Impact statement: Any method that learns from finite data is subject to statistical estimation errors and model assumptions that necessarily limit the full applicability of its findings. Unfortunately, study outcomes are not always communicated with the required qualifications. As an example, statistical hypothesis testing is often employed carelessly, e.g. by using p-values to claim “statistical significance” without paying attention to the underlying assumptions [5]. There is a danger that this problem gets exacerbated when one aims to estimate causal structures. Estimates from causal inference algorithms could be claimed to “prove” a given causal relationship, ruling out various alternative explanations that one would consider when explaining a statistical association. For example, ethnicity could be claimed to have a causal effect on criminality and thereby used as a justification for oppressive political measures. While this would represent a clear abuse of the technology, we as researchers have to ensure that similar mistakes in interpretation are not made unintentionally. This implies being conscientious about understanding as well as stating the limitations of our research. While there is a risk that causal inference methods are misused as described above, there is of course also an array of settings where causal learning—and in particular active causal learning—can be extremely useful. As our main motivation we envision the empirical sciences where interventions correspond to physical experiments which can be extremely costly in terms of time and/or money. For complex systems, as for example gene regulatory networks in biology, it might be difficult for human scientists to choose informative experiments, particularly if they are forced to rely on data alone. Our goal is to develop methods to aid scientists to better understand their data and perform more effective experiments, resulting in significant resource savings. The specific impact of our proposed methodology will depend on the application. For the method we propose in this work, one requirement for application would be that the experiments yield more than one data point (and ideally many), so that our invariance-based approach can be employed. In future work, we aim to develop methodology that is geared towards the setting where only very few data points per experiment are available.