用拓扑结构差异衡量因果效应，突破复杂数据空间限制。
Topological Causal Effects
- 基于持久性图的轮廓函数捕捉潜在结果的拓扑差异
- 提出高效双重稳健估计器，实现功能弱收敛与假设检验
- 适用于复杂非欧空间数据，适合拓扑分析研究者
在结果分布于复杂非欧空间的情况下，传统因果推断方法难以捕捉有意义的结构变异。本文提出一种拓扑因果推断框架，通过持久性图的加权轮廓函数总结潜在结果的拓扑结构差异来定义处理效应。在完全非参数模型下，开发了高效的双重稳健估计器，建立了功能弱收敛性，并构建了零假设（无拓扑效应）的正式检验。实证研究表明，该方法能可靠地量化多种复杂结果类型中的拓扑处理效应。
原文摘要 · Abstract (English)
Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes, summarized by power-weighted silhouette functions of persistence diagrams. We develop an efficient, doubly robust estimator in a fully nonparametric model, establish functional weak convergence, and construct a formal test of the null hypothesis of no topological effect. Empirical studies illustrate that the proposed method reliably quantifies topological treatment effects across diverse complex outcome types.
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