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 estimate high-dimensional conditional mutual
information and form 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.

本研究提出了一种名为 LM-PMIME 的新的基于信息理论的非均匀嵌入方法，旨在探测多元时间序列的因果关系，该方法集成了条件互信息的低维近似和混合搜索策略来构建混合嵌入向量，通过对线性随机、非线性随机和混沌系统的模拟试验，证明了该方法在传统的非均匀嵌入方案中具有更好的表现，尤其对于耦合弱的混沌系统，可以应用于癫痫多通道电 corticogram 记录。