How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?

Graphs are a powerful data structure for representing relational data and are widely used to describe complex real-world systems. Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) can both leverage graph-structured data, but their inherent functioning is different. The question is how do they compare in capturing the information contained in networked datasets? We address this objective by solving a link prediction task and we conduct three main experiments, on both synthetic and real networks: one focuses on how PGMs and GNNs handle input features, while the other two investigate their robustness to noisy features and increasing heterophily of the graph. PGMs do not necessarily require features on nodes, while GNNs cannot exploit the network edges alone, and the choice of input features matters. We find that GNNs are outperformed by PGMs when input features are low-dimensional or noisy, mimicking many real scenarios where node attributes might be scalar or noisy. Then, we find that PGMs are more robust than GNNs when the heterophily of the graph is increased. Finally, to assess performance beyond prediction tasks, we also compare the two frameworks in terms of their computational complexity and interpretability.