Transfer entropy is a measure of the magnitude and the direction ofinformation flow between jointly distributed stochastic processes. In recentyears, its permutation analogues are considered in the literature to estimatethe transfer entropy by counting the number of occurrences of orderings ofvalues, not the values themselves. It has been suggested that the method ofpermutation is easy to implement, computationally low cost and robust to noisewhen applying to real world time series data. In this paper, we initiate atheoretical treatment of the corresponding rates. In particular, we considerthe transfer entropy rate and its permutation analogue, the symbolic transferentropy rate, and show that they are equal for any bivariate finite-alphabetstationary ergodic Markov process. This result is an illustration of theduality method introduced in [T. Haruna and K. Nakajima, Physica D 240, 1370(2011)]. We also discuss the relationship among the transfer entropy rate, thetime-delayed mutual information rate and their permutation analogues.
展开▼
机译:转移熵是联合分布的随机过程之间信息流的大小和方向的度量。近年来,在文献中考虑了其排列类似物,通过计算值排序的次数而不是值本身来估计转移熵。已经提出,当应用于现实世界时间序列数据时,置换方法易于实现,计算成本低并且对噪声鲁棒。在本文中,我们开始对相应利率进行理论处理。特别地,我们考虑了转移熵率及其排列类似物,符号转移熵率,并表明它们对于任何二元有限字母平稳的遍历马尔可夫过程都是相等的。此结果说明了[T. Haruna and K. Nakajima,Physica D 240,1370(2011)]。我们还讨论了传输熵率,时延互信息率及其排列类似物之间的关系。
展开▼