  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.
