We present BackboneLearn: an open-source software package and framework for scaling mixed-integer optimization (MIO) problems with indicator variables to high-dimensional problems. This optimization paradigm can naturally be used to formulate fundamental problems in interpretable supervised learning (e.g., sparse regression and decision trees), in unsupervised learning (e.g., clustering), and beyond; BackboneLearn solves the aforementioned problems faster than exact methods and with higher accuracy than commonly used heuristics. The package is built in Python and is user-friendly and easily extensible: users can directly implement a backbone algorithm for their MIO problem at hand. The source code of BackboneLearn is available on GitHub (link: https://github.com/chziakas/backbone_learn).

我们提出了BackboneLearn：一个用于扩展具有指示变量的混合整数优化问题到高维问题的开源软件包和框架。该优化范式可自然地用于构建解释性监督学习（如稀疏回归和决策树）、非监督学习（如聚类）等基本问题，而且BackboneLearn比精确方法解决这些问题更快且准确率更高。该软件包使用Python构建，用户友好且易于扩展：用户可以直接为其手头的MIO问题实现一个骨干算法。BackboneLearn的源代码可以在GitHub上找到（链接：https://github.com）。

BackboneLearn: 缩放混合整数优化机器学习的库