Autoregressive graph Volterra models and applications

Graph-based learning and estimation are fundamental problems in various applications involving power, social, and brain networks, to name a few. While learning pair-wise interactions in network data is a well-studied problem, discovering higher-order interactions among subsets of nodes is still not yet fully explored. To this end, encompassing and leveraging (non)linear structural equation models as well as vector autoregressions, this paper proposes autoregressive graph Volterra models (AGVMs) that can capture not only the connectivity between nodes but also higher-order interactions presented in the networked data. The proposed overarching model inherits the identifiability and expressibility of the Volterra series. Furthermore, two tailored algorithms based on the proposed AGVM are put forth for topology identification and link prediction in distribution grids and social networks, respectively. Real-data experiments on different real-world collaboration networks highlight the impact of higher-order interactions in our approach, yielding discernible differences relative to existing methods.

Automated summary

Graph-based learning and estimation are important problems in various applications, but higher-order interactions in network data have not been fully explored. This paper proposes autoregressive graph Volterra models (AGVMs) to capture both connectivity between nodes and higher-order interactions. The model inherits the identifiability and expressiveness of the Volterra series. Two algorithms based on AGVM for topology identification and link prediction are introduced, and experiments on real-world collaboration networks demonstrate the impact of higher-order interactions.