Permutation Complexity and Coupling Measures in Hidden Markov Models
Recently, the duality between values (words) and orderings (permutations) has been proposed by the authors as a basis to discuss the relationship between information theoretic measures for finite-alphabet stationary stochastic processes and their permutatio nanalogues. It has been used to give a sim...
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/9/3910 |
| _version_ | 1798003665870520320 |
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| author | Taichi Haruna Kohei Nakajima |
| author_facet | Taichi Haruna Kohei Nakajima |
| author_sort | Taichi Haruna |
| collection | DOAJ |
| description | Recently, the duality between values (words) and orderings (permutations) has been proposed by the authors as a basis to discuss the relationship between information theoretic measures for finite-alphabet stationary stochastic processes and their permutatio nanalogues. It has been used to give a simple proof of the equality between the entropy rate and the permutation entropy rate for any finite-alphabet stationary stochastic process and to show some results on the excess entropy and the transfer entropy for finite-alphabet stationary ergodic Markov processes. In this paper, we extend our previous results to hidden Markov models and show the equalities between various information theoretic complexity and coupling measures and their permutation analogues. In particular, we show the following two results within the realm of hidden Markov models with ergodic internal processes: the two permutation analogues of the transfer entropy, the symbolic transfer entropy and the transfer entropy on rank vectors, are both equivalent to the transfer entropy if they are considered as the rates, and the directed information theory can be captured by the permutation entropy approach. |
| first_indexed | 2024-04-11T12:11:24Z |
| format | Article |
| id | doaj.art-20af90b8261e477aaa571558cabef1b7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:11:24Z |
| publishDate | 2013-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-20af90b8261e477aaa571558cabef1b72022-12-22T04:24:36ZengMDPI AGEntropy1099-43002013-09-011593910393010.3390/e15093910Permutation Complexity and Coupling Measures in Hidden Markov ModelsTaichi HarunaKohei NakajimaRecently, the duality between values (words) and orderings (permutations) has been proposed by the authors as a basis to discuss the relationship between information theoretic measures for finite-alphabet stationary stochastic processes and their permutatio nanalogues. It has been used to give a simple proof of the equality between the entropy rate and the permutation entropy rate for any finite-alphabet stationary stochastic process and to show some results on the excess entropy and the transfer entropy for finite-alphabet stationary ergodic Markov processes. In this paper, we extend our previous results to hidden Markov models and show the equalities between various information theoretic complexity and coupling measures and their permutation analogues. In particular, we show the following two results within the realm of hidden Markov models with ergodic internal processes: the two permutation analogues of the transfer entropy, the symbolic transfer entropy and the transfer entropy on rank vectors, are both equivalent to the transfer entropy if they are considered as the rates, and the directed information theory can be captured by the permutation entropy approach.http://www.mdpi.com/1099-4300/15/9/3910dualitypermutation entropyexcess entropytransfer entropydirected information |
| spellingShingle | Taichi Haruna Kohei Nakajima Permutation Complexity and Coupling Measures in Hidden Markov Models Entropy duality permutation entropy excess entropy transfer entropy directed information |
| title | Permutation Complexity and Coupling Measures in Hidden Markov Models |
| title_full | Permutation Complexity and Coupling Measures in Hidden Markov Models |
| title_fullStr | Permutation Complexity and Coupling Measures in Hidden Markov Models |
| title_full_unstemmed | Permutation Complexity and Coupling Measures in Hidden Markov Models |
| title_short | Permutation Complexity and Coupling Measures in Hidden Markov Models |
| title_sort | permutation complexity and coupling measures in hidden markov models |
| topic | duality permutation entropy excess entropy transfer entropy directed information |
| url | http://www.mdpi.com/1099-4300/15/9/3910 |
| work_keys_str_mv | AT taichiharuna permutationcomplexityandcouplingmeasuresinhiddenmarkovmodels AT koheinakajima permutationcomplexityandcouplingmeasuresinhiddenmarkovmodels |