# Identifying counterfactual probabilities using bivariate distributions and uplift modeling

arXiv: https://arxiv.org/abs/2512.08805 · HTML: https://mlsanity.com/paper/2512.08805/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 6 of 6)

- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [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)
- [Constructions for a bivariate beta distribution](https://mlsanity.com/paper/1406.5881/) (2014)
- [Partial counterfactual identification and uplift modeling: theoretical results and real-world assessment](https://mlsanity.com/paper/2211.07264/) (2022)

## Abstract (arXiv)

Uplift modeling estimates the causal effect of an intervention as the difference between potential outcomes under treatment and control, whereas counterfactual identification aims to recover the joint distribution of these potential outcomes (e.g., "Would this customer still have churned had we given them a marketing offer?"). This joint counterfactual distribution provides richer information than the uplift but is harder to estimate. However, the two approaches are synergistic: uplift models can be leveraged for counterfactual estimation. We propose a counterfactual estimator that fits a bivariate beta distribution to predicted uplift scores, yielding posterior distributions over counterfactual outcomes. Our approach requires no causal assumptions beyond those of uplift modeling. Simulations show the efficacy of the approach, which can be applied, for example, to the problem of customer churn in telecom, where it reveals insights unavailable to standard ML or uplift models alone.