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If $X,Y,Z$ denote sets of random variables, two different data sources maycontain samples from $P_{X,Y}$ and $P_{Y,Z}$, respectively. We argue thatcausal inference can help inferring properties of the 'unobserved jointdistributions' $P_{X,Y,Z}$ or $P_{X,Z}$. The properties may be conditionalindependences or also quantitative statements about dependences.  More generally, we define a learning scenario where the input is a subset ofvariables and the label is some statistical property of that subset. Sets ofjointly observed variables define the training points, while unobserved setsare possible test points. To solve this learning task, we infer, as anintermediate step, a causal model from the observations that then entailsproperties of unobserved sets. Accordingly, we can define the VC dimension of aclass of causal models and derive generalization bounds for the predictions.  Here, causal inference becomes more modest and better accessible to empiricaltests than usual: rather than trying to find a causal hypothesis that is 'true'(which is a problematic term when it is unclear how to define interventions) acausal hypothesis is useful whenever it correctly predicts statisticalproperties of unobserved joint distributions.  Within such a 'pragmatic' application of causal inference, some popularheuristic approaches become justified in retrospect. It is, for instance,allowed to infer DAGs from partial correlations instead of conditionalindependences if the DAGs are only used to predict partial correlations.  I hypothesize that our pragmatic view on causality may even cover the usualmeaning in terms of interventions and sketch why predicting the impact ofinterventions can sometimes also be phrased as a task of the above type.

Merging joint distributions via causal model classes with low VC dimension