Causal inference using invariant prediction: identification and confidence intervals

Causal models are in general invariant in the following sense: we can intervene on predictor variables or change the whole experimental setting and the predictions in the causal model are still valid. Here, we propose to exploit this invariance for causal inference: given different experimental settings (for example various interventions), one can look for submodels that do show invariance across settings. The causal model will be a member of this set with high probability. This yields valid confidence intervals for the causal relationships in quite general scenarios. We examine some sufficient assumptions and investigate identifiability for structural equation models in more detail. The empirical properties are studied for various data sets, including gene perturbation experiments.