Causal attribution by the chain rule: unifying natural selection, learning, economics, and other disciplines
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链式法则下的因果归因：统一自然选择、学习、经济学及其他学科
- 研究问题
- 论文关注如何将总体变化分解为不同组成因素的贡献，以及这类描述性分解在什么额外条件下能够获得反事实因果解释。
- 方法与思路
- 作者用链式法则的有限差分乘积形式构造回归分解，串联进化、工资差异等问题，并讨论附加假设如何赋予分解因果含义。
- 材料陈述的贡献
- 摘要称，链式法则为多学科的变化分解提供共同结构，并连接费舍尔基本定理、Oaxaca–Blinder 分解与现代反事实因果分析。
- 阅读关注点
- 应核对有限差分分解的具体定义、描述性贡献与因果效应的区别，以及各学科案例获得因果解释所需的附加假设。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未列出附加因果假设，不能将代数分解直接视为因果识别。
原文摘要
Analysis often splits change into components. For example, how much of the observed variance is caused by genes or environment? In many cases, the split is ultimately made by the logic of the chain rule, which divides the difference of a product into two terms. Each term quantifies the partial difference associated with change in one component while holding the other component constant. The chain rule is of course widely known. However, this article argues that its deep fundamental role often goes unrecognized. The article shows how simply the basic chain rule unifies Fisher's fundamental theorem of natural selection, the Price equation description of evolutionary change, the Oaxaca-Blinder decomposition of wage differences in economics, the Kitagawa decomposition of mortality differences in demography, many expressions of thermodynamics, and most strikingly back propagation, the core optimization method of modern machine learning and artificial intelligence. The success in creating good designs and finding good solutions in both natural selection and artificial intelligence depends on how the chain rule propagates causes from instances of success or failure back to the underlying genes or parameters of the system. The mathematical analysis presented here shows that, for finite differences, the product rule form of the chain rule yields a basic decomposition of change into two components of a regression equation. That regression decomposition is purely a description of change with no explicit causal meaning. However, simple additional assumptions lead naturally to the modern counterfactual analysis of causality. From that perspective, we can easily understand the causal interpretation that Fisher gave to his fundamental theorem, and we can see the same causal structure in the Oaxaca-Blinder decomposition of economics and in causal analyses across many disciplines.