Estimating the effect of joint interventions from observational data in sparse high-dimensional settings

TL;DR

This paper introduces new methods for estimating the effects of multiple simultaneous interventions from observational data in high-dimensional, sparse settings, assuming linear structural models and extending to nonparanormal distributions.

Contribution

It develops novel estimators for joint causal effects, providing asymptotic variances and high-dimensional consistency proofs, applicable even when the causal structure is unknown.

Findings

Estimators perform well in simulation studies.

Methods successfully applied to DREAM4 challenge data.

Extended to nonparanormal distribution models.

Abstract

We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency when the causal structure is fully unknown and the joint distribution is multivariate Gaussian. We also propose a generalization of our methodology to the class of nonparanormal distributions. We evaluate the estimators in simulation studies and also illustrate them on data from the DREAM4 challenge.