# Partial counterfactual identification and uplift modeling: theoretical results and real-world assessment

arXiv: https://arxiv.org/abs/2211.07264 · HTML: https://mlsanity.com/paper/2211.07264/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 14 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Nested Counterfactual Identification from Arbitrary Surrogate Experiments](https://mlsanity.com/paper/2107.03190/) (2021)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Causal Decision Making and Causal Effect Estimation Are Not the Same... and Why It Matters](https://mlsanity.com/paper/2104.04103/) (2021)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)

## Built on by (most cited first, 3 of 3)

- [Uplift vs. predictive modeling: a theoretical analysis](https://mlsanity.com/paper/2309.12036/) (2023)
- [A churn prediction dataset from the telecom sector: a new benchmark for uplift modeling](https://mlsanity.com/paper/2312.07206/) (2023)
- [Identifying counterfactual probabilities using bivariate distributions and uplift modeling](https://mlsanity.com/paper/2512.08805/) (2025)

## Abstract (arXiv)

Counterfactuals are central in causal human reasoning and the scientific discovery process. The uplift, also called conditional average treatment effect, measures the causal effect of some action, or treatment, on the outcome of an individual. This paper discusses how it is possible to derive bounds on the probability of counterfactual statements based on uplift terms. First, we derive some original bounds on the probability of counterfactuals and we show that tightness of such bounds depends on the information of the feature set on the uplift term. Then, we propose a point estimator based on the assumption of conditional independence between the counterfactual outcomes. The quality of the bounds and the point estimators are assessed on synthetic data and a large real-world customer data set provided by a telecom company, showing significant improvement over the state of the art.