Estimating high-dimensional intervention effects from observational data

2008/10/31 by Marloes H. Maathuis, Markus Kalisch, Peter Bühlmann · 3 citations
Computer Science · Mathematics · #Advanced Causal Inference Techniques #Algorithm #Artificial intelligence #Bayesian Modeling and Causal Inference #Causal inference #Causal model #Class (philosophy) #Computer science #Covariate #Data set #Directed acyclic graph #Discrete mathematics #Econometrics #Equivalence (formal languages) #Graph #Mathematics #Observational equivalence #Observational study #Set (abstract data type) #Statistical Methods and Bayesian Inference #Statistics #Theoretical computer science #msc:62-09 #msc:62H99 #stat.ME

paper · pdf · doi:10.1214/09-aos685

published as Annals of Statistics 2009, Vol. 37, No. 6A, 3133-3164 · Published in at http://dx.doi.org/10.1214/09-AOS685 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2009/08/17 · arxiv created 2009/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Causal Inference and Causal Explanation with Background Knowledge
• On rigid circuit graphs
• Causal diagrams for empirical research
• Incidence matrices and interval graphs
• Estimating high-dimensional directed acyclic graphs with the PC-algorithm
• Stability Selection
• Statistics and Causal Inference
• Causal Diagrams for Epidemiologic Research

Cited by

• Towards personalised intervention: A causal-dynamical framework to determine psychological treatment trajectories
• A Local Method for Identifying Causal Relations under Markov Equivalence
• Geometry of the faithfulness assumption in causal inference

Related

• Learning and scoring Gaussian latent variable causal models with unknown additive interventions
• Characterization and Learning of Causal Graphs from Hard Interventions
• Bayesian causal discovery from unknown general interventions
• Structural restrictions in local causal discovery: identifying direct causes of a target variable
• Towards Bounding Causal Effects under Markov Equivalence