Network inference combining mutual information rate and statistical tests

In this paper, we present a method that combines information-theoretical and statistical approaches to infer connectivity in complex networks using time-series data. The met-hod is based on estimations of the Mutual Information Rate for pairs of time-series and on statistical significance tests for connectivity acceptance using the false discovery rate method for multiple hypothesis testing. We provide the mathematical background on Mutual Information Rate, discuss the statistical significance tests and the false dis-covery rate. Further on, we present results for correlated normal-variates data, coupled circle and coupled logistic maps, coupled Lorenz systems and coupled stochastic Ku-ramoto phase oscillators. Following up, we study the effect of noise on the presented methodology in networks of coupled stochastic Kuramoto phase oscillators and of coup-ling heterogeneity degree on networks of coupled circle maps. We show that the met-hod can infer the correct number and pairs of connected nodes, by means of receiver operating characteristic curves. In the more realistic case of stochastic data, we demon-strate its ability to infer the structure of the initial connectivity matrices. The method is also shown to recover the initial connectivity matrices for dynamics on the nodes of Erdos-Renyi and small-world networks with varying coupling heterogeneity in their connections. The highlight of the proposed methodology is its ability to infer the und-erlying network connectivity based solely on the recorded datasets.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper introduces a method that combines information-theoretical and statistical approaches to infer connectivity in complex networks using time-series data. The method is based on estimations of the Mutual Information Rate for pairs of time-series and on statistical significance tests for connectivity acceptance using the false discovery rate method for multiple hypothesis testing. The method shows promising results in various scenarios, including correlated normal-variates data, coupled circle and logistic maps, coupled Lorenz systems, and coupled stochastic Kuramoto phase oscillators. It is able to accurately infer the number and pairs of connected nodes, even in the presence of noise, and can recover the initial connectivity matrices for different network structures. The proposed methodology has the advantage of relying solely on the recorded datasets to infer underlying network connectivity.