Topological Ignorability for Structural Causal Effects Beyond Means
超越均值的结构性因果效应与拓扑可忽略性AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究干预分布的拓扑结构差异及其因果识别，直接涉及超越均值的分布效应。
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超越均值的结构性因果效应与拓扑可忽略性
- 研究问题
- 当干预改变结果分布的连通性、孔洞或分支却几乎不改变均值时，如何定义并识别这些分布结构上的因果效应？
- 方法与思路
- 作者以Betti、Euler及持久同调摘要构造拓扑几何效应，提出只要求目标结构特征保持不变的拓扑可忽略性，并进行协变量标准化。
- 材料陈述的贡献
- 摘要称，非单射摘要可在不识别完整干预分布时识别目标特征；两个隐藏混杂基准中，部分Betti与Euler对比保持稳定。
- 阅读关注点
- 应核对拓扑可忽略性的形式、特征选择与单射性的作用，以及密度阈值、标准化和实际估计如何影响结构效应。
- 阅读边界
- 这是arXiv预印本，同行评审或期刊接收未经核实。特定基准中的稳定性不足以证明普遍抗混杂，摘要未说明完整识别与推断条件。
原文摘要
Many interventions alter the structure of an outcome distribution rather than its mean: they can split a population into disconnected regimes, create loops or holes, generate branches, or reorganize an outcome cloud while leaving the average response nearly unchanged. In such settings, mean-based causal estimands such as the average treatment effect may miss important structural effects. We introduce topological-geometrical causal metrics based on summaries of interventional outcome laws, including density-superlevel Betti summaries, Euler signatures, and persistent-homology summaries. These metrics quantify structural differences between treated and untreated outcome laws beyond averages. We also study the assumptions needed for causal interpretation. We introduce topological ignorability, a topological analogue of conditional ignorability that requires invariance of the chosen structural feature rather than the full counterfactual distribution. When the chosen summary is injective, this condition coincides with weak ignorability; for noninjective summaries, it can identify the structural feature of interest without identifying the full interventional law. We define a covariate-standardized topological-geometrical causal effect and develop practical estimators. We validate the framework in two hidden-confounding benchmarks: a fully synthetic exact benchmark and a real-covariate semi-synthetic benchmark using Wisconsin breast-cancer covariates. In both, weak ignorability fails and balancing observed covariates nearly eliminates standardized mean differences, yet the coordinate-mean average treatment effect remains biased. By contrast, selected finite density-superlevel Betti and Euler contrasts remain stable across oracle, observational, and weighted analyses.