Autoregressive graph Volterra models and applications

Qiuling Yang, Mario Coutino, Geert Leus, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number4
JournalEurasip Journal on Advances in Signal Processing
Issue number1
StatePublished - Dec 2023
Externally publishedYes

Bibliographical note

Funding 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.

Publisher Copyright:
© 2023, The Author(s).


  • Graph inference
  • Higher-order interactions
  • Link prediction
  • Volterra series


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