Successful network inference from time-series data using mutual information rate

E. Bianco-Martinez, Nicolas Rubido Obrer, Ch. G. Antonopoulos, M. S. Baptista

Research output: Contribution to journalArticle

15 Citations (Scopus)
19 Downloads (Pure)

Abstract

This work uses an information-based methodology to infer the connectivity of complex systems from observed time-series data. We first derive analytically an expression for the Mutual Information Rate (MIR), namely, the amount of information exchanged per unit of time, that can be used to estimate the MIR between two finite-length low-resolution noisy time-series, and then apply it after a proper normalization for the identification of the connectivity structure of small networks of interacting dynamical systems. In particular, we show that our methodology successfully infers the connectivity for heterogeneous networks, different time-series lengths or coupling strengths, and even in the presence of additive noise. Finally, we show that our methodology based on MIR successfully infers the connectivity of networks composed of nodes with different time-scale dynamics, where inference based on Mutual Information fails.
The Mutual Information Rate (MIR) measures the time rate of information exchanged between two non-random and correlated variables. Since variables in complex systems are not purely random, the MIR is an appropriate quantity to access the amount of information exchanged in complex systems. However, its calculation requires infinitely long measurements with arbitrary resolution. Having in mind that it is impossible to perform infinitely long measurements with perfect accuracy, this work shows how to estimate the MIR taking into consideration this fundamental limitation and how to use it for the characterization and understanding of dynamical and complex systems. Moreover, we introduce a novel normalized form of MIR that successfully infers the structure of small networks of interacting dynamical systems. The proposed inference methodology is robust in the presence of additive noise, different time-series lengths, and heterogeneous node dynamics and coupling strengths. Moreover, it also outperforms inference methods based on Mutual Information when analysing networks formed by nodes possessing different time-scales
Original languageEnglish
Article number043102
Pages (from-to)1-9
Number of pages9
JournalChaos
Volume26
Issue number4
Early online date12 Apr 2016
DOIs
Publication statusPublished - Apr 2016

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