动力系统符号表示的因果熵
Causation entropy from symbolic representations of dynamical systems
摘要：
复杂系统中因果结构的识别和直接信息流的量化是一项具有挑战性的重要任务，在许多领域都有实际应用。动态过程或大规模系统产生的数据通常被符号化，这要么是因为测量仪器的分辨率有限，要么是因为需要统计估计。通过因果熵的算法应用，我们研究了符号化对帐篷映射的马尔可夫序和因果结构等重要概念的影响。我们发现，这些数量依赖于非单调的，最重要的是，敏感地选择的象征。事实上，我们表明，马尔可夫顺序和因果结构不一定收敛到原来的模拟对应的分区的分辨率变得更精细。
英文摘要：
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 nonmontonically 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.
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