# Recover Experimental Data with Selection Bias using Counterfactual Logic

arXiv: https://arxiv.org/abs/2506.00335 · HTML: https://mlsanity.com/paper/2506.00335/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 7 of 7)

- [Annotation Artifacts in Natural Language Inference Data](https://mlsanity.com/paper/1803.02324/) (2018)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Are We Modeling the Task or the Annotator? An Investigation of Annotator Bias in Natural Language Understanding Datasets](https://mlsanity.com/paper/1908.07898/) (2019)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Stereotype and Skew: Quantifying Gender Bias in Pre-trained and Fine-tuned Language Models](https://mlsanity.com/paper/2101.09688/) (2021)
- [It Is Different When Items Are Older: Debiasing Recommendations When Selection Bias and User Preferences Are Dynamic](https://mlsanity.com/paper/2111.12481/) (2021)
- [Selection Bias Induced Spurious Correlations in Large Language Models](https://mlsanity.com/paper/2207.08982/) (2022)

## Abstract (arXiv)

Selection bias, arising from the systematic inclusion or exclusion of certain samples, poses a significant challenge to the validity of causal inference. While Bareinboim et al. introduced methods for recovering unbiased observational and interventional distributions from biased data using partial external information, the complexity of the backdoor adjustment and the method's strong reliance on observational data limit its applicability in many practical settings. In this paper, we formally discover the recoverability of P(Y^*x^*) under selection bias with experimental data. By explicitly constructing counterfactual worlds via Structural Causal Models (SCMs), we analyze how selection mechanisms in the observational world propagate to the counterfactual domain. We derive a complete set of graphical and theoretical criteria to determine that the experimental distribution remain unaffected by selection bias. Furthermore, we propose principled methods for leveraging partially unbiased observational data to recover P(Y^*x^*) from biased experimental datasets. Simulation studies replicating realistic research scenarios demonstrate the practical utility of our approach, offering concrete guidance for mitigating selection bias in applied causal inference.