Uncertainty Quantification of Network Inference with Data Sufficiency

Network inference, which involves reconstructing the connectivity structure of a network from recorded data, is essential for broadening our understanding of physical, biological, and chemical systems. Although data-driven network inference algorithms have made significant strides in recent years, determining how much data is required so that the inferred network topology faithfully mirrors the underlying network remains an essential but often overlooked subject. In this paper, we present a statistical method to determine whether the recorded data carries sufficient variability to ensure an accurate reconstruction of the true network topology. Our approach leverages parametric confidence intervals to establish the bounds of true connection strengths, which subsequently enable the uncertainty quantification of inferred connectivity. The proposed technique is validated using noisy data generated from networks of Kuramoto and Stuart-Landau oscillators. Additionally, the method is applied to experimentally obtained data from an electrochemical oscillator network, where we find that the data sufficiency technique can successfully predict the accuracy of the inferred network.