# Conservative Inference for Counterfactuals

arXiv: https://arxiv.org/abs/2310.12757 · HTML: https://mlsanity.com/paper/2310.12757/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [What is a good matching of probability measures? A counterfactual lens on transport maps](https://mlsanity.com/paper/2509.16027/) (2025)

## Abstract (arXiv)

In causal inference, the joint law of a set of counterfactual random variables is generally not identified. We show that a conservative version of the joint law - corresponding to the smallest treatment effect - is identified. Finding this law uses recent results from optimal transport theory. Under this conservative law we can bound causal effects and we may construct inferences for each individual's counterfactual dose-response curve. Intuitively, this is the flattest counterfactual curve for each subject that is consistent with the distribution of the observables. If the outcome is univariate then, under mild conditions, this curve is simply the quantile function of the counterfactual distribution that passes through the observed point. This curve corresponds to a nonparametric rank preserving structural model.