Generalized and Scalable Optimal Sparse Decision Trees

TL;DR

This paper introduces a scalable, general framework for constructing optimal sparse decision trees that handle imbalanced data and continuous variables, enabling efficient optimization of various objectives in interpretable machine learning.

Contribution

It provides a novel, scalable optimization framework for decision trees that addresses key open problems and supports multiple objectives beyond traditional methods.

Findings

Produces optimal decision trees for multiple objectives like F-score and AUC.

Handles imbalanced data effectively within the optimization process.

Speeds up decision tree construction by several orders of magnitude.

Abstract

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been made that have allowed practical algorithms to find optimal decision trees. These new techniques have the potential to trigger a paradigm shift where it is possible to construct sparse decision trees to efficiently optimize a variety of objective functions without relying on greedy splitting and pruning heuristics that often lead to suboptimal solutions. The contribution in this work is to provide a general framework for decision tree optimization that addresses the two significant open problems in the area: treatment of imbalanced data and fully optimizing over continuous variables. We present techniques that produce optimal decision trees over a variety of objectives including F-score, AUC, and partial area under the ROC convex hull. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables and speeds up decision tree construction by several orders of magnitude relative to the state-of-the art.