Network inference combining mutual information rate and statistical tests

TL;DR

This paper introduces a novel method combining mutual information rate estimations and statistical significance tests to accurately infer network connectivity from time-series data, even under noisy and heterogeneous conditions.

Contribution

The paper presents a new approach that integrates information-theoretic and statistical methods for network inference, demonstrating its effectiveness on various simulated and real-world network models.

Findings

Accurately infers connected node pairs using ROC curves.

Effective in noisy stochastic data for recovering initial connectivity.

Performs well on different network topologies like Erdős-Rényi and small-world.

Abstract

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 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. We provide the mathematical background on Mutual Information Rate, discuss the statistical significance tests and the false discovery rate. Further on, we present results for correlated normal-variates data, coupled circle and coupled logistic maps, coupled Lorenz systems and coupled stochastic Kuramoto phase oscillators. Following up, we study the effect of noise on the presented methodology in networks of coupled stochastic Kuramoto phase oscillators and of coupling heterogeneity degree on networks of coupled circle maps. We show that the method 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 demonstrate 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 Erd\H{o}s-R\'enyi and small-world networks with varying coupling heterogeneity in their connections. The highlight of the proposed methodology is its ability to infer the underlying network connectivity based solely on the recorded datasets.