs.

The implementation offers a new benchmark for evaluating GNNs.

Abstract

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.