ESTIMATING HIGH-DIMENSIONAL INTERVENTION EFFECTS FROM OBSERVATIONAL DATA

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...

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Bibliographic Details
Published in:The Annals of statistics 2009-12, Vol.37 (6A), p.3133-3164
Main Authors: Maathuis, Marloes H., Kalisch, Markus, Bühlmann, Peter
Format: Article
Language:English
Subjects:
62-09
62H99
Absolute value
Algorithms
Calculus
Causal analysis
Causality
Combinatorics
Combinatorics. Ordered structures
Consistent estimators
Datasets
directed acyclic graph (DAG)
Directed acyclic graphs
Equivalence relation
Estimation methods
Exact sciences and technology
General topics
Graph representations
Graph theory
graphical modeling
Inference
intervention calculus
Mathematics
Multisets
PC-algorithm
Probability and statistics
Sample size
Sciences and techniques of general use
sparsity
Statistics
Studies
Vertices
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/09-AOS685