This paper discusses the foundation of methods for accurately grasping the interaction effects. Among the existing methods that capture the interaction effects as terms, PD and ALE are known as global modelagnostic methods in the IML field. ALE, among the two, can theoretically provide a functional decomposition of the prediction function, and this study focuses on functional decomposition. Specifically, we mathematically formalize what we consider to be the requirements that must always be met by a decomposition (interaction decomposition, hereafter, ID) that decomposes the prediction function into main and interaction effect terms. We also present a theorem about how to produce a decomposition that meets these requirements. Furthermore, we confirm that while ALE is ID, PD is not, and we present examples of decomposition that meet the requirements of ID using methods other than existing ones (i.e., new methods).

翻译：本文探讨了准确捕捉交互作用效应方法的基础。在现有将交互作用效应作为项进行捕捉的方法中，PD和ALE是IML领域已知的全局模型无关方法。其中，ALE在理论上能够提供预测函数的函数分解，本研究聚焦于函数分解。具体而言，我们数学形式化了我们认为分解（以下简称交互分解，ID）必须始终满足的要求，该分解将预测函数分解为主效应项和交互效应项。我们还提出了关于如何生成满足这些要求的分解的定理。此外，我们确认了ALE是ID而PD不是，并展示了使用现有方法之外的方法（即新方法）满足ID要求的分解示例。