# Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach

arXiv: https://arxiv.org/abs/2603.27320 · HTML: https://mlsanity.com/paper/2603.27320/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 67 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Builds on (most cited first, 30 of 41)

- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [Bayesian Causal Inference: A Critical Review](https://mlsanity.com/paper/2206.15460/) (2022)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Causal Inference: A Missing Data Perspective](https://mlsanity.com/paper/1712.06170/) (2017)
- [Kandinsky Conformal Prediction: Beyond Class- and Covariate-Conditional Coverage](https://mlsanity.com/paper/2502.17264/) (2025)
- [Conformal Inference under High-Dimensional Covariate Shifts via Likelihood-Ratio Regularization](https://mlsanity.com/paper/2502.13030/) (2025)
- [PCS-UQ: Uncertainty Quantification via the Predictability-Computability-Stability Framework](https://mlsanity.com/paper/2505.08784/) (2025)
- [Decomposing Treatment Effect Variation](https://mlsanity.com/paper/1605.06566/) (2016)
- [Conformal Convolution and Monte Carlo Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2402.04906/) (2024)
- [Insights into the "cross-world" independence assumption of causal mediation analysis](https://mlsanity.com/paper/2003.10341/) (2020)
- [On Doubly Robust Inference for Double Machine Learning in Semiparametric Regression](https://mlsanity.com/paper/2107.06124/) (2021)
- [Counterfactual Cocycles: A Framework for Robust and Coherent Counterfactual Transports](https://mlsanity.com/paper/2405.13844/) (2024)
- [Adapting Prediction Sets to Distribution Shifts Without Labels](https://mlsanity.com/paper/2406.01416/) (2024)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)

## Built on by (most cited first, 1 of 1)

- [CAFE: Counterfactual Prediction via Fast Posterior Estimation](https://mlsanity.com/paper/2609.32167/) (2026)

## Abstract (arXiv)

Retrospective causal questions ask what would have happened to an observed individual had they received a different treatment. We study the problem of estimating μ(x,y)=mathbbE[Y(1)mid X=x,Y(0)=y], the expected counterfactual outcome for an individual with covariates x and observed outcome y, and constructing valid prediction intervals under the Neyman-Rubin superpopulation model. This quantity is generally not identified without additional assumptions. To link the observed and unobserved potential outcomes, we work with a cross-world correlation ρ(x)=cor(Y(1),Y(0)mid X=x); plausible bounds on ρ(x) enable a principled approach to this otherwise unidentified problem. We introduce retrospective counterfactual estimators hatμρ(x,y) and prediction intervals Cρ(x,y) that asymptotically satisfy P[Y(1)∈ Cρ(x,y)mid X=x, Y(0)=y]≥1-α under standard causal assumptions. Many common baselines implicitly correspond to endpoint choices ρ=0 or ρ=1 (ignoring the factual outcome or treating the counterfactual as a shifted factual outcome). Interpolating between these cases through cross-world dependence yields substantial gains in both theory and practice.