Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Data
This addresses the challenge of counterfactual inference from heterogeneous data for causal modeling, though it appears incremental as an extension of existing methods to multiple datasets.
The paper tackles the problem of computing counterfactual bounds in structural causal models by integrating multiple observational and interventional datasets, which may be biased. It shows that the likelihood has no local maxima, enabling the use of causal expectation-maximization to compute approximate bounds, with systematic experiments and a palliative care case study demonstrating effectiveness and accuracy.
We address the problem of integrating data from multiple, possibly biased, observational and interventional studies, to eventually compute counterfactuals in structural causal models. We start from the case of a single observational dataset affected by a selection bias. We show that the likelihood of the available data has no local maxima. This enables us to use the causal expectation-maximisation scheme to compute approximate bounds for partially identifiable counterfactual queries, which are the focus of this paper. We then show how the same approach can solve the general case of multiple datasets, no matter whether interventional or observational, biased or unbiased, by remapping it into the former one via graphical transformations. Systematic numerical experiments and a case study on palliative care show the effectiveness and accuracy of our approach, while hinting at the benefits of integrating heterogeneous data to get informative bounds in case of partial identifiability.