# Scalable Bayesian Rule Lists

arXiv: https://arxiv.org/abs/1602.08610 · HTML: https://mlsanity.com/paper/1602.08610/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2016.

## Built on by (most cited first, 30 of 64)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Logic Explained Networks](https://mlsanity.com/paper/2108.05149/) (2021)
- [RePrompt: Automatic Prompt Editing to Refine AI-Generative Art Towards Precise Expressions](https://mlsanity.com/paper/2302.09466/) (2023)
- [Explainable Artificial Intelligence Approaches: A Survey](https://mlsanity.com/paper/2101.09429/) (2021)
- [SAT-Based Rigorous Explanations for Decision Lists](https://mlsanity.com/paper/2105.06782/) (2021)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [Self-explaining deep models with logic rule reasoning](https://mlsanity.com/paper/2210.07024/) (2022)
- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [Q-SENN: Quantized Self-Explaining Neural Networks](https://mlsanity.com/paper/2312.13839/) (2023)
- [Human-AI Co-design for Clinical Prediction Models](https://mlsanity.com/paper/2601.09072/) (2026)
- [Evaluating the Correctness of Explainable AI Algorithms for Classification](https://mlsanity.com/paper/2105.09740/) (2021)
- [TESTSGD: Interpretable Testing of Neural Networks Against Subtle Group Discrimination](https://mlsanity.com/paper/2208.11321/) (2022)
- [On the Safety of Interpretable Machine Learning: A Maximum Deviation Approach](https://mlsanity.com/paper/2211.01498/) (2022)
- [Efficient learning of large sets of locally optimal classification rules](https://mlsanity.com/paper/2301.09936/) (2023)
- [Take 5: Interpretable Image Classification with a Handful of Features](https://mlsanity.com/paper/2303.13166/) (2023)
- [Categorical Foundations of Explainable AI: A Unifying Theory](https://mlsanity.com/paper/2304.14094/) (2023)
- [Truly Unordered Probabilistic Rule Sets for Multi-class Classification](https://mlsanity.com/paper/2206.08804/) (2022)
- [An Exploration And Validation of Visual Factors in Understanding Classification Rule Sets](https://mlsanity.com/paper/2109.09160/) (2021)
- [May I Ask a Follow-up Question? Understanding the Benefits of Conversations in Neural Network Explainability](https://mlsanity.com/paper/2309.13965/) (2023)
- [Robust subgroup discovery](https://mlsanity.com/paper/2103.13686/) (2021)
- [Fair Decision Rules for Binary Classification](https://mlsanity.com/paper/2107.01325/) (2021)
- [Generating Explainable Rule Sets from Tree-Ensemble Learning Methods by Answer Set Programming](https://mlsanity.com/paper/2109.08290/) (2021)
- [Rationalizing Predictions by Adversarial Information Calibration](https://mlsanity.com/paper/2301.06009/) (2023)
- [Invisible Users: Uncovering End-Users' Requirements for Explainable AI via Explanation Forms and Goals](https://mlsanity.com/paper/2302.06609/) (2023)
- [Scalable Rule Lists Learning with Sampling](https://mlsanity.com/paper/2406.12803/) (2024)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Quantifying Explainability in NLP and Analyzing Algorithms for Performance-Explainability Tradeoff](https://mlsanity.com/paper/2107.05693/) (2021)
- [bsnsing: A decision tree induction method based on recursive optimal boolean rule composition](https://mlsanity.com/paper/2205.15263/) (2022)

## Abstract (arXiv)

We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees; further, in many cases, the computational time is practical and often less than that of decision trees. The result is a probabilistic classifier (which estimates P(y = 1|x) for each x) that optimizes the posterior of a Bayesian hierarchical model over rule lists.