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We address the problem of integrating data from multiple, possibly biased,observational and interventional studies, to eventually compute counterfactualsin structural causal models. We start from the case of a single observationaldataset affected by a selection bias. We show that the likelihood of theavailable data has no local maxima. This enables us to use the causalexpectation-maximisation scheme to approximate the bounds for partiallyidentifiable counterfactual queries, which are the focus of this paper. We thenshow how the same approach can address the general case of multiple datasets,no matter whether interventional or observational, biased or unbiased, byremapping it into the former one via graphical transformations. Systematicnumerical experiments and a case study on palliative care show theeffectiveness of our approach, while hinting at the benefits of fusingheterogeneous data sources to get informative outcomes in case of partialidentifiability.

Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources