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

2025-07-16

AI Summary

This paper addresses the challenge of constructing prediction intervals for individual treatment effects (ITE), which are inherently unidentifiable due to the fundamental problem of causal inference—the simultaneous observation of potential outcomes is impossible, complicating uncertainty quantification. To tackle this, we introduce a covariate-dependent cross-world correlation parameter ρ(x) that captures the dependence structure between potential outcomes, incorporating domain knowledge to impose plausible bounds. Within the Neyman–Rubin superpopulation framework, we develop conditional correlation modeling and establish Gaussian asymptotic theory, providing the first systematic theoretical justification for the central role of ρ(x) in ITE interval estimation. Our method achieves asymptotically optimal coverage—guaranteeing nominal 1−α coverage—while substantially narrowing interval width: empirical results show over a two-thirds reduction compared to state-of-the-art methods, markedly enhancing reliability and decision utility in individualized causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 $Pig(Y(1) - Y(0) in C_{ITE}(X)ig) geq 1 - α$ 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.

Problem

• Estimating individual treatment effects with uncertainty quantification
• Addressing unidentifiability of cross-world correlation in potential outcomes
• Designing narrower, valid prediction intervals for ITE using domain-informed bounds

Innovation

• Uses cross-world correlation parameter for ITE
• Imposes interpretable bounds via expert knowledge
• Designs narrower, stable ITE prediction intervals