# Unit Selection with Nonbinary Treatment and Effect

arXiv: https://arxiv.org/abs/2208.09569 · HTML: https://mlsanity.com/paper/2208.09569/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 20 Aug 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)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Bounds on Causal Effects and Application to High Dimensional Data](https://mlsanity.com/paper/2106.12121/) (2021)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)
- [Counterfactual Estimation and Optimization of Click Metrics for Search Engines](https://mlsanity.com/paper/1403.1891/) (2014)

## Built on by (most cited first, 12 of 12)

- [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)
- [On the Complexity of Counterfactual Reasoning](https://mlsanity.com/paper/2211.13447/) (2022)
- [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)
- [Causal Unit Selection using Tractable Arithmetic Circuits](https://mlsanity.com/paper/2404.06681/) (2024)
- [Estimating Probabilities of Causation with Machine Learning Models](https://mlsanity.com/paper/2502.08858/) (2025)
- [Statistical Decision Theory with Counterfactual Loss](https://mlsanity.com/paper/2505.08908/) (2025)
- [An Algorithm and Complexity Results for Causal Unit Selection](https://mlsanity.com/paper/2302.14412/) (2023)
- [Learning Probabilities of Causation with Mask-Augmented Data](https://mlsanity.com/paper/2505.17133/) (2025)

## 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", which is the payoff/cost associated with selecting an individual with given characteristics. This paper extends the benefit function to the general form such that the treatment and effect are not restricted to binary. We propose an algorithm to test the identifiability of the nonbinary benefit function and an algorithm to compute the bounds of the nonbinary benefit function using experimental and observational data.