Graph-valued regression: Prediction of unlabelled networks in a non-Euclidean graph space

Abstract

Understanding how unlabelled graphs depend on input values or vectors is of extreme interest in a range of applications. In this paper, we propose a regression model taking values in graph space, representing unlabelled graphs which can be weighted or unweighted, one or multi-layer, and have same or different numbers of nodes, as a function of real valued regressor. As graph space is not a manifold, well-known manifold regression models are not applicable. We provide flexible parametrized regression models for graph space, along with precise and computationally efficient estimation procedures given by the introduced align all and compute regression algorithm. We show the potential of the proposed model for three real datasets: a time dependent cryptocurrency correlation matrices, a set of bus mobility usage network in Copenhagen (DK) during the pandemic, and a set of team players’ passing networks for all the matches in Fifa World Championship 2018.