Permutation Approach to Finite-Alphabet Stationary Stochastic Processes Based on the Duality between Values and Orderings
Permutation Approach to Finite-Alphabet Stationary Stochastic Processes Based on the Duality between Values and Orderings
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基于值与序对偶性的有限字母平稳随机过程的排列方法
DOI：
10.1140/epjst/e2013-01848-5
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Taichi Haruna and Kohei Nakajima
中科院分区：
文献类型：
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作者：
Taichi Haruna and Kohei Nakajima
值与序之间的对偶性是讨论离散时间有限字母表平稳随机过程（SSP）的各种信息论测度及其置换类似物之间关系的有力工具。将其应用于具有遍历内部过程的隐马尔可夫模型的输出过程，我们在以前的工作中已经证明了过剩熵和转移熵率与它们的置换类似物一致。在本文中，我们讨论了一般遍历SSP的两个措施，不一定具有马尔可夫性质，在我们以前的工作中假设的两个置换特征。在第一种方法中，我们证明了遍历SSP的过剩熵和转移熵率可以分别作为它们在隐马尔可夫模型的N阶近似下的置换模拟的极限。在第二种方法中，我们采用修改的排列划分的一组字，它认为平等的符号，除了排列的字。我们证明了遍历SSP的过剩熵和转移熵率分别等于它们的修正置换类似物。
The duality between values and orderings is a powerful tool to discuss relationships between various information-theoretic measures and their permutation analogues for discrete-time finite-alphabet stationary stochastic processes (SSPs). Applying it to output processes of hidden Markov models with ergodic internal processes, we have shown in our previous work that the excess entropy and the transfer entropy rate coincide with their permutation analogues. In this paper, we discuss two permutation characterizations of the two measures for general ergodic SSPs not necessarily having the Markov property assumed in our previous work. In the first approach, we show that the excess entropy and the transfer entropy rate of an ergodic SSP can be obtained as the limits of permutation analogues of them for theN-th order approximation by hidden Markov models, respectively. In the second approach, we employ the modified permutation partition of the set of words which considers equalities of symbols in addition to permutations of words. We show that the excess entropy and the transfer entropy rate of an ergodic SSP are equal to their modified permutation analogues, respectively.