Fast Sparse Decision Tree Optimization via Reference Ensembles

TL;DR

This paper introduces a novel approach for optimizing sparse decision trees by using strategic guesses, significantly reducing computation time and enabling the construction of accurate, interpretable models that rival black box methods.

Contribution

The authors propose a guessing strategy that enhances branch-and-bound decision tree algorithms, making sparse decision tree optimization more practical and scalable for real-world datasets.

Findings

Run time reduced by multiple orders of magnitude

Ability to match black box model accuracy with sparse trees

Effective guessing strategies for feature binning and tree size

Abstract

Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and despite steady effort since the 1960's, breakthroughs have only been made on the problem within the past few years, primarily on the problem of finding optimal sparse decision trees. However, current state-of-the-art algorithms often require impractical amounts of computation time and memory to find optimal or near-optimal trees for some real-world datasets, particularly those having several continuous-valued features. Given that the search spaces of these decision tree optimization problems are massive, can we practically hope to find a sparse decision tree that competes in accuracy with a black box machine learning model? We address this problem via smart guessing strategies that can be applied to any optimal branch-and-bound-based decision tree algorithm. We show that by using these guesses, we can reduce the run time by multiple orders of magnitude, while providing bounds on how far the resulting trees can deviate from the black box's accuracy and expressive power. Our approach enables guesses about how to bin continuous features, the size of the tree, and lower bounds on the error for the optimal decision tree. Our experiments show that in many cases we can rapidly construct sparse decision trees that match the accuracy of black box models. To summarize: when you are having trouble optimizing, just guess.