A fundamental difficulty of causal learning is that causal models can generally not be fully identified based on observational data only. Interventional data, that is, data originating from different experimental environments, improves identifiability. However, the improvement depends critically on the target and nature of the interventions carried out in each experiment. Since in real applications experiments tend to be costly, there is a need to perform the right interventions such that as few as possible are required. In this work we propose a new active learning (i.e.

A.2 Stable sets vs. plausible causal predictors Example A.2. Take the following SCM, Here we present a slightly adapted version of Invariant Causal Prediction [27]. A-ICP (algorithm 1) does not require testing all subsets in each iteration. In the experiments of section 5, we test invariance by performing a least-squares regression of the response on the predictors, and then running a two-sample t-test and an F-test [27, section 3.1.2] Definition 2.2), which in the worst case (all sets are accepted) incurs a cost of O (p 2 By Corollary 3.1, at each iteration it suffices for ICP to consider only the sets accepted in the previous In section D.1, we show the average number of interventions until exact recovery (Figure D.5) for the finite-sample experiments presented in section 5. In section D.2, we provide additional results for the total 50 iterations over which the policies are run: the family-wise error rate is shown in Figure D.6, Figures D.8 and D.7 show the Finally, section D.5 contains additional results comparing the interplay between Figure D.5: (finite regime) Average number of interventions until the causal parents are recovered The "e" policy performs well across all sample sizes, and is the best performer except at 1000 The results in Figure D.7 and Figure D.8 illustrate the fact that if there are no constraints on the number of interventions, the random policy is among the most robust options, as its choice of Overall, the empty-set strategy is the best performer across all sample sizes for a large range of intervention numbers.

We would like to thank you for your time and valuable feedback. Thank you for helping us to improve our manuscript! We hope to have correctly understood your questions, and will try to exhaustively address all your comments. We agree to be more specific as to what we mean by "other types of interventions" in footnote 1, p. 3, and will We thank reviewer 4 for the additional comments on the manuscript. Combining this method with A-ICP is interesting future work.

A fundamental difficulty of causal learning is that causal models can generally not be fully identified based on observational data only. Interventional data, that is, data originating from different experimental environments, improves identifiability. However, the improvement depends critically on the target and nature of the interventions carried out in each experiment. Since in real applications experiments tend to be costly, there is a need to perform the right interventions such that as few as possible are required. In this work we propose a new active learning (i.e.

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