用最优传输理论重新理解因果推断，揭示其背后的数学基础
A primer on optimal transport for causal inference with observational data
- 将最优传输框架用于对比概率分布，建立因果推断的数学基础
- 发现已有因果模型隐含最优传输原理，但长期未被识别
- 适合统计、数学与计量经济学交叉研究者阅读
最优传输理论已发展为比较概率分布的强大而优美的框架，广泛应用于科学各领域。其通过分析潜在状态空间来比较概率的思想，天然契合因果推断的核心——理解与量化反事实状态。尽管这一联系直觉上明显，但最优传输与因果推断的显式研究仍处于起步阶段。然而，许多因果推断的经典模型几十年来实际上隐含依赖最优传输原理，却未意识到这一联系。本文旨在系统梳理最优传输与观测数据下因果效应识别之间的深层关联，强调最优传输不仅是可选工具，更是模型假设的基础。通过统一统计、数学与计量经济学的术语与符号，本文希望促进两领域融合，并提出未来可探索的新问题与方向。
原文摘要 · Abstract (English)
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection of optimal transport and causal inference is only beginning to develop. Yet, many foundational models in causal inference have implicitly relied on optimal transport principles for decades, without recognizing the underlying connection. Therefore, the goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data -- where optimal transport is not just a set of potential tools, but actually builds the foundation of model assumptions. As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics, by pointing out these existing connections, and to explore novel problems and directions for future work in both areas derived from this realization.
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