Machine learning models, particularly the black-box models, are widely favored for their outstanding predictive capabilities. However, they often face scrutiny and criticism due to the lack of interpretability. Paradoxically, their strong predictive capabilities suggest a deep understanding about the underlying data, implying significant potential for interpretation. Leveraging the emerging concept of knowledge distillation, we introduced the method of distillation decision tree (DDT). This method enables the distillation of knowledge about the data from a black-box model into a decision tree, thereby facilitating the interpretation of the black-box model. Constructed through the knowledge distillation process, the interpretability of DDT relies significantly on the stability of its structure. We establish the theoretical foundations for the structural stability of DDT, demonstrating that its structure can achieve stability under mild assumptions. Furthermore, we develop algorithms for efficient construction of (hybrid) DDTs. A comprehensive simulation study validates DDT's ability to provide accurate and reliable interpretations. Additionally, we explore potential application scenarios and provide corresponding case studies to illustrate how DDT can be applied to real-world problems.

翻译：机器学习模型，尤其是黑箱模型，因其卓越的预测能力而广受欢迎。然而，由于缺乏可解释性，它们常面临质疑与批评。矛盾的是，其强大的预测能力暗示着对底层数据的深刻理解，蕴含着巨大的解释潜力。借助知识蒸馏这一新兴概念，我们提出了蒸馏决策树（DDT）方法。该方法能将黑箱模型关于数据的知识蒸馏至决策树中，从而促进对黑箱模型的解释。通过知识蒸馏过程构建的DDT，其可解释性很大程度上依赖于其结构的稳定性。我们为DDT的结构稳定性奠定了理论基础，证明在温和假设下其结构可达到稳定。此外，我们开发了高效构建（混合）DDT的算法。综合仿真研究验证了DDT提供准确可靠解释的能力。最后，我们探索了潜在应用场景，并提供相应案例研究，阐释DDT如何应用于现实问题。