Open Access
December 2009 Estimating high-dimensional intervention effects from observational data
Marloes H. Maathuis, Markus Kalisch, Peter Bühlmann
Ann. Statist. 37(6A): 3133-3164 (December 2009). DOI: 10.1214/09-AOS685


We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in high-dimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.


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Marloes H. Maathuis. Markus Kalisch. Peter Bühlmann. "Estimating high-dimensional intervention effects from observational data." Ann. Statist. 37 (6A) 3133 - 3164, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1191.62118
MathSciNet: MR2549555
Digital Object Identifier: 10.1214/09-AOS685

Primary: 62-09 , 62H99

Keywords: Causal analysis , directed acyclic graph (DAG) , graphical modeling , intervention calculus , PC-algorithm , Sparsity

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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