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.

本研究针对最优传输理论与因果推断之间的交集进行探讨，填补了其间的研究空白。文章提出，最优传输不仅是潜在工具，也构成了因果效应识别模型假设的基础。重要发现是，通过识别这些深层次的联系，可以统一统计学、数学和计量经济学领域的语言，并为未来的研究指明了新的方向。

因果推断中最优传输的基础知识：基于观察数据的研究