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This research introduces sparse oblique rules to improve rule-based ensembles, allowing models to achieve higher accuracy with fewer components without relying on manual feature engineering. By enabling decision regions defined by general polyhedrons rather than axis-parallel shapes, the method offers a more favorable trade-off between interpretability and predictive performance across various tasks.
Sparse Oblique Rule Boosting for Simpler Additive Rule Ensembles
arXiv:2609.06426v1 Announce Type: new Abstract: Small additive ensembles of symbolic rules offer interpretable prediction models. Traditionally, these ensembles use rule conditions based on conjunctions of simple threshold propositions $x \geq t$ on a single input variable $x$ and threshold $t$, resulting geometrically in axis-parallel polytopes as decision regions. While this form ensures a high degree of interpretability for individual rules and can be learned efficiently using the gradient boosting approach, it relies on having access to a curated set of expressive input features so that a small ensemble of axis-parallel regions can describe the target variable well. Absent such features, reaching sufficient accuracy requires increasing the number and complexity of individual rules, which diminishes the interpretability of the model. Here, we extend classical rule ensembles by introducing logical propositions with learnable sparse linear transformations of input variables, i.e., propositions of the form $\mathbf{x}^T\mathbf{w} \geq t$, where $\mathbf{w}$ is a learnable sparse weight vector, enabling decision regions as general polyhedrons with oblique faces. We propose a learning method using gradient boosting based on a weighted logistic regression. Empirical results across 14 regression and classification tasks demonstrate that the proposed method achieves lower model complexity than competitive baselines while maintaining similar or better predictive accuracy. Hence, the approach provides a favorable trade-off between interpretability and accuracy and reduces the reliance on manual feature engineering.
Abstract:Small additive ensembles of symbolic rules offer interpretable prediction models. Traditionally, these ensembles use rule conditions based on conjunctions of simple threshold propositions $x \geq t$ on a single input variable $x$ and threshold $t$, resulting geometrically in axis-parallel polytopes as decision regions. While this form ensures a high degree of interpretability for individual rules and can be learned efficiently using the gradient boosting approach, it relies on having access to a curated set of expressive input features so that a small ensemble of axis-parallel regions can describe the target variable well. Absent such features, reaching sufficient accuracy requires increasing the number and complexity of individual rules, which diminishes the interpretability of the model. Here, we extend classical rule ensembles by introducing logical propositions with learnable sparse linear transformations of input variables, i.e., propositions of the form $\mathbf{x}^T\mathbf{w} \geq t$, where $\mathbf{w}$ is a learnable sparse weight vector, enabling decision regions as general polyhedrons with oblique faces. We propose a learning method using gradient boosting based on a weighted logistic regression. Empirical results across 14 regression and classification tasks demonstrate that the proposed method achieves lower model complexity than competitive baselines while maintaining similar or better predictive accuracy. Hence, the approach provides a favorable trade-off between interpretability and accuracy and reduces the reliance on manual feature engineering.
Accepted for publication in Journal of Data Mining and Knowledge Discovery. The Version of Record is forthcoming
Machine Learning (cs.LG)
arXiv:2609.06426 [cs.LG]
(or arXiv:2609.06426v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.06426 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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