Bounding Counterfactuals under Selection Bias
This work addresses selection bias in causal inference, which is a common issue in data analysis, but it appears incremental as it builds on prior identifiability work with a new algorithmic approach.
The paper tackles the problem of causal analysis under selection bias by proposing an algorithm that handles both identifiable and unidentifiable queries, using a causal expectation-maximisation scheme to compute exact values or bounds, with experiments showing practical viability.
Causal analysis may be affected by selection bias, which is defined as the systematic exclusion of data from a certain subpopulation. Previous work in this area focused on the derivation of identifiability conditions. We propose instead a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal. This enables us to use the causal expectation-maximisation scheme to obtain the values of causal queries in the identifiable case, and to compute bounds otherwise. Experiments demonstrate the approach to be practically viable. Theoretical convergence characterisations are provided.