通用最优分类树：一种混合整数规划方法
Generalized Optimal Classification Trees: A Mixed-Integer Programming Approach
AI总结：
本文提出一种基于混合整数规划的框架，用于在非线性性能度量下学习最优分类树，通过定制算法和热启动策略提升可扩展性，并在多个数据集上验证了其有效性。
摘要：
决策树的全局优化是组合优化领域长期存在的挑战，尽管这些模型在可解释机器学习中起着重要作用。虽然该问题已研究数十年，但只有最近的离散优化进展才使在真实世界数据集上解决最优分类树问题的实用算法成为可能。混合整数规划（MIP）提供了高度的建模灵活性，因此我们提出了一种基于MIP的框架，用于在非线性性能度量（如F1分数）下学习最优分类树，明确处理类别不平衡问题。为提高可扩展性，我们开发了问题特定的加速技术，包括定制的分支定界算法、实例减少方案和热启动策略。我们在50个基准数据集上评估了所提出的方法。计算结果表明，该框架能够高效地优化非线性度量，同时在预测性能和求解时间上优于现有方法。
英文摘要：
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only recent advances in discrete optimization have enabled practical algorithms for solving optimal classification tree problems on real-world datasets. Mixed-integer programming (MIP) offers a high degree of modeling flexibility, and we therefore propose a MIP-based framework for learning optimal classification trees under nonlinear performance metrics, such as the F1-score, that explicitly addresses class imbalance. To improve scalability, we develop problem-specific acceleration techniques, including a tailored branch-and-cut algorithm, an instance-reduction scheme, and warm-start strategies. We evaluate the proposed approach on 50 benchmark datasets. The computational results show that the framework can efficiently optimize nonlinear metrics while achieving strong predictive performance and reduced solution times compared with existing methods.
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