A Intervention stable sets, plausible causal predictors and informative interventions A.1 Intervention stable sets A set of predictors

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.