# Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects

arXiv: https://arxiv.org/abs/2507.12581 · HTML: https://mlsanity.com/paper/2507.12581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 16 Jul 2025.

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

- [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)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [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)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [A comparison of methods for model selection when estimating individual treatment effects](https://mlsanity.com/paper/1804.05146/) (2018)
- [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)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Stable discovery of interpretable subgroups via calibration in causal studies](https://mlsanity.com/paper/2008.10109/) (2020)
- [Counterfactual Generative Modeling with Variational Causal Inference](https://mlsanity.com/paper/2410.12730/) (2024)
- [Conformal prediction intervals for the individual treatment effect](https://mlsanity.com/paper/2006.01474/) (2020)
- [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)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions](https://mlsanity.com/paper/2110.06627/) (2021)
- [Identifiability of causal graphs under nonadditive conditionally parametric causal models](https://mlsanity.com/paper/2303.15376/) (2023)
- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Quantifying Individual Risk for Binary Outcomes](https://mlsanity.com/paper/2402.10537/) (2024)
- [Ensemble Method for Estimating Individualized Treatment Effects](https://mlsanity.com/paper/2202.12445/) (2022)
- [Extreme Treatment Effect: Extrapolating Dose-Response Function Into Extreme Treatment Domain](https://mlsanity.com/paper/2403.11003/) (2024)

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

- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)

## Abstract (arXiv)

While average treatment effects (ATE) and conditional average treatment effects (CATE) provide valuable population- and subgroup-level summaries, they fail to capture uncertainty at the individual level. For high-stakes decision-making, individual treatment effect (ITE) estimates must be accompanied by valid prediction intervals that reflect heterogeneity and unit-specific uncertainty. However, the fundamental unidentifiability of ITEs limits the ability to derive precise and reliable individual-level uncertainty estimates. To address this challenge, we investigate the role of a cross-world correlation parameter,  ρ(x) = cor(Y(1), Y(0) | X = x) , which describes the dependence between potential outcomes, given covariates, in the Neyman-Rubin super-population model with i.i.d. units. Although  ρ  is fundamentally unidentifiable, we argue that in most real-world applications, it is possible to impose reasonable and interpretable bounds informed by domain-expert knowledge. Given ρ, we design prediction intervals for ITE, achieving more stable and accurate coverage with substantially shorter widths; often less than 1/3 of those from competing methods. The resulting intervals satisfy coverage guarantees Pbig(Y(1) - Y(0) ∈ CITE(X)big) ≥ 1 - α and are asymptotically optimal under Gaussian assumptions. We provide strong theoretical and empirical arguments that cross-world assumptions can make individual uncertainty quantification both practically informative and statistically valid.