Causation entropy from symbolic representations of dynamical systems

TL;DR

This paper explores how symbolic representations of dynamical systems affect the estimation of causal structures and information flows, revealing that symbolization can significantly alter these inferred properties.

Contribution

It demonstrates that causation entropy and related causal measures are highly sensitive to the choice of symbolization, challenging assumptions about convergence with finer partitions.

Findings

Causation entropy estimates depend non-monotonically on symbolization.

Markov order and causal structure may not converge to original values with finer partitions.

Symbolization can significantly distort causal inference in dynamical systems.

Abstract

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.