Network inference using mutual information rate, statistical tests and amplitude-phase modulated surrogate data

In this paper, we propose a new method to infer connectivity in networks using the mutual information rate (MIR), statistical tests and amplitude-phase modulated surrogate data (APMSD). The method is addressing the case where one wants to infer the structure of the network when the equations of motion and the coupling adjacency matrix are known, that is the reverse-engineering problem. It is based on the computation of MIR and statistical, hypothesis tests to infer network connectivity, introducing a new method to generate surrogate data, called the APMSD method, that removes correlation and phase synchronisation in the recorded signals, by randomising their amplitudes and instantaneous phases. The proposed method compares MIR of pairs of signals from the network with the MIR values of pairs of APMSD generated from the signals. We discuss the mathematical aspects of the APMSD method and present numerical results for networks of coupled maps, Gaussian-distributed correlated data, coupled continuous deterministic systems, coupled stochastic Kuramoto systems and for dynamics on heterogeneous networks. We show that in all cases, the method can find at least one pair of percentages of randomisation in amplitudes and instantaneous phases that leads to perfect recovery of the initial network that was used to generate the data. The importance of our method stems from the analytic signal concept, introduced by Gabor in 1946 and Hilbert transform as it provides us with a quantification of the contribution of amplitude (linear or nonlinear) correlation and phase synchronisation in the connectivity among nodes in a network. Our method shows great potential in recovering the network structure in coupled deterministic and stochastic systems and in heterogeneous networks with weighted connectivity.