# Unit Selection with Causal Diagram

arXiv: https://arxiv.org/abs/2109.07556 · HTML: https://mlsanity.com/paper/2109.07556/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [Counterfactual Estimation and Optimization of Click Metrics for Search Engines](https://mlsanity.com/paper/1403.1891/) (2014)

## Built on by (most cited first, 17 of 17)

- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Unit Selection with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09569/) (2022)
- [Probabilities of Causation: Adequate Size of Experimental and Observational Samples](https://mlsanity.com/paper/2210.05027/) (2022)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [Unit Selection: Learning Benefit Function from Finite Population Data](https://mlsanity.com/paper/2210.08203/) (2022)
- [Unit Selection: Case Study and Comparison with A/B Test Heuristic](https://mlsanity.com/paper/2210.05030/) (2022)
- [Probabilities of Causation: Role of Observational Data](https://mlsanity.com/paper/2210.08874/) (2022)
- [Epsilon-Identifiability of Causal Quantities](https://mlsanity.com/paper/2301.12022/) (2023)
- [Partial counterfactual identification and uplift modeling: theoretical results and real-world assessment](https://mlsanity.com/paper/2211.07264/) (2022)
- [Bounding the Probabilities of Benefit and Harm Through Sensitivity Parameters and Proxies](https://mlsanity.com/paper/2303.05396/) (2023)
- [Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2402.09165/) (2024)
- [Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2407.15273/) (2024)
- [An Algorithm and Complexity Results for Causal Unit Selection](https://mlsanity.com/paper/2302.14412/) (2023)
- [Distribution-consistency Structural Causal Models](https://mlsanity.com/paper/2401.15911/) (2024)
- [Identification of Probabilities of Causation: from Recursive to Closed-Form Bounds](https://mlsanity.com/paper/2505.15274/) (2025)
- [Causality-Based Feature Importance Quantifying Methods: PN-FI, PS-FI and PNS-FI](https://mlsanity.com/paper/2308.14474/) (2023)
- [General sample size analysis for probabilities of causation: a delta method approach](https://mlsanity.com/paper/2602.17070/) (2026)

## Abstract (arXiv)

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged. Using a combination of experimental and observational data, Li and Pearl derived tight bounds on the "benefit function" - the payoff/cost associated with selecting an individual with given characteristics. This paper shows that these bounds can be narrowed significantly (enough to change decisions) when structural information is available in the form of a causal model. We address the problem of estimating the benefit function using observational and experimental data when specific graphical criteria are assumed to hold.