Causality Analysis with Information Geometry: A Comparison

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The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction of one process based on the knowledge of another process at an earlier time. However, they have their own limitations, e.g., in applications to nonlinear, non-stationary data, or non-parametric models. In this study, we propose an alternative approach to quantify causality through information geometry that overcomes such limitations. Specifically, based on the information rate that measures the rate of change of the time-dependent distribution, we develop a model-free approach called information rate causality that captures the occurrence of the causality based on the change in the distribution of one process caused by another. This measurement is suitable for analyzing numerically generated non-stationary, nonlinear data. The latter are generated by simulating different types of discrete autoregressive models which contain linear and nonlinear interactions in unidirectional and bidirectional time-series signals. Our results show that information rate causality can capture the coupling of both linear and nonlinear data better than GC and TE in the several examples explored in the paper.
Original languageEnglish
Article number806
Number of pages59
Issue number5
Publication statusPublished - 16 May 2023

Bibliographical note

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


E.-j.K.and F.H. are partly supported by EPSRC Grant EP/W036770/1.


  • causality
  • information geometry
  • Transfer Entropy
  • Granger Causality
  • information causal rate
  • signal processing
  • nonlinear models
  • non-stationary
  • probability distribution


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