Estimating Aleatoric Uncertainty in the Causal Treatment Effect

Previous work on causal inference has primarily focused on averages and conditional averages of treatment effects, with significantly less attention on variability and uncertainty in individual treatment responses. In this paper, we introduce the variance of the treatment effect (VTE) and conditional variance of treatment effect (CVTE) as the natural measure of aleatoric uncertainty inherent in treatment responses, and we demonstrate that these quantities are identifiable from observed data under mild assumptions, even in the presence of unobserved confounders. We further propose nonparametric kernel-based estimators for VTE and CVTE, and our theoretical analysis establishes their convergence. We also test the performance of our method through extensive empirical experiments on both synthetic and semi-simulated datasets, where it demonstrates superior or comparable performance to naive baselines.

💡 Research Summary

The paper tackles a largely overlooked aspect of causal inference: the aleatoric uncertainty inherent in individual treatment responses. While most prior work focuses on average treatment effects (ATE) or conditional average treatment effects (CATE), the authors introduce two new causal parameters—the variance of the treatment effect (VTE) and its conditional counterpart (CVTE)—as natural measures of this uncertainty. VTE is defined as the variance of the individual causal contrast Y(1) − Y(0), and CVTE(v) is the same variance conditioned on a covariate V = v, allowing a granular view of heterogeneity across sub‑populations.

The authors first establish that VTE and CVTE are not identifiable under the standard ignorability assumption alone, because the covariance between the two potential outcomes cannot be recovered from observed data. To overcome this, they add a second, mild assumption: conditional uncorrelatedness of the potential outcomes given observed covariates X (E