基于核方法的函数型因果效应估计，提升复杂动态数据建模能力
Kernel-based estimators for functional causal effects
- 用经验弗雷歇均值与算子核构建函数型因果估计器
- 理论保证一致性，实证显示在生物监测中有效捕捉时序动态
- 适合处理高维、有序、非线性函数数据，尤其适用于医学时间序列
我们提出基于经验弗雷歇均值和算子值核的因果效应估计器，专为函数型数据空间设计。这些方法应对高维性、序列顺序性和模型复杂性挑战，同时保持对治疗设定错误的鲁棒性。通过结构假设，获得潜在结果的紧凑表示，实现随时间及协变量变化的可扩展因果效应估计。提供关于功能因果效应一致性的理论分析，以及多种提议估计器的实证比较。在具有函数型结果的二元处理设置中的应用展示了该框架在生物监测中的实用性，其中结果表现出复杂的时序动态。估计器能处理注册协变量和结果，将其对齐至弗雷歇均值，也可采用高阶表示以捕捉复杂的协变量-结果交互。这些进展将因果推断拓展至动态和非线性领域，为函数型数据场景下的复杂治疗效应理解提供了新工具。
原文摘要 · Abstract (English)
We propose causal effect estimators based on empirical Fréchet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity while preserving robustness to treatment misspecification. Using structural assumptions, we obtain compact representations of potential outcomes, enabling scalable estimation of causal effects over time and across covariates. We provide both theoretical, regarding the consistency of functional causal effects, as well as empirical comparison of a range of proposed causal effect estimators. Applications to binary treatment settings with functional outcomes illustrate the framework's utility in biomedical monitoring, where outcomes exhibit complex temporal dynamics. Our estimators accommodate scenarios with registered covariates and outcomes, aligning them to the Fréchet means, as well as cases requiring higher-order representations to capture intricate covariate-outcome interactions. These advancements extend causal inference to dynamic and non-linear domains, offering new tools for understanding complex treatment effects in functional data settings.
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