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

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 obser-vational data come from an unknown Gaussian linear structural equation model. 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 unknown. We compare the estimators in simulation studies and also illustrate them on data from the DREAM4 challenge.