# From global to local MDI variable importances for random forests and when they are Shapley values

arXiv: https://arxiv.org/abs/2111.02218 · HTML: https://mlsanity.com/paper/2111.02218/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 3 Nov 2021.

## Builds on (most cited first, 8 of 8)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Understanding Random Forests: From Theory to Practice](https://mlsanity.com/paper/1407.7502/) (2014)
- [On Explaining Decision Trees](https://mlsanity.com/paper/2010.11034/) (2020)
- [A Debiased MDI Feature Importance Measure for Random Forests](https://mlsanity.com/paper/1906.10845/) (2019)
- [Explainable Matrix -- Visualization for Global and Local Interpretability of Random Forest Classification Ensembles](https://mlsanity.com/paper/2005.04289/) (2020)
- [Trees, forests, and impurity-based variable importance](https://mlsanity.com/paper/2001.04295/) (2020)
- [Importance measures derived from random forests: characterisation and extension](https://mlsanity.com/paper/2106.09473/) (2021)
- [Random Subspace with Trees for Feature Selection Under Memory Constraints](https://mlsanity.com/paper/1709.01177/) (2017)

## Built on by (most cited first, 4 of 4)

- [Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees](https://mlsanity.com/paper/2204.09938/) (2022)
- [Local MDI+: Local Feature Importances for Tree-Based Models](https://mlsanity.com/paper/2506.08928/) (2025)
- [Online High-Frequency Trading Stock Forecasting with Automated Feature Clustering and Radial Basis Function Neural Networks](https://mlsanity.com/paper/2412.16160/) (2024)
- [Kernel of Partition Paths: A Unified Representation for Tree Ensembles](https://mlsanity.com/paper/2606.18853/) (2026)

## Abstract (arXiv)

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods based on Shapley values have been introduced to refine the analysis of feature relevance in tree-based models to a local (per instance) level. In this context, we first show that the global Mean Decrease of Impurity (MDI) variable importance scores correspond to Shapley values under some conditions. Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature. The measures are illustrated through experiments on several classification and regression problems.