An improved column-generation-based matheuristic for learning classification trees

TL;DR

This paper enhances a column-generation-based heuristic for learning decision trees, improving scalability and efficiency for large multiclass datasets by modifying subproblems, using implied constraints as cuts, and generating violated constraints.

Contribution

The paper introduces specific modifications to the existing column-generation approach, including subproblem reduction, constraint implication, and separation models, to improve scalability in multiclass classification.

Findings

Enhanced scalability demonstrated on large datasets

Reduced number of subproblems in multiclass cases

Improved computational performance over previous methods

Abstract

Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete optimization models in the literature address the optimality problem but only work well on relatively small datasets. \cite{firat2020column} proposed a column-generation-based heuristic approach for learning decision trees. This approach improves scalability and can work with large datasets. In this paper, we describe improvements to this column generation approach. First, we modify the subproblem model to significantly reduce the number of subproblems in multiclass classification instances. Next, we show that the data-dependent constraints in the master problem are implied, and use them as cutting planes. Furthermore, we describe a separation model to generate data points for which the linear programming relaxation solution violates their corresponding constraints. We conclude by presenting computational results that show that these modifications result in better scalability.