This paper discusses the foundation of methods for accurately grasping interaction effects. The partial dependence (PD) and accumulated local effects (ALE) methods, which capture interaction effects as terms, are known as global model-agnostic methods in the interpretable machine learning field. ALE provides a functional decomposition of the prediction function. In the present study, we propose and mathematically formalize the requirements of an interaction decomposition (ID) that decomposes a prediction function into its main and interaction effect terms. We also present a theorem by which a decomposition method meeting these requirements can be generated. Furthermore, we confirm that ALE is an ID but PD is not. Finally, we present examples of decomposition methods that meet the requirements of ID, using both existing methods and methods that differ from the existing ones.

翻译：本文讨论了精确捕捉交互作用效应的方法基础。在可解释机器学习领域，将交互作用效应作为项进行捕获的部分依赖（PD）和累积局部效应（ALE）方法被称为全局模型无关方法。ALE提供了预测函数的函数分解。在本研究中，我们提出并数学形式化了交互分解（ID）的要求，该分解将预测函数分解为其主效应项和交互效应项。我们还提出了一个定理，通过该定理可以生成满足这些要求的分解方法。进一步地，我们确认ALE是一种ID，而PD不是。最后，我们使用既有方法以及不同于既有方法的方法，展示了满足ID要求的分解方法示例。