# Detecting causality in multivariate time series via non-uniform embedding

## TL;DR

This paper introduces LM-PMIME, a new information-theoretic method for detecting causality in multivariate time series, improving accuracy especially in weakly coupled and chaotic systems.

## Contribution

The paper presents LM-PMIME, a novel non-uniform embedding approach that combines low-dimensional mutual information approximation with a mixed search strategy.

## Key findings

- Outperforms PMIME in simulations of stochastic and chaotic systems.
- Effective in detecting causality with weak coupling.
- Successfully applied to epilepsy electrocorticographic data.

## 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 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.