Better Short than Greedy: Interpretable Models through Optimal Rule Boosting

TL;DR

This paper introduces an optimal rule boosting method using a branch-and-bound algorithm that significantly improves predictive accuracy and interpretability over traditional greedy rule ensemble methods.

Contribution

It presents a novel, efficient branch-and-bound algorithm for optimal rule ensemble fitting within the gradient boosting framework, enhancing model interpretability and accuracy.

Findings

Outperforms greedy rule boosting in predictive accuracy

Efficiently finds optimal rules with linear bounding techniques

Demonstrates effectiveness on various benchmark datasets

Abstract

Rule ensembles are designed to provide a useful trade-off between predictive accuracy and model interpretability. However, the myopic and random search components of current rule ensemble methods can compromise this goal: they often need more rules than necessary to reach a certain accuracy level or can even outright fail to accurately model a distribution that can actually be described well with a few rules. Here, we present a novel approach aiming to fit rule ensembles of maximal predictive power for a given ensemble size (and thus model comprehensibility). In particular, we present an efficient branch-and-bound algorithm that optimally solves the per-rule objective function of the popular second-order gradient boosting framework. Our main insight is that the boosting objective can be tightly bounded in linear time of the number of covered data points. Along with an additional novel pruning technique related to rule redundancy, this leads to a computationally feasible approach for boosting optimal rules that, as we demonstrate on a wide range of common benchmark problems, consistently outperforms the predictive performance of boosting greedy rules.