Cafaro Carlo, Lord Warren M, Sun Jie, Bollt Erik M
Department of Mathematics, Clarkson University, 8 Clarkson Ave, Potsdam, New York, 13699-5815, USA.
Chaos. 2015 Apr;25(4):043106. doi: 10.1063/1.4916902.
Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale systems are often symbolized, either because of the finite resolution of the measurement apparatus, or because of the need of statistical estimation. By algorithmic application of causation entropy, we investigated the effects of symbolization on important concepts such as Markov order and causal structure of the tent map. We uncovered that these quantities depend nonmonotonically and, most of all, sensitively on the choice of symbolization. Indeed, we show that Markov order and causal structure do not necessarily converge to their original analog counterparts as the resolution of the partitioning becomes finer.
识别复杂系统中的因果结构并量化直接信息流是一项具有挑战性但又很重要的任务，在许多领域都有实际应用。动态过程或大规模系统生成的数据通常会被符号化，这要么是由于测量仪器的有限分辨率，要么是出于统计估计的需要。通过因果熵的算法应用，我们研究了符号化对诸如帐篷映射的马尔可夫阶数和因果结构等重要概念的影响。我们发现这些量对符号化的选择呈现非单调依赖，最重要的是敏感依赖。事实上，我们表明随着划分分辨率变得更精细，马尔可夫阶数和因果结构不一定会收敛到它们原来的类似对应物。
