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.
|Original language||English (US)|
|Journal||Eurasip Journal on Advances in Signal Processing|
|State||Published - Dec 2023|
Bibliographical noteFunding Information:
This work was supported in part by ASPIRE project 14926 (within the STW OTP program) financed by the Netherlands Organization for Scientific Research (NWO), NSF Grants 1509040, 1711471, and 1901134.
© 2023, The Author(s).
- Graph inference
- Higher-order interactions
- Link prediction
- Volterra series