最佳装箱：数学规划公式
Optimal binning: mathematical programming formulation
摘要：
最优分箱是给定离散或连续数值目标，将变量最优离散化为箱。我们提出了一个严格的和可扩展的数学规划制定解决二进制，连续和多类目标类型的最佳装箱问题，将以前没有解决的约束。对于所有这三种目标类型，我们引入了一个凸混合整数规划公式。几个算法的增强，如通过基于机器学习的分类器和实现方面的最合适的单调趋势的自动确定周到的讨论。新的数学编程公式在开源python库OptBinning中仔细实现。
英文摘要：
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not previously addressed. For all three target types, we introduce a convex mixed-integer programming formulation. Several algorithmic enhancements, such as automatic determination of the most suitable monotonic trend via a Machine-Learning-based classifier and implementation aspects are thoughtfully discussed. The new mathematical programming formulations are carefully implemented in the open-source python library OptBinning.
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