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Mixed Integer Linear Optimization Formulations for Learning Optimal Binary Classification Trees
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DOI：10.1287/ijoc.2023.0068.png)
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Abstract
En 中文
Decision trees are powerful supervised machine learning tools for classification and regression that attract many academic researchers and industry professionals. In particular, decision trees provide interpretability, which is often preferred over other higheraccuracy methods that are relatively uninterpretable. An optimal binary classification tree has two types of vertices and is obtainable by solving a bi-objective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. In this paper, we propose two mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees: a maximum flow-based formulation and a minimum cut-based formulation, both of which share a common base model. The formulations enforce connected feasible paths for training datapoints through flow-based or cut-based connectivity constraints while maintaining computational tractability without the need for decomposition techniques commonly used to combat scaling concerns. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available data sets to demonstrate our models' ability to scale, strength against traditional branch-and-bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub.
Keywords:
optimal classification tree
mixed integer linear optimization
max-flow min-cut
fractional separation
Journal
I
IF:
2.1
Papers:
86
Citations:
3.2K
