# ArborEnum: Decision Tree Rashomon Sets over Continuous Features

arXiv: https://arxiv.org/abs/2608.04310 · HTML: https://mlsanity.com/paper/2608.04310/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [Exploring the Whole Rashomon Set of Sparse Decision Trees](https://mlsanity.com/paper/2209.08040/) (2022)
- [MurTree: Optimal Classification Trees via Dynamic Programming and Search](https://mlsanity.com/paper/2007.12652/) (2020)
- [It's COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks](https://mlsanity.com/paper/2106.05498/) (2021)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features](https://mlsanity.com/paper/2206.11844/) (2022)
- [Rashomon Sets for Prototypical-Part Networks: Editing Interpretable Models in Real-Time](https://mlsanity.com/paper/2503.01087/) (2025)
- [Near Optimal Decision Trees in a SPLIT Second](https://mlsanity.com/paper/2502.15988/) (2025)
- [SORTeD Rashomon Sets of Sparse Decision Trees: Anytime Enumeration](https://mlsanity.com/paper/2511.03344/) (2025)
- [Anytime Optimal Decision Tree Learning with Continuous Features](https://mlsanity.com/paper/2601.14765/) (2026)
- [From Rashomon Theory to PRAXIS: Efficient Decision Tree Rashomon Sets](https://mlsanity.com/paper/2606.00202/) (2026)

## Abstract (arXiv)

The Rashomon effect describes the phenomenon that many models can achieve nearly equivalent performance on the same learning task, with significant ramifications for robustness, feature importance, and customizability. These use cases motivate the computation of Rashomon sets: the set of all models whose regularized loss is near-optimal. Decision trees are one of the few model classes for which Rashomon sets can be fully enumerated, but this computation has always been conditional on a binarization of the original data, either restricting which splits each tree is allowed to make or substantially increasing the complexity of an already difficult combinatorial problem. We introduce the first algorithm that exactly enumerates decision-tree Rashomon sets while exploiting the ordered structure of continuous features. We further develop a relaxation for approximate enumeration and an anytime algorithm that progressively refines the set of candidate thresholds, producing increasingly detailed approximations that converge to the continuous-feature Rashomon set. Experiments show that coarse binarization can miss many trees, important features, and predictive multiplicity; our algorithms achieve orders-of-magnitude speedups over existing enumeration methods, with approximations providing further speedups while maintaining near-perfect recall.