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Estimating the decomposition of predictive information in multivariate systems

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The integrative neuroscience of behavioral control (Neuroscience)
Abstract
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.
Keywords
Information, Brain, cardiorespiratory, sleep, entropy, heart, HEART-RATE-VARIABILITY, PHYSIOLOGICAL TIME-SERIES, TRANSFER ENTROPY, APPROXIMATE ENTROPY, GRANGER CAUSALITY, SLEEP EEG, MECHANISMS, TOOL, OSCILLATIONS, COMPLEXITY

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Citation

Please use this url to cite or link to this publication:

Chicago
Faes, Luca, Dimitris Kugiumtzis, Giandomenico Nollo, Fabrice Jurysta, and Daniele Marinazzo. 2015. “Estimating the Decomposition of Predictive Information in Multivariate Systems.” Physical Review E 91 (3).
APA
Faes, L., Kugiumtzis, D., Nollo, G., Jurysta, F., & Marinazzo, D. (2015). Estimating the decomposition of predictive information in multivariate systems. PHYSICAL REVIEW E, 91(3).
Vancouver
1.
Faes L, Kugiumtzis D, Nollo G, Jurysta F, Marinazzo D. Estimating the decomposition of predictive information in multivariate systems. PHYSICAL REVIEW E. 2015;91(3).
MLA
Faes, Luca, Dimitris Kugiumtzis, Giandomenico Nollo, et al. “Estimating the Decomposition of Predictive Information in Multivariate Systems.” PHYSICAL REVIEW E 91.3 (2015): n. pag. Print.
@article{5877482,
  abstract     = {In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.},
  articleno    = {032904},
  author       = {Faes, Luca and Kugiumtzis, Dimitris and Nollo, Giandomenico and Jurysta, Fabrice and Marinazzo, Daniele},
  issn         = {1539-3755},
  journal      = {PHYSICAL REVIEW E},
  language     = {eng},
  number       = {3},
  pages        = {16},
  title        = {Estimating the decomposition of predictive information in multivariate systems},
  url          = {http://dx.doi.org/10.1103/PhysRevE.91.032904},
  volume       = {91},
  year         = {2015},
}

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