On the stability of spectral graph filters and beyond

Data collected in network domains, hence supported by an (irregular) graph rather than a (regular) grid-like structure, are becoming pervasive. Typical examples include gene expression data associated with a protein-protein interaction graph, or behaviours of a group of individuals in a social network. Graph-based signal processing and machine learning are recent techniques that have been developed to handle such graph-structured data and have seen applications in such diverse fields as drug discovery, fake news detection, and traffic prediction. However, a theoretical understanding of the robustness of these models against perturbation to the input graph domain has been lacking. In this talk, I will present our results on the stability bounds of spectral graph filters as well as other recent work on the robustness of graph machine learning models, which together will contribute to the deployment of these models in real-world scenarios.