# Falling Trees: A Model Class for Interpretable Risk Prioritization

arXiv: https://arxiv.org/abs/2609.23780 · HTML: https://mlsanity.com/paper/2609.23780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 45 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
- [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)
- [Falling Rule Lists](https://mlsanity.com/paper/1411.5899/) (2014)
- [Amazing Things Come From Having Many Good Models](https://mlsanity.com/paper/2407.04846/) (2024)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance](https://mlsanity.com/paper/2309.13775/) (2023)
- [Computing the Collection of Good Models for Rule Lists](https://mlsanity.com/paper/2204.11285/) (2022)
- [An Optimization Approach to Learning Falling Rule Lists](https://mlsanity.com/paper/1710.02572/) (2017)
- [Efficient Exploration of the Rashomon Set of Rule Set Models](https://mlsanity.com/paper/2406.03059/) (2024)
- [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)
- [Fast and Interpretable Mortality Risk Scores for Critical Care Patients](https://mlsanity.com/paper/2311.13015/) (2023)
- [Doctor Rashomon and the UNIVERSE of Madness: Variable Importance with Unobserved Confounding and the Rashomon Effect](https://mlsanity.com/paper/2510.12734/) (2025)
- [From Rashomon Theory to PRAXIS: Efficient Decision Tree Rashomon Sets](https://mlsanity.com/paper/2606.00202/) (2026)

## Abstract (arXiv)

Many real-world decisions require prioritizing high-risk cases, such as clinicians prioritizing high-risk patients before lower-risk ones. Falling rule lists (FRLs), which are ordered if--then rules with monotonically decreasing risks, provide an interpretable framework for such tasks; however, their single-path structure yields a highly restricted model class. We introduce falling trees, a new family of interpretable models that enforces the same monotonic risk constraint while permitting tree-structured branching. We present GRAVITree, a novel dynamic-programming-with-bounds algorithm for learning the Rashomon set of falling trees under depth and branching constraints. Our formulation can interpolate between rule lists and full decision trees, enabling user-desired model expressivity. In a new clinical dataset and in many public classification benchmarks, falling trees match or outperform FRLs and other interpretable baselines, often producing more sparse decisions for high-risk instances. Our results show that falling trees strike a practical balance between interpretability, expressiveness, and risk prioritization for high-stakes settings.