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Measuring Information-Transfer Delays

Author

Listed:
  • Michael Wibral
  • Nicolae Pampu
  • Viola Priesemann
  • Felix Siebenhühner
  • Hannes Seiwert
  • Michael Lindner
  • Joseph T Lizier
  • Raul Vicente

Abstract

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

Suggested Citation

  • Michael Wibral & Nicolae Pampu & Viola Priesemann & Felix Siebenhühner & Hannes Seiwert & Michael Lindner & Joseph T Lizier & Raul Vicente, 2013. "Measuring Information-Transfer Delays," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-19, February.
  • Handle: RePEc:plo:pone00:0055809
    DOI: 10.1371/journal.pone.0055809
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    References listed on IDEAS

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    1. J. T. Lizier & M. Prokopenko, 2010. "Differentiating information transfer and causal effect," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(4), pages 605-615, February.
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    Cited by:

    1. David L Gibbs & Ilya Shmulevich, 2017. "Solving the influence maximization problem reveals regulatory organization of the yeast cell cycle," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-19, June.
    2. Libor Pekař & Radek Matušů & Roman Prokop, 2017. "Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-23, June.
    3. Coulibaly, Saliya & Bessin, Florent & Clerc, Marcel G. & Mussot, Arnaud, 2022. "Precursors-driven machine learning prediction of chaotic extreme pulses in Kerr resonators," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Xiaogeng Wan & Lanxi Xu, 2018. "A study for multiscale information transfer measures based on conditional mutual information," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-30, December.
    5. Shinya Ito & Fang-Chin Yeh & Emma Hiolski & Przemyslaw Rydygier & Deborah E Gunning & Pawel Hottowy & Nicholas Timme & Alan M Litke & John M Beggs, 2014. "Large-Scale, High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-16, August.
    6. Nicholas Timme & Shinya Ito & Maxym Myroshnychenko & Fang-Chin Yeh & Emma Hiolski & Pawel Hottowy & John M Beggs, 2014. "Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-43, December.
    7. Leonidas Sandoval Junior & Asher Mullokandov & Dror Y. Kenett, 2015. "Dependency Relations among International Stock Market Indices," JRFM, MDPI, vol. 8(2), pages 1-39, May.
    8. Daniel Toker & Friedrich T Sommer, 2019. "Information integration in large brain networks," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-26, February.
    9. Sourabh Lahiri & Philippe Nghe & Sander J Tans & Martin Luc Rosinberg & David Lacoste, 2017. "Information-theoretic analysis of the directional influence between cellular processes," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-26, November.

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