Mixed integer linear optimization formulations for learning optimal binary classification trees
This work addresses the need for interpretable and accurate decision trees in machine learning, though it is incremental as it builds upon existing MILO formulations.
The authors tackled the problem of designing optimal binary classification trees by proposing four mixed integer linear optimization (MILO) formulations, including flow-based and cut-based approaches, and demonstrated their scalability and effectiveness through experiments on 13 datasets using Pareto frontiers.
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is often preferred over other higher accuracy methods that are relatively uninterpretable. A binary classification tree has two types of vertices: (i) branching vertices which have exactly two children and where datapoints are assessed on a set of discrete features; and (ii) leaf vertices at which datapoints are given a discrete prediction. An optimal binary classification tree can be obtained by solving a biobjective 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 four mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees: two flow-based formulations and two-cut based formulations. We provide theoretical comparisons between our proposed formulations and the strongest flow-based MILO formulation of Aghaei et al. (2021). We conduct experiments on 13 publicly available datasets to show the models' ability to scale and the strength of a biobjective approach using Pareto frontiers. Our code and data are available on GitHub.