Abstract
In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time series data. In Sinha and Vaidya (in: IEEE conference on decision and control, pp 7329–7334, 2016), we have shown that the existing measures of information transfer, namely directed information, Granger causality and transfer entropy, fail to capture the causal interaction in a dynamical system and proposed a new definition of information transfer that captures direct causal interactions. The novelty of the information transfer definition used in this paper is the fact that it can differentiate between direct and indirect influences Sinha and Vaidya (2016). The main contribution of this paper is to show that the proposed definition of information transfers in Sinha and Vaidya (2016) and Sinha and Vaidya (in: Indian control conference, pp 303–308, 2017) can be computed from time series data, and thus, the direct influences in a dynamical system can be identified from time series data. We use transfer operator theoretic framework, involving Perron–Frobenius and Koopman operators for the data-driven approximation of the system dynamics and computation of information transfer. Several examples, involving linear and nonlinear system dynamics, are presented to verify the efficiency of the developed algorithm.
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Notes
For convenience of notation, from here on we denote the entropy of any variable x as H(x), instead of \(H(\rho (x))\).
with some abuse of notation we are using the same notation for the P–F operator defined on the space of measure and densities.
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Communicated by Clarence W. Rowley.
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Sinha, S., Vaidya, U. On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems. J Nonlinear Sci 30, 1651–1676 (2020). https://doi.org/10.1007/s00332-020-09620-1
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DOI: https://doi.org/10.1007/s00332-020-09620-1