Local MDI+: Local Feature Importances for Tree-Based Models

Abstract

Tree-based ensembles such as random forests remain the go-to for tabular data over deep learning models due to their prediction performance and computational efficiency. These advantages have led to their widespread deployment in high-stakes domains, where interpretability is essential for ensuring trustworthy predictions. This has motivated the development of popular local feature importance methods such as LIME and TreeSHAP. However, these approaches rely on approximations that ignore the model's internal structure and instead depend on potentially unstable perturbations. These issues are addressed in the global setting by MDI+, a global feature importance method which combines tree-based and linear feature importances by exploiting an equivalence between decision trees and least squares on a transformed node basis. However, the global MDI+ scores are not able to explain predictions when faced with heterogeneous individual characteristics. To address this gap, we propose Local MDI+ (LMDI+), a novel extension of the MDI+ framework that quantifies feature importances for each particular sample. Across twelve real-world benchmark datasets, LMDI+ outperforms existing baselines at identifying instance-specific predictive features, yielding an average 10% improvement in predictive performance when using only the selected features. It further demonstrates greater stability by consistently producing similar instance-level feature importance rankings across repeated model fits with different random seeds. Ablation experiments show that each component of LMDI+ contributes to these gains, and that the improvements extend beyond random forests to gradient boosting models. Finally, we show that LMDI+ enables local interpretability use cases by identifying closely matched counterfactuals for each classification benchmark and discovering homogeneous subgroups in a housing dataset case study.