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Confounding ghost channels and causality: a new approach to causal information flows
Citation Link: https://doi.org/10.15480/882.3763
Publikationstyp
Journal Article
Date Issued
2021-06
Sprache
English
Author(s)
Institut
TORE-DOI
Journal
Volume
49
Issue
2
Start Page
547
End Page
576
Citation
Vietnam Journal of Mathematics 49 (2): 547-576 (2021-06)
Publisher DOI
Scopus ID
Publisher
Springer
Information theory provides a fundamental framework for the quantification of information flows through channels, formally Markov kernels. However, quantities such as mutual information and conditional mutual information do not necessarily reflect the causal nature of such flows. We argue that this is often the result of conditioning based on σ-algebras that are not associated with the given channels. We propose a version of the (conditional) mutual information based on families of σ-algebras that are coupled with the underlying channel. This leads to filtrations which allow us to prove a corresponding causal chain rule as a basic requirement within the presented approach.
Subjects
Causality
Conditional mutual information
Filtration
Information flow
Mutual information
DDC Class
004: Informatik
510: Mathematik
Funding Organisations
More Funding Information
The author acknowledges the support of the Deutsche Forschungsgemeinschaft Priority Programme “The Active Self” (SPP 2134).
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