Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability
超越均值：持久同调可忽略性下的拓扑因果效应AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究处理引起的结果分布形状变化，并明确提出拓扑因果效应的识别问题。
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超越均值：持久同调可忽略性下的拓扑因果效应
- 研究问题
- 当处理改变结果分布的形状而保持均值不变时，如何定义并识别拓扑因果效应，补充平均处理效应遗漏的信息？
- 方法与思路
- 作者以持久同调构造条件拓扑效应，提出相应可忽略性条件，并在近似条件下建立带显式误差界的识别结果。
- 材料陈述的贡献
- 摘要称条件拓扑效应可识别，并指出条件可忽略性不足以识别边际持久图效应；合成实验展示均值保持的拓扑变化。
- 阅读关注点
- 应核对拓扑效应的数学定义、近似可忽略性的含义与误差界，以及条件效应为何不能直接混合成边际持久图效应。
- 阅读边界
- 这是 arXiv 预印本，不能据此声称已同行评审或期刊接收。摘要未给出误差界公式，合成实验也不足以判断实际数据适用性。
原文摘要
Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.