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 to 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.
翻译:最佳的硬化是将变量优化地分解成基于离散或连续数字目标的垃圾箱。 我们提出了一个严格和可扩展的数学编程配方,以解决二进制、连续和多级目标类型的最佳拆解问题,包括以前未处理的制约因素。 对于所有这三种目标类型,我们引入了convex混合整数编程配方。一些算法改进,例如通过机器学习分类和执行方面自动确定最合适的单调趋势,经过深思熟虑的讨论。新的数学编程配方在开放源 Python 库 OptBinning 中仔细实施。