ArticleJournal of the Royal Society, Interface2022
Embedding entropy: a nonlinear measure of dynamical causality.
Article in Journal of the Royal Society, Interface, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Advances in causal discovery methods for ecological time series.Biological reviews of the Cambridge Philosophical Society · 2026Review
- Best practices for moving from correlation to causation in ecological research.Nature communications · 2026Review
- Utilizing Causal Network Markers to Identify Tipping Points ahead of Critical Transition.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Detecting dynamical causality by intersection cardinal concavity.Fundamental research · 2025Article
- Transfer learning of multicellular organization via single-cell and spatial transcriptomics.PLoS computational biology · 2025Article
- Dynamics of directional motor tuning in the primate premotor and primary motor cortices during sensorimotor learning.Nature communications · 2024Article
- Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series.Royal Society open science · 2023Article
- Embedding entropy: a nonlinear measure of dynamical causality.Journal of the Royal Society, Interface · 2022Article
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Authors and funding
3 authors.
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Abstract
Research on concepts and computational methods of causality has a long history, and there are various concepts of causality as well as corresponding computing algorithms based on measured data. Here, by considering causes and effects from a dynamical perspective, we present a unified mathematical framework for the so-called dynamical causality (DC), which can detect causal interactions over time; notably, this framework covers Granger causality, transfer entropy, embedding causality and their conditional versions. Based on this framework, we further propose a causality criterion called embedding entropy (EE) to measure the DC between two variables. Moreover, its conditional version, conditional embedding entropy (cEE), is also derived for detecting conditional/direct causality. The significant advantages of EE and cEE are that they can be employed for solving not only nonlinear causal inference but also the non-separability problem, and they can reduce the scale bias in numerical calculation. The performance and robustness of EE and cEE were demonstrated through numerical simulations, and causal inference on various real-world datasets validated their effectiveness.
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