Permutation Complexity and Coupling Measures in Hidden Markov Models

Entropy

Taichi Haruna¹ 

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

关键词: duality;    permutation entropy;    excess entropy;    transfer entropy;    directed information;   

DOI  :  10.3390/e15093910

来源: mdpi

【 摘 要 】

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 permutation analogues. 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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.