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观测数据因果推断的最优传输理论入门

文章背景与核心概要

本文介绍了最优传输（Optimal Transport）与利用观测数据进行因果推断（Causal Inference）之间深厚的理论联系。尽管最优传输传统上用于比较概率分布，但其通过检查底层状态空间来分析概率的基本方法，直接呼应了因果推断的核心挑战——量化反事实状态。

该综述表明，许多基础的因果推断模型在几十年来一直隐式地依赖于最优传输原理。通过统一统计学、数学和计量经济学之间的语言和符号，这篇入门文章为模型假设提供了凝聚力强的基础，并为该交叉领域未来的研究开辟了新的途径。

文章详情

  • arXiv ID: 2503.07811
  • 主要学科: 方法论 (stat.ME)
  • 其他学科: 人工智能 (cs.AI)、计量经济学 (econ.EM)
  • 作者: Florian F. Gunsilius
  • 提交时间: 2025年3月10日
  • 最后修订: 2026年8月7日（版本 v3）
  • 许可证: 知识共享署名 4.0 国际 license icon

摘要

最优传输理论已发展成为一个强大且优雅的框架，用于比较概率分布，在科学各个领域有着广泛的应用。通过比较其底层状态空间来分析概率的基本思想，自然地与因果推断的核心理念相契合，在因果推断中，理解和量化反事实状态至关重要。尽管存在这种直观的联系，但最优传输与因果推断交叉领域的显性研究才刚刚开始发展。然而，因果推断中的许多基础模型在几十年里一直隐式地依赖于最优传输原理，却没有认识到这种潜在的联系。因此，本综述的目的是介绍最优传输与利用观测数据识别因果效应之间令人惊叹的深层联系——在这里，最优传输不仅仅是一组潜在的工具，实际上还构成了模型假设的基础。因此，本综述旨在通过指出这些现有的联系，统一统计学、数学和计量经济学不同领域之间的语言和符号，并探索源自这一认识的两个领域未来工作的新问题和新方向。

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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