Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Data

TL;DR

This paper introduces a method to compute bounds for counterfactual queries by integrating biased observational and interventional data, using a causal EM scheme and graphical transformations, demonstrated through experiments and a case study.

Contribution

It develops a novel approach to bound counterfactuals from heterogeneous data sources, including biased observational and interventional data, via a causal EM algorithm and graphical transformations.

Findings

The likelihood function has no local maxima, enabling reliable optimization.

The approach provides accurate bounds for counterfactuals in complex data scenarios.

Numerical experiments and a case study validate the method's effectiveness.

Abstract

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.