# Computing the Collection of Good Models for Rule Lists

arXiv: https://arxiv.org/abs/2204.11285 · HTML: https://mlsanity.com/paper/2204.11285/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 24 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [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)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Falling Rule Lists](https://mlsanity.com/paper/1411.5899/) (2014)
- [Learning Certifiably Optimal Rule Lists for Categorical Data](https://mlsanity.com/paper/1704.01701/) (2017)
- [Characterizing the risk of fairwashing](https://mlsanity.com/paper/2106.07504/) (2021)

## Built on by (most cited first, 12 of 12)

- [Amazing Things Come From Having Many Good Models](https://mlsanity.com/paper/2407.04846/) (2024)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [Efficient Exploration of the Rashomon Set of Rule Set Models](https://mlsanity.com/paper/2406.03059/) (2024)
- [Be Intentional About Fairness!: Fairness, Size, and Multiplicity in the Rashomon Set](https://mlsanity.com/paper/2501.15634/) (2025)
- [Quantifying Prediction Consistency Under Fine-Tuning Multiplicity in Tabular LLMs](https://mlsanity.com/paper/2407.04173/) (2024)
- [Fairness and Sparsity within Rashomon sets: Enumeration-Free Exploration and Characterization](https://mlsanity.com/paper/2502.05286/) (2025)
- [CASHomon Sets: Efficient Rashomon Sets Across Multiple Model Classes and their Hyperparameters](https://mlsanity.com/paper/2603.15321/) (2026)
- [MOSS: Multi-Objective Optimization for Stable Rule Sets](https://mlsanity.com/paper/2506.08030/) (2025)
- [When Interpretability Is Unequally Distributed: Fairness in Hybrid Interpretable Models](https://mlsanity.com/paper/2605.28626/) (2026)
- [Algebraic Model Counting for Global Analysis of Optimal Decision Trees](https://mlsanity.com/paper/2607.02069/) (2026)
- [Falling Trees: A Model Class for Interpretable Risk Prioritization](https://mlsanity.com/paper/2609.23780/) (2026)

## Abstract (arXiv)

Since the seminal paper by Breiman in 2001, who pointed out a potential harm of prediction multiplicities from the view of explainable AI, global analysis of a collection of all good models, also known as a `Rashomon set,' has been attracted much attention for the last years. Since finding such a set of good models is a hard computational problem, there have been only a few algorithms for the problem so far, most of which are either approximate or incomplete. To overcome this difficulty, we study efficient enumeration of all good models for a subclass of interpretable models, called rule lists. Based on a state-of-the-art optimal rule list learner, CORELS, proposed by Angelino et al. in 2017, we present an efficient enumeration algorithm CorelsEnum for exactly computing a set of all good models using polynomial space in input size, given a dataset and a error tolerance from an optimal model. By experiments with the COMPAS dataset on recidivism prediction, our algorithm CorelsEnum successfully enumerated all of several tens of thousands of good rule lists of length at most ℓ = 3 in around 1,000 seconds, while a state-of-the-art top-K rule list learner based on Lawler's method combined with CORELS, proposed by Hara and Ishihata in 2018, found only 40 models until the timeout of 6,000 seconds. For global analysis, we conducted experiments for characterizing the Rashomon set, and observed large diversity of models in predictive multiplicity and fairness of models.