# Multi forests: Variable importance for multi-class outcomes

arXiv: https://arxiv.org/abs/2409.08925 · HTML: https://mlsanity.com/paper/2409.08925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [OpenML Benchmarking Suites](https://mlsanity.com/paper/1708.03731/) (2017)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Interpretable Machine Learning -- A Brief History, State-of-the-Art and Challenges](https://mlsanity.com/paper/2010.09337/) (2020)
- [Tunability: Importance of Hyperparameters of Machine Learning Algorithms](https://mlsanity.com/paper/1802.09596/) (2018)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [PMLB v1.0: An open source dataset collection for benchmarking machine learning methods](https://mlsanity.com/paper/2012.00058/) (2020)
- [Unbiased Measurement of Feature Importance in Tree-Based Methods](https://mlsanity.com/paper/1903.05179/) (2019)
- [A Debiased MDI Feature Importance Measure for Random Forests](https://mlsanity.com/paper/1906.10845/) (2019)
- [Unbiased variable importance for random forests](https://mlsanity.com/paper/2003.02106/) (2020)

## Abstract (arXiv)

In prediction tasks with multi-class outcomes, identifying covariates specifically associated with one or more outcome classes can be important. Conventional variable importance measures (VIMs) from random forests (RFs), like permutation and Gini importance, focus on overall predictive performance or node purity, without differentiating between the classes. Therefore, they can be expected to fail to distinguish class-associated covariates from covariates that only distinguish between groups of classes. We introduce a VIM called multi-class VIM, tailored for identifying exclusively class-associated covariates, via a novel RF variant called multi forests (MuFs). The trees in MuFs use both multi-way and binary splitting. The multi-way splits generate child nodes for each class, using a split criterion that evaluates how well these nodes represent their respective classes. This setup forms the basis of the multi-class VIM, which measures the discriminatory ability of the splits performed in the respective covariates with regard to this split criterion. Alongside the multi-class VIM, we introduce a second VIM, the discriminatory VIM. This measure, based on the binary splits, assesses the strength of the general influence of the covariates, irrespective of their class-associatedness. Simulation studies demonstrate that the multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs which also rank other types of covariates highly. Analyses of 121 datasets reveal that MuFs often have slightly lower predictive performance compared to conventional RFs. This is, however, not a limiting factor given the algorithm's primary purpose of calculating the multi-class VIM.