# Learning Optimized Or's of And's

arXiv: https://arxiv.org/abs/1511.02210 · HTML: https://mlsanity.com/paper/1511.02210/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2015.

## Built on by (most cited first, 14 of 14)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Learning Interpretable Decision Rule Sets: A Submodular Optimization Approach](https://mlsanity.com/paper/2206.03718/) (2022)
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- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [Efficient Exploration of the Rashomon Set of Rule Set Models](https://mlsanity.com/paper/2406.03059/) (2024)
- [Boolformer: Symbolic Regression of Logic Functions with Transformers](https://mlsanity.com/paper/2309.12207/) (2023)
- [Rule Generation for Classification: Scalability, Interpretability, and Fairness](https://mlsanity.com/paper/2104.10751/) (2021)
- [Fair Decision Rules for Binary Classification](https://mlsanity.com/paper/2107.01325/) (2021)
- [Explainable AI using expressive Boolean formulas](https://mlsanity.com/paper/2306.03976/) (2023)
- [Explainable AI for clinical risk prediction: a survey of concepts, methods, and modalities](https://mlsanity.com/paper/2308.08407/) (2023)
- [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)
- [Iterative Rule Extension for Logic Analysis of Data: an MILP-based heuristic to derive interpretable binary classification from large datasets](https://mlsanity.com/paper/2110.13664/) (2021)
- [Optimizing Sparse Boolean Rule Networks using Mixed Integer Linear Programming](https://mlsanity.com/paper/2610.20170/) (2026)

## Abstract (arXiv)

Or's of And's (OA) models are comprised of a small number of disjunctions of conjunctions, also called disjunctive normal form. An example of an OA model is as follows: If (x1 =  `blue' AND x2= `middle') OR (x1 =  `yellow'), then predict Y=1, else predict Y=0. Or's of And's models have the advantage of being interpretable to human experts, since they are a set of conditions that concisely capture the characteristics of a specific subset of data. We present two optimization-based machine learning frameworks for constructing OA models, Optimized OA (OOA) and its faster version, Optimized OA with Approximations (OOAx). We prove theoretical bounds on the properties of patterns in an OA model. We build OA models as a diagnostic screening tool for obstructive sleep apnea, that achieves high accuracy with a substantial gain in interpretability over other methods.