Falling trees improve risk sorting with clear decision paths

Falling Trees: A Model Class for Interpretable Risk Prioritization

Machine Learning

Summary

Many situations require sorting things or people by risk, like doctors figuring out which patients need urgent care. Previous methods used simple lists of rules that always reduced risk as you moved down the list, but these were limited because they only followed one path. This paper introduces "falling trees," which keep the risk always going down but allow branching decisions like a tree, making models more flexible and just as easy to understand. The authors developed a new method to find the best such trees and showed they often work better than older methods, especially in medical data. Falling trees balance being easy to understand with being powerful enough to catch important risk patterns.

What this means in practice

  • For hospital data teams: Sort patients by risk to prioritize care using easily understandable models that balance accuracy and simplicity.
  • For risk management teams: Create transparent risk prioritization tools that allow branching decisions while ensuring risk scores consistently decrease.

Authors

Varun Babbar, Zachery Boner, Margo Seltzer, Cynthia Rudin

Abstract

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.
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