# Optimal Pattern Detection Tree for Symbolic Rule-Based Classification

arXiv: https://arxiv.org/abs/2605.14374 · HTML: https://mlsanity.com/paper/2605.14374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 55 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 7 of 7)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Strong Optimal Classification Trees](https://mlsanity.com/paper/2103.15965/) (2021)
- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [RRULES: An improvement of the RULES rule-based classifier](https://mlsanity.com/paper/2106.07296/) (2021)

## Abstract (arXiv)

Pattern discovery in data plays a crucial role across diverse domains, including healthcare, risk assessment, and machinery maintenance. In contrast to black-box deep learning models, symbolic rule discovery emerges as a key data mining task, generating human-interpretable rules that offer both transparency and intuitive explainability. This paper introduces the Optimal Pattern Detection Tree (OPDT), a rule-based machine learning model based on novel mixed-integer programming to discover a single optimal pattern in data through binary classification. To incorporate prior knowledge and compliance requirements, we further introduce the Branching Structure Constraints (BSC) framework, which enables decision makers to encode domain knowledge and constraints directly into the model. This optimization-based approach discovers a hidden underlying pattern in datasets, when it exists, by identifying an optimal rule that maximizes coverage while minimizing the false positive rate due to misclassification. Our computational experiments show that OPDT discovers a pattern with optimality guarantees on moderately sized datasets within reasonable runtime.