Information-Theoretic Sequential Framework to Elicit Dynamic High-Order Interactions in High-Dimensional Network Processes

Helder Pinto (), Yuri Antonacci, Gorana Mijatovic, Laura Sparacino, Sebastiano Stramaglia, Luca Faes and Ana Paula Rocha
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Helder Pinto: Centro de Matemática da Universidade do Porto (CMUP), Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal
Yuri Antonacci: Department of Engineering, University of Palermo, 90128 Palermo, Italy
Gorana Mijatovic: Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
Laura Sparacino: Department of Engineering, University of Palermo, 90128 Palermo, Italy
Sebastiano Stramaglia: Department of Physics, University of Bari Aldo Moro, and INFN Sezione di Bari, 70126 Bari, Italy
Luca Faes: Department of Engineering, University of Palermo, 90128 Palermo, Italy
Ana Paula Rocha: Centro de Matemática da Universidade do Porto (CMUP), Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal

Mathematics, 2025, vol. 13, issue 13, 1-18

Abstract: Complex networks of stochastic processes are crucial for modeling the dynamics of interacting systems, particularly those involving high-order interactions (HOIs) among three or more components. Traditional measures—such as mutual information (MI), interaction information (II), the redundancy-synergy index (RSI), and O-information (OI)—are typically limited to static analyses not accounting for temporal correlations and become computationally unfeasible in large networks due to the exponential growth of the number of interactions to be analyzed. To address these challenges, first a framework is introduced to extend these information-theoretic measures to dynamic processes. This includes the II rate (IIR), RSI rate (RSIR), and the OI rate gradient ( Δ OIR ), enabling the dynamic analysis of HOIs. Moreover, a stepwise strategy identifying groups of nodes (multiplets) that maximize either redundant or synergistic HOIs is devised, offering deeper insights into complex interdependencies. The framework is validated through simulations of networks composed of cascade, common drive, and common target mechanisms, modelled using vector autoregressive (VAR) processes. The feasibility of the proposed approach is demonstrated through its application in climatology, specifically by analyzing the relationships between climate variables that govern El Niño and the Southern Oscillation (ENSO) using historical climate data.

Keywords: complex systems; high order interactions; information theory; redundancy; synergy; stochastic processes; time-series analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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