Network inference using information-theoretical approaches, statistical hypothesis tests, and the amplitude-phase modulated surrogate data method

The last few decades have witnessed the emergence of network science aimed at modelling natural phenomena across a diverse spectrum of disciplines, including biology, social sciences, and neuroscience, among others. One of the notable advances in this field is the concept of MIR, which quantifies the information flow per unit of time between different components (nodes) within a network. The MIR framework holds the potential to reveal connectivity patterns in complex networks using time-series data. A critical challenge in using MIR is the establishment of appropriate thresholds for successful network inference. We propose a new method to infer connectivity in networks using MIR, statistical tests and APMSD. The method uses MIR and statistical hypothesis tests to infer network connectivity, introducing a new method to generate surrogate data, which removes the correlation of amplitude and synchronisation of the phases in the recorded signals, by randomising their instantaneous amplitudes and phases. The APMSD method compares MIR between the pairs of nodes of the data from the coupled or stochastic models with those of the APMSD generated from the data randomising instantaneous amplitudes and/or phases. We discuss the mathematical aspects of the APMSD method and present numerical results for Gaussian-distributed correlated data, networks of coupled maps and continuous deterministic systems, the stochastic Kuramoto system, and for dynamics on heterogeneous networks. The importance of our method stems from the analytic signal concept, introduced by Gabor in 1946 and the Hilbert transform, as it provides us with the quantification of the contribution of amplitude correlation (linear or nonlinear) and phase synchronisation in the connectivity among nodes within a network. Our method shows great potential for recovering the network structure in coupled deterministic and stochastic systems and in heterogeneous networks with weighted connectivity.