Causation entropy from symbolic representations of dynamical systems

摘要

Identification of causal structures and quantification of direct informationflows in complex systems is a challenging yet important task, with practicalapplications in many fields. Data generated by dynamical processes orlarge-scale systems are often symbolized, either because of the finiteresolution of the measurement apparatus, or because of the need of statisticalestimation. By algorithmic application of causation entropy, we investigatedthe effects of symbolization on important concepts such as Markov order andcausal structure of the tent map. We uncovered that these quantities dependnonmontonically and, most of all, sensitively on the choice of symbolization.Indeed, we show that Markov order and causal structure do not necessarilyconverge to their original analog counterparts as the resolution of thepartitioning becomes finer.