A mean-field approximation-based linearization framework for network reconstruction from binary time series.

Abstract

A captivating challenge in network research is the reconstruction of complex network structures from limited binary-state time series data. Although some reconstruction approaches based on dynamical rules or sparse system of linear equations have been proposed, these approaches either rely on known dynamical rules, limiting their generality, or the system of linear equations is often empirically determined, with weak interpretability and the performance being sensitive to parameter settings. To address these limitations, we propose a network reconstruction method based on linearization grounded in mean-field approximation. By incorporating the mean-field approximation, the interpretability of the linearization process is enhanced. The method exploits a common feature of binary-state dynamics-nodes become active under the influence of active neighbors-and is independent of any specific dynamical model, thus ensuring broad applicability. While the structure of the linearization coefficients suggests a data partitioning (blocking) strategy, this approach is often computationally complex. To overcome this, we develop a non-blocking, parameter-free alternative and theoretically demonstrate that it achieves reconstruction performance comparable to that of the ideal blocking method. Finally, we conduct extensive tests on both artificial and real networks to verify the effectiveness of our approach and demonstrate its robustness using noisy binary state time series data.