# Unboxing Tree Ensembles for interpretability: a hierarchical visualization tool and a multivariate optimal re-built tree

arXiv: https://arxiv.org/abs/2302.07580 · HTML: https://mlsanity.com/paper/2302.07580/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 7 of 7)

- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Born-Again Tree Ensembles](https://mlsanity.com/paper/2003.11132/) (2020)
- [Margin Optimal Classification Trees](https://mlsanity.com/paper/2210.10567/) (2022)
- [ggRandomForests: Exploring Random Forest Survival](https://mlsanity.com/paper/1612.08974/) (2016)

## Built on by (most cited first, 2 of 2)

- [Interpretable Ensembles of Hyper-Rectangles as Base Models](https://mlsanity.com/paper/2303.08625/) (2023)
- [A Unified Approach to Extract Interpretable Rules from Tree Ensembles via Integer Programming](https://mlsanity.com/paper/2407.00843/) (2024)

## Abstract (arXiv)

The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real-world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools for classification tasks. However, while combining multiple trees may provide higher prediction quality than a single one, it sacrifices the interpretability property resulting in "black-box" models. In light of this, we aim to develop an interpretable representation of a tree-ensemble model that can provide valuable insights into its behavior. First, given a target tree-ensemble model, we develop a hierarchical visualization tool based on a heatmap representation of the forest's feature use, considering the frequency of a feature and the level at which it is selected as an indicator of importance. Next, we propose a mixed-integer linear programming (MILP) formulation for constructing a single optimal multivariate tree that accurately mimics the target model predictions. The goal is to provide an interpretable surrogate model based on oblique hyperplane splits, which uses only the most relevant features according to the defined forest's importance indicators. The MILP model includes a penalty on feature selection based on their frequency in the forest to further induce sparsity of the splits. The natural formulation has been strengthened to improve the computational performance of {mixed-integer} software. Computational experience is carried out on benchmark datasets from the UCI repository using a state-of-the-art off-the-shelf solver. Results show that the proposed model is effective in yielding a shallow interpretable tree approximating the tree-ensemble decision function.