# Bounding Counterfactuals under Selection Bias

arXiv: https://arxiv.org/abs/2208.01417 · HTML: https://mlsanity.com/paper/2208.01417/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 26 Jul 2022.

## Builds on (most cited first, 6 of 6)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [Structural Causal Models Are (Solvable by) Credal Networks](https://mlsanity.com/paper/2008.00463/) (2020)
- [Causal Inference Using Tractable Circuits](https://mlsanity.com/paper/2202.02891/) (2022)
- [Causal Expectation-Maximisation](https://mlsanity.com/paper/2011.02912/) (2020)
- [Conservative Inference Rule for Uncertain Reasoning under Incompleteness](https://mlsanity.com/paper/1401.3471/) (2014)

## Built on by (most cited first, 6 of 6)

- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Approximating Counterfactual Bounds while Fusing Observational, Biased and Randomised Data Sources](https://mlsanity.com/paper/2307.16577/) (2023)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [Tractable Bounding of Counterfactual Queries by Knowledge Compilation](https://mlsanity.com/paper/2310.03352/) (2023)
- [Learning to Bound Counterfactual Inference from Observational, Biased and Randomised Data](https://mlsanity.com/paper/2212.02932/) (2022)

## Abstract (arXiv)

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.