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Publisher DOI: 10.1007/s10013-021-00511-w
Title: Confounding ghost channels and causality: a new approach to causal information flows
Language: English
Authors: Ay, Nihat 
Keywords: Causality;Conditional mutual information;Filtration;Information flow;Mutual information
Issue Date: Jun-2021
Publisher: Springer
Source: Vietnam Journal of Mathematics 49 (2): 547-576 (2021-06)
Journal: Vietnam journal of mathematics 
Abstract (english): 
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.
DOI: 10.15480/882.3763
ISSN: 2305-2228
Institute: Data Science Foundations E-21 
Document Type: Article
Funded by: Deutsche Forschungsgemeinschaft (DFG) 
More Funding information: The author acknowledges the support of the Deutsche Forschungsgemeinschaft Priority Programme “The Active Self” (SPP 2134).
Project: Projekt DEAL 
SPP 2134: Die sensomotorische Architektur des Selbst: Theorie der Informationsintegration in verkörperten Systemen 
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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