Bounding Counterfactuals under Selection Bias

TL;DR

This paper introduces an algorithm for bounding counterfactuals under selection bias, capable of handling both identifiable and unidentifiable cases, with proven convergence and practical effectiveness.

Contribution

It presents the first algorithm that addresses both identifiable and unidentifiable causal queries under selection bias using a causal EM scheme.

Findings

Likelihood of available data is unimodal despite missingness.

The proposed method effectively computes bounds and causal estimates.

The approach is practically viable with proven convergence.

Abstract

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.