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October 2013 Quantifying causal influences
Dominik Janzing, David Balduzzi, Moritz Grosse-Wentrup, Bernhard Schölkopf
Ann. Statist. 41(5): 2324-2358 (October 2013). DOI: 10.1214/13-AOS1145


Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other $n-1$ variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question.

Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution.

Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.


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Dominik Janzing. David Balduzzi. Moritz Grosse-Wentrup. Bernhard Schölkopf. "Quantifying causal influences." Ann. Statist. 41 (5) 2324 - 2358, October 2013.


Published: October 2013
First available in Project Euclid: 5 November 2013

zbMATH: 1281.62030
MathSciNet: MR3127868
Digital Object Identifier: 10.1214/13-AOS1145

Primary: 62-09 , 62M10

Keywords: Bayesian networks , causality , Information flow , transfer entropy

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 5 • October 2013
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