# Very fast, approximate counterfactual explanations for decision forests

arXiv: https://arxiv.org/abs/2303.02883 · HTML: https://mlsanity.com/paper/2303.02883/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [Measurable Counterfactual Local Explanations for Any Classifier](https://mlsanity.com/paper/1908.03020/) (2019)
- [FOCUS: Flexible Optimizable Counterfactual Explanations for Tree Ensembles](https://mlsanity.com/paper/1911.12199/) (2019)
- [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021)
- [Counterfactual Explanations for Oblique Decision Trees: Exact, Efficient Algorithms](https://mlsanity.com/paper/2103.01096/) (2021)

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

- [Learning Decision Trees and Forests with Algorithmic Recourse](https://mlsanity.com/paper/2406.01098/) (2024)
- [Counterfactual Maps: What They Are and How to Find Them](https://mlsanity.com/paper/2602.09128/) (2026)
- [Optimal Counterfactual Search in Tree Ensembles: A Study Across Modeling and Solution Paradigms](https://mlsanity.com/paper/2605.06561/) (2026)
- [Inverse classification with logistic and softmax classifiers: efficient optimization](https://mlsanity.com/paper/2309.08945/) (2023)

## Abstract (arXiv)

We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest outputs a desired value. Finding an exact solution has a cost that is exponential on the number of leaves in the forest. We propose a simple but very effective approach: we constrain the optimization to only those input space regions defined by the forest that are populated by actual data points. The problem reduces to a form of nearest-neighbor search using a certain distance on a certain dataset. This has two advantages: first, the solution can be found very quickly, scaling to large forests and high-dimensional data, and enabling interactive use. Second, the solution found is more likely to be realistic in that it is guided towards high-density areas of input space.