# Generalized Linear Rule Models

arXiv: https://arxiv.org/abs/1906.01761 · HTML: https://mlsanity.com/paper/1906.01761/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2019.

## Built on by (most cited first, 30 of 36)

- [Human-Centered Explainable AI (XAI): From Algorithms to User Experiences](https://mlsanity.com/paper/2110.10790/) (2021)
- [The Who in XAI: How AI Background Shapes Perceptions of AI Explanations](https://mlsanity.com/paper/2107.13509/) (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)
- [Digital Twin-Enhanced Wireless Indoor Navigation: Achieving Efficient Environment Sensing with Zero-Shot Reinforcement Learning](https://mlsanity.com/paper/2306.06766/) (2023)
- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [AI Explainability 360: Impact and Design](https://mlsanity.com/paper/2109.12151/) (2021)
- [On the Safety of Interpretable Machine Learning: A Maximum Deviation Approach](https://mlsanity.com/paper/2211.01498/) (2022)
- [Explainability in Process Outcome Prediction: Guidelines to Obtain Interpretable and Faithful Models](https://mlsanity.com/paper/2203.16073/) (2022)
- [FIRE: An Optimization Approach for Fast Interpretable Rule Extraction](https://mlsanity.com/paper/2306.07432/) (2023)
- [Learning Cut Generating Functions for Integer Programming](https://mlsanity.com/paper/2405.13992/) (2024)
- [Rule Generation for Classification: Scalability, Interpretability, and Fairness](https://mlsanity.com/paper/2104.10751/) (2021)
- [A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tables](https://mlsanity.com/paper/2208.08609/) (2022)
- [TT-TFHE: a Torus Fully Homomorphic Encryption-Friendly Neural Network Architecture](https://mlsanity.com/paper/2302.01584/) (2023)
- [Feature Cross Search via Submodular Optimization](https://mlsanity.com/paper/2107.02139/) (2021)
- [MINTY: Rule-based Models that Minimize the Need for Imputing Features with Missing Values](https://mlsanity.com/paper/2311.14108/) (2023)
- [Distilled Datamodel with Reverse Gradient Matching](https://mlsanity.com/paper/2404.14006/) (2024)
- [Orthogonal Gradient Boosting for Simpler Additive Rule Ensembles](https://mlsanity.com/paper/2402.15691/) (2024)
- [Neural Reasoning Networks: Efficient Interpretable Neural Networks With Automatic Textual Explanations](https://mlsanity.com/paper/2410.07966/) (2024)
- [Compact Rule-Based Classifier Learning via Gradient Descent](https://mlsanity.com/paper/2502.01375/) (2025)
- [Bias Detection via Maximum Subgroup Discrepancy](https://mlsanity.com/paper/2502.02221/) (2025)
- [A Unified Approach to Extract Interpretable Rules from Tree Ensembles via Integer Programming](https://mlsanity.com/paper/2407.00843/) (2024)
- [Deep Explainable Learning with Graph Based Data Assessing and Rule Reasoning](https://mlsanity.com/paper/2211.04693/) (2022)
- [Personalized Interpretable Classification](https://mlsanity.com/paper/2302.02528/) (2023)
- [Explaining with Greater Support: Weighted Column Sampling Optimization for q-Consistent Summary-Explanations](https://mlsanity.com/paper/2302.04528/) (2023)
- [Learning Locally Interpretable Rule Ensemble](https://mlsanity.com/paper/2306.11481/) (2023)
- [Reinforcement Logic Rule Learning for Temporal Point Processes](https://mlsanity.com/paper/2308.06094/) (2023)
- [A New Interpretable Neural Network-Based Rule Model for Healthcare Decision Making](https://mlsanity.com/paper/2309.11101/) (2023)
- [The Value of AI Advice: Personalized and Value-Maximizing AI Advisors Are Necessary to Reliably Benefit Experts and Organizations](https://mlsanity.com/paper/2412.19530/) (2024)
- [MOSS: Multi-Objective Optimization for Stable Rule Sets](https://mlsanity.com/paper/2506.08030/) (2025)

## Abstract (arXiv)

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences and interactions. Our problem formulation accordingly trades off rule set complexity and prediction accuracy. Column generation is used to optimize over an exponentially large space of rules without pre-generating a large subset of candidates or greedily boosting rules one by one. The column generation subproblem is solved using either integer programming or a heuristic optimizing the same objective. In experiments involving logistic and linear regression, the proposed methods obtain better accuracy-complexity trade-offs than existing rule ensemble algorithms. At one end of the trade-off, the methods are competitive with less interpretable benchmark models.