Abstract
Causal analysis based on non-uniform embedding schemes is an important way to detect the underlying interactions between dynamic systems. However, there are still some obstacles to estimating high-dimensional conditional mutual information and forming optimal mixed embedding vector in traditional non-uniform embedding schemes. In this study, we present a new non-uniform embedding method framed in information theory to detect causality for multivariate time series, named LM-PMIME, which integrates the low-dimensional approximation of conditional mutual information and the mixed search strategy for the construction of the mixed embedding vector. We apply the proposed method to simulations of linear stochastic, nonlinear stochastic, and chaotic systems, demonstrating its superiority over partial conditional mutual information from mixed embedding (PMIME) method. Moreover, the proposed method works well for multivariate time series with weak coupling strengths, especially for chaotic systems. In the actual application, we show its applicability to epilepsy multichannel electrocorticographic recordings.
Highlights
In recent years, various time series analysis methods have been proposed to detect interactions between complex systems [1,2,3]
In order to overcome the above shortcomings, we propose a new non-uniform embedding method named LM-partial conditional mutual information from mixed embedding (PMIME) for multivariate time series based on the low-dimensional approximation of conditional mutual information(CMI) and the mixed search strategy
We propose the LM-PMIME method to detect the directional coupling in multivariable time series according to the low-dimensional approximation of CMI and the mixed search strategy
Summary
Various time series analysis methods have been proposed to detect interactions between complex systems [1,2,3]. Transfer entropy [5,6] Both methods are based on time series prediction for causal analysis. One shortcoming is the curse of dimensionality, which makes the estimation of mutual information inaccurate as the dimension of the embedded space increases [21,22,23,24] Another shortcoming is related to the mixed embedding vector. In order to overcome the above shortcomings, we propose a new non-uniform embedding method named LM-PMIME for multivariate time series based on the low-dimensional approximation of conditional mutual information(CMI) and the mixed search strategy.
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