Estimation of Information Flow-Based Causality with Coarsely Sampled Time Series.

Area of Science:

• Dynamical Systems
• Information Theory
• Causality Analysis

Background:

• Information flow-based causality analysis is increasingly used, with a concise maximum likelihood estimator formula.
• Current estimation algorithms based on differential dynamical systems face challenges with coarsely sampled time series, particularly for nonlinear systems.

Purpose of the Study:

• To address the limitations of current causality analysis methods with coarsely sampled time series.
• To develop a more robust causality analysis technique applicable to scarce observational data.

Main Methods:

• The study proposes a novel approach by utilizing Lie groups instead of Lie algebras for causality analysis.
• An explicit formula is derived using only sample covariances, suitable for coarsely sampled data.

Main Results:

• The new method demonstrates qualitative suitability for linear systems and significantly reduces bias in nonlinear systems with reduced sampling frequency.
• The approach was successfully applied to a system of coupled Rössler oscillators, showing remarkable performance even when oscillators are nearly synchronized.

Conclusions:

• This research offers a partial but timely solution for conducting faithful causality analysis on coarsely sampled time series.
• The Lie group-based method enhances the applicability of causality analysis in scenarios with limited observational data, such as in synchronized dynamical systems.