Generalized Additive Models for Graph-Valued Data with an Application to European Air Transportation

Marco Simnacher, Humboldt-Universität zu Berlin

Co-authors: Matthias Eckardt, Humboldt-Universität zu Berlin; Sonja Greven, Humboldt-Universität zu Berlin

Abstract: Regression models for a sample of unlabeled graphs are of interest if node labels for the graphs are not available, change or are irrelevant. They model how edge attributes vary with covariates, while allowing for node permutations. For many real-world processes, these graph attributes may be non-metric, follow general not necessarily Gaussian distributions, and vary nonlinearly with covariates. To address these challenges, we extend the linear regression framework of Calissano et al. (2022) to generalized additive models for unlabeled graph-valued responses. This extension offers greater flexibility regarding (i) the functional form of the covariate–response relationships and (ii) the conditional distribution of the graph attributes. We show the usefulness of our approach by analyzing weekly air passenger networks in parts of the European Union during the Covid-19 pandemic. The resulting models capture the evolving network structure over time and in response to pandemic-related changes.