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Practical Measures of Integrated Information for Time-Series Data

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  • Adam B Barrett
  • Anil K Seth

Abstract

A recent measure of ‘integrated information’, ΦDM, quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, ΦDM is defined only for discrete Markov systems, which are unusual in biology; as a result, ΦDM can rarely be measured in practice. Here, we describe two new measures, ΦE and ΦAR, that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.Author Summary: A key feature of the human brain is its ability to represent a vast amount of information, and to integrate this information in order to produce specific and selective behaviour, as well as a stream of unified conscious scenes. Attempts have been made to quantify so-called ‘integrated information’ by formalizing in mathematics the extent to which a system as a whole generates more information than the sum of its parts. However, so far, the resulting measures have turned out to be inapplicable to real neural systems. In this paper we introduce two new measures that can be applied to both realistic neural models and to time-series data garnered from a broad range of neuroimaging and electrophysiological methods. Our work provides new opportunities for examining the role of integrated information in cognition and consciousness, and indeed in the function of any complex biological system. However, our results also pose challenges for theories that ascribe a direct physical meaning to any version of integrated information so far described.

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  • Adam B Barrett & Anil K Seth, 2011. "Practical Measures of Integrated Information for Time-Series Data," PLOS Computational Biology, Public Library of Science, vol. 7(1), pages 1-18, January.
    • Handle: RePEc:plo:pcbi00:1001052
    DOI: 10.1371/journal.pcbi.1001052
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    References listed on IDEAS

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    1. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    2. David Balduzzi & Giulio Tononi, 2009. "Qualia: The Geometry of Integrated Information," PLOS Computational Biology, Public Library of Science, vol. 5(8), pages 1-24, August.
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    Cited by:

    1. Masafumi Oizumi & Larissa Albantakis & Giulio Tononi, 2014. "From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-25, May.
    2. Masafumi Oizumi & Shun-ichi Amari & Toru Yanagawa & Naotaka Fujii & Naotsugu Tsuchiya, 2016. "Measuring Integrated Information from the Decoding Perspective," PLOS Computational Biology, Public Library of Science, vol. 12(1), pages 1-18, January.
    3. Hyunwoo Jang & George A. Mashour & Anthony G. Hudetz & Zirui Huang, 2024. "Measuring the dynamic balance of integration and segregation underlying consciousness, anesthesia, and sleep in humans," Nature Communications, Nature, vol. 15(1), pages 1-18, December.
    4. Max Tegmark, 2016. "Improved Measures of Integrated Information," PLOS Computational Biology, Public Library of Science, vol. 12(11), pages 1-34, November.
    5. 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.
    6. Jeffrey A Edlund & Nicolas Chaumont & Arend Hintze & Christof Koch & Giulio Tononi & Christoph Adami, 2011. "Integrated Information Increases with Fitness in the Evolution of Animats," PLOS Computational Biology, Public Library of Science, vol. 7(10), pages 1-13, October.
    7. David Engel & Thomas W Malone, 2018. "Integrated information as a metric for group interaction," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-19, October.
    8. Adam B Barrett & Michael Murphy & Marie-Aurélie Bruno & Quentin Noirhomme & Mélanie Boly & Steven Laureys & Anil K Seth, 2012. "Granger Causality Analysis of Steady-State Electroencephalographic Signals during Propofol-Induced Anaesthesia," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-12, January.
    9. Antonio J. Ibáñez-Molina & Sergio Iglesias-Parro, 2018. "A Comparison between Theoretical and Experimental Measures of Consciousness as Integrated Information in an Anatomically Based Network of Coupled Oscillators," Complexity, Hindawi, vol. 2018, pages 1-8, April.

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