Active Invariant Causal Prediction: Experiment Selection through\n Stability

A fundamental difficulty of causal learning is that causal models can\ngenerally not be fully identified based on observational data only.\nInterventional data, that is, data originating from different experimental\nenvironments, improves identifiability. However, the improvement depends\ncritically on the target and nature of the interventions carried out in each\nexperiment. Since in real applications experiments tend to be costly, there is\na need to perform the right interventions such that as few as possible are\nrequired. In this work we propose a new active learning (i.e. experiment\nselection) framework (A-ICP) based on Invariant Causal Prediction (ICP) (Peters\net al., 2016). For general structural causal models, we characterize the effect\nof interventions on so-called stable sets, a notion introduced by (Pfister et\nal., 2019). We leverage these results to propose several intervention selection\npolicies for A-ICP which quickly reveal the direct causes of a response\nvariable in the causal graph while maintaining the error control inherent in\nICP. Empirically, we analyze the performance of the proposed policies in both\npopulation and finite-regime experiments.\n