Graph-based semi-supervised learning through the lens of safety.

Graph-based semi-supervised learning (G-SSL) algorithms have witnessed rapid development and widespread usage across a variety of applications in recent years. However, the theoretical characterisation of the efficacy of such algorithms has remained an under-explored area. We introduce a novel algorithm for G-SSL, CSX, whose objective function extends those of Label Propagation and Expander, two popular G-SSL algorithms. We provide data-dependent generalisation error bounds for all three aforementioned algorithms when they are applied to graphs drawn from a partially labelled extension of a versatile latent space graph generative model. The bounds we obtain enable us to characterise the predictive performance as measured by accuracy in terms of homophily and label quantity. Building on this we develop a key notion of GLM-safety which enables us to compare G-SSL algorithms on the basis of the range of graphs on which they obtain a guaranteed accuracy. We show that the proposed algorithm CSX has a better GLM-safety profile than Label Propagation and Expander while achieving comparable or better accuracy on synthetic as well as real-world benchmark networks.