arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2610.15212stat.ME
收藏

基于最优传输的稳定因果估计

Stable Causal Estimation with Optimal Transport

Department of Statistics, University of Michigan(密歇根大学统计系)

Yidan Xu, Yixin Wang, XuanLong Nguyen

AI总结:

针对观察性研究中重叠不足导致的估计量不稳定问题,提出基于最优传输的稳定传输估计量STE,其无需密度估计或倾向得分建模,在合成与真实数据集上表现出更优性能。

摘要:

在观察性研究中,重叠假设(又称正性)在实践中常难以满足。有限的重叠会导致逆概率加权(IPW)等广泛使用的估计量不稳定,其方差取决于密度比,而当倾向得分趋近于0或1时,密度比会爆炸式增长。为应对这一挑战,我们提出稳定传输估计量(STE),这是一种基于最优传输的方法,用于在重叠成立但严格重叠不满足时估计平均因果效应。与IPW不同,STE的方差不含密度比因子,其由传输映射本身决定,在矩有界的情况下保持有限,即使密度比发散也不受影响。通过用感知几何的传输映射替代重加权,STE构建了稳定的反事实比较,无需密度估计或倾向得分建模。STE还可扩展到重叠条件被违反的场景:当协变量支撑仅部分重叠时,线性插值传输映射能实现有原则的外推,且具有明确的偏差-方差权衡。我们证明了STE的一致性、渐近正态性和方差特性,该特性明确了估计传输映射对渐近方差的贡献。在合成数据集和真实数据集上,与现有估计量相比,STE表现出更好的鲁棒性、更低的偏差和显著更稳定的方差。

英文摘要:

In observational studies, the overlap assumption, also called positivity, is frequently strained in practice. Limited overlap destabilizes widely used estimators such as inverse propensity weighting (IPW), whose variance depends on density ratios that explode as propensity scores approach zero or one. To address this challenge, we propose the Stable Transport Estimator (STE), an optimal transport-based approach for estimating average causal effects when overlap holds but strict overlap fails. Unlike IPW, the variance of STE contains no density-ratio factor; it is governed by the transport map itself and stays finite under bounded moments, even when density ratios diverge. By replacing reweighting with a geometry-aware transport map, STE constructs stable counterfactual comparisons without requiring density estimation or propensity score modeling. STE further extends to settings where the overlap condition is violated: when covariate supports overlap only partially, a linear interpolation transport map enables principled extrapolation with explicit bias-variance trade-offs. We establish consistency, asymptotic normality, and a variance characterization that makes explicit the contribution of the estimated transport map to the asymptotic variance. Across synthetic and real datasets, STE demonstrates improved robustness, reduced bias, and markedly more stable variance compared to existing estimators.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑