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Information Theoretic Causal Effect Quantification

Department of Mathematics and Computer Science, University of Basel, CH-4051 Basel, Switzerland
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Entropy 2019, 21(10), 975; https://doi.org/10.3390/e21100975
Received: 31 August 2019 / Revised: 23 September 2019 / Accepted: 30 September 2019 / Published: 5 October 2019
(This article belongs to the Special Issue Information Theoretic Learning and Kernel Methods)
Modelling causal relationships has become popular across various disciplines. Most common frameworks for causality are the Pearlian causal directed acyclic graphs (DAGs) and the Neyman-Rubin potential outcome framework. In this paper, we propose an information theoretic framework for causal effect quantification. To this end, we formulate a two step causal deduction procedure in the Pearl and Rubin frameworks and introduce its equivalent which uses information theoretic terms only. The first step of the procedure consists of ensuring no confounding or finding an adjustment set with directed information. In the second step, the causal effect is quantified. We subsequently unify previous definitions of directed information present in the literature and clarify the confusion surrounding them. We also motivate using chain graphs for directed information in time series and extend our approach to chain graphs. The proposed approach serves as a translation between causality modelling and information theory.
Keywords: directed information; conditional mutual information; directed mutual information; confounding; causal effect; back-door criterion; average treatment effect; potential outcomes; time series; chain graph directed information; conditional mutual information; directed mutual information; confounding; causal effect; back-door criterion; average treatment effect; potential outcomes; time series; chain graph
MDPI and ACS Style

Wieczorek, A.; Roth, V. Information Theoretic Causal Effect Quantification. Entropy 2019, 21, 975.

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