Estimating high-dimensional intervention effects from observational data

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.

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)

References in corpus (5)

• High-dimensional graphs and variable selection with the Lasso
• Estimating high-dimensional directed acyclic graphs with the PC-algorithm
• Causal Inference and Causal Explanation with Background Knowledge
• Strong Faithfulness and Uniform Consistency in Causal Inference
• Stability Selection

Cited by in corpus (59)

• Learning high-dimensional directed acyclic graphs with latent and selection variables
• Geometry of the faithfulness assumption in causal inference
• A fast PC algorithm for high dimensional causal discovery with multi-core PCs
• ${\ell }_0$-penalized maximum likelihood for sparse directed acyclic graphs
• The Risks of Invariant Risk Minimization
• A generalized back-door criterion
• Foundations of Structural Causal Models with Cycles and Latent Variables
• Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs
• Graphical Criteria for Efficient Total Effect Estimation via Adjustment in Causal Linear Models
• Partition MCMC for inference on acyclic digraphs
• Causal Inference in Genetic Trio Studies
• A Complete Generalized Adjustment Criterion
• Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs
• Causal interpretation of stochastic differential equations
• backShift: Learning causal cyclic graphs from unknown shift interventions
• On efficient adjustment in causal graphs
• Towards Efficient Local Causal Structure Learning
• Interpreting and using CPDAGs with background knowledge
• Causality on Cross-Sectional Data: Stable Specification Search in Constrained Structural Equation Modeling
• A Unifying Causal Framework for Analyzing Dataset Shift-stable Learning Algorithms
• High dimensional sparse covariance estimation via directed acyclic graphs
• Towards Privacy-Aware Causal Structure Learning in Federated Setting
• Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-based Approach
• A Local Method for Identifying Causal Relations under Markov Equivalence
• Inferring network structure from interventional time-course experiments
• Statistical Perspective on Functional and Causal Neural Connectomics: The Time-Aware PC Algorithm
• Order-independent constraint-based causal structure learning
• Formulas for Counting the Sizes of Markov Equivalence Classes of Directed Acyclic Graphs
• Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical Models
• Causal Network Learning from Multiple Interventions of Unknown Manipulated Targets
• Discussion of Big Bayes Stories and BayesBag
• Evaluating structure learning algorithms with a balanced scoring function
• On sampling graphical Markov models
• Causal network inference using biochemical kinetics
• Bayesian network structure learning with causal effects in the presence of latent variables
• Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables
• ParallelPC: an R package for efficient constraint based causal exploration
• Learning Sparse Additive Models with Interactions in High Dimensions
• Efficient least squares for estimating total effects under linearity and causal sufficiency
• Causal query in observational data with hidden variables
• Towards Scalable Bayesian Learning of Causal DAGs
• Marginal integration for nonparametric causal inference
• A review of some recent advances in causal inference
• Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
• Nonparametric Causal Feature Selection for Spatiotemporal Risk Mapping of Malaria Incidence in Madagascar
• Identification of Strong Edges in AMP Chain Graphs
• Practically Effective Adjustment Variable Selection in Causal Inference
• Towards unique and unbiased causal effect estimation from data with hidden variables
• Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders
• Stable specification search in structural equation model with latent variables
• Minimal enumeration of all possible total effects in a Markov equivalence class
• A New Statistical Framework for Genetic Pleiotropic Analysis of High Dimensional Phenotype Data
• Data-Driven Confounder Selection via Markov and Bayesian Networks
• Fully integrative data analysis of NMR metabolic fingerprints with comprehensive patient data: a case report based on the German Chronic Kidney Disease (GCKD) study
• Joint estimation of causal effects from observational and intervention gene expression data
• Evaluation of Causal Structure Learning Algorithms via Risk Estimation
• Ancestral causal learning in high dimensions with a human genome-wide application
• Estimation Rates for Sparse Linear Cyclic Causal Models
• Local search for efficient causal effect estimation