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Permutation Excess Entropy and Mutual Information between the Past and Future

Taichi Haruna and Kohei Nakajima

p. 197-209

    Abstract

    We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite blocks in the space of orderings for finite-state stationary ergodic Markov processes. This result may spread a new light on the relationship between complexity and anticipation.

    Index

    Keywords

    permutation entropy, excess entropy, mutual information, complexity, duality

    Text

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    References

    Bibliographical reference

    Taichi Haruna and Kohei Nakajima, « Permutation Excess Entropy and Mutual Information between the Past and Future », CASYS, 26 | 2014, 197-209.

    Electronic reference

    Taichi Haruna and Kohei Nakajima, « Permutation Excess Entropy and Mutual Information between the Past and Future », CASYS [Online], 26 | 2014, Online since 01 October 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=3959

    Authors

    Taichi Haruna

    Department of Earth & Planetary Sciences, Graduate School of Science, Kobe University, 1-1 Rokkodaicho, Nada, Kobe 657-8501, Japan

    By this author

    Kohei Nakajima

    Artificial Intelligence Laboratory, Department of Informatics, University of Zurich, Andreasstrasse 15, 8050 Zurich, Switzerland

    By this author

    Copyright

    CC BY-SA 4.0 Deed