# Probabilistic Truly Unordered Rule Sets

arXiv: https://arxiv.org/abs/2401.09918 · HTML: https://mlsanity.com/paper/2401.09918/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 10 of 10)

- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [Minimum Description Length Revisited](https://mlsanity.com/paper/1908.08484/) (2019)
- [Interpretable multiclass classification by MDL-based rule lists](https://mlsanity.com/paper/1905.00328/) (2019)
- [The Minimum Description Length Principle for Pattern Mining: A Survey](https://mlsanity.com/paper/2007.14009/) (2020)
- [Learning Interpretable Decision Rule Sets: A Submodular Optimization Approach](https://mlsanity.com/paper/2206.03718/) (2022)
- [Diverse Rule Sets](https://mlsanity.com/paper/2006.09890/) (2020)
- [Truly Unordered Probabilistic Rule Sets for Multi-class Classification](https://mlsanity.com/paper/2206.08804/) (2022)

## Built on by (most cited first, 1 of 1)

- [Interpretable Classification via a Rule Network with Selective Logical Operators](https://mlsanity.com/paper/2408.11918/) (2024)

## Abstract (arXiv)

Rule set learning has recently been frequently revisited because of its interpretability. Existing methods have several shortcomings though. First, most existing methods impose orders among rules, either explicitly or implicitly, which makes the models less comprehensible. Second, due to the difficulty of handling conflicts caused by overlaps (i.e., instances covered by multiple rules), existing methods often do not consider probabilistic rules. Third, learning classification rules for multi-class target is understudied, as most existing methods focus on binary classification or multi-class classification via the ``one-versus-rest" approach. To address these shortcomings, we propose TURS, for Truly Unordered Rule Sets. To resolve conflicts caused by overlapping rules, we propose a novel model that exploits the probabilistic properties of our rule sets, with the intuition of only allowing rules to overlap if they have similar probabilistic outputs. We next formalize the problem of learning a TURS model based on the MDL principle and develop a carefully designed heuristic algorithm. We benchmark against a wide range of rule-based methods and demonstrate that our method learns rule sets that have lower model complexity and highly competitive predictive performance. In addition, we empirically show that rules in our model are empirically ``independent" and hence truly unordered.