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

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

doi:10.1063/1.4945420

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

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

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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 language	English
Article number	043102
Pages (from-to)	1-9
Number of pages	9
Journal	Chaos
Volume	26
Issue number	4
Early online date	12 Apr 2016
DOIs	https://doi.org/10.1063/1.4945420
Publication status	Published - Apr 2016

Bibliographical note

ACKNOWLEDGMENTS
E.B.M., M.S.B., and C.G.A. acknowledge the financial support provided by the EPSRC “EP/I032606/1” grant. C.G.A. contributed to this work while working at the University of Aberdeen and then, while working at the University of Essex, United Kingdom. N.R. acknowledges the support of PEDECIBA, Uruguay

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Successful network inference from time-series data using mutual information rate
On the authors’ personal web page and employers’ web page: The right to: Post the Accepted Manuscript (AM) to their personal web page or their employer’s web page immediately after acceptance by AIP Publishing. Post the Version of Record (VOR) to their personal web page or their employer’s web page 12 months after publication by AIP Publishing. (An appropriate credit line must be included that references the full citation for the published paper, along with a link to the VOR after publication on AIP Publishing’s site.)
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Successful network inference from time-series data using mutual information rate
Baptista, M. (Creator), University of Aberdeen, 28 Apr 2016
DOI: 10.20392/998cad91-390c-4014-a96c-b333046a0bde
Dataset

Cite this

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title = "Successful network inference from time-series data using mutual information rate",

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",

author = "E. Bianco-Martinez and {Rubido Obrer}, Nicolas and Antonopoulos, {Ch. G.} and Baptista, {M. S.}",

note = "ACKNOWLEDGMENTS E.B.M., M.S.B., and C.G.A. acknowledge the financial support provided by the EPSRC “EP/I032606/1” grant. C.G.A. contributed to this work while working at the University of Aberdeen and then, while working at the University of Essex, United Kingdom. N.R. acknowledges the support of PEDECIBA, Uruguay",

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AU - Bianco-Martinez, E.

AU - Rubido Obrer, Nicolas

AU - Antonopoulos, Ch. G.

AU - Baptista, M. S.

N1 - ACKNOWLEDGMENTS E.B.M., M.S.B., and C.G.A. acknowledge the financial support provided by the EPSRC “EP/I032606/1” grant. C.G.A. contributed to this work while working at the University of Aberdeen and then, while working at the University of Essex, United Kingdom. N.R. acknowledges the support of PEDECIBA, Uruguay

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N2 - 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

AB - 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

U2 - 10.1063/1.4945420

DO - 10.1063/1.4945420

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SN - 1054-1500

VL - 26

SP - 1

EP - 9

JO - Chaos

JF - Chaos

IS - 4

M1 - 043102

ER -

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

Abstract

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

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