Estimating high-dimensional intervention effects from observational data

TL;DR

This paper introduces a computationally efficient method to estimate and analyze high-dimensional causal effects from observational data by leveraging DAG equivalence classes and intervention calculus.

Contribution

It combines DAG equivalence class estimation with intervention calculus to estimate causal effects efficiently in high-dimensional settings.

Findings

Method accurately estimates causal effects in simulations.

Approach identifies important variables using effect bounds.

Demonstrated effectiveness on riboflavin production 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.