用数学优化找数据中最佳可解释规则，兼顾准确与效率
Optimal Pattern Detection Tree for Symbolic Rule-Based Classification
- 基于混合整数规划构建决策树，直接求解最优规则
- 在合理时间内发现高覆盖率低误报率的隐藏模式
- 支持领域知识嵌入，适合医疗等需透明决策场景
数据中的模式发现广泛应用于医疗、风险评估和设备维护等领域。与黑箱深度学习模型不同，符号化规则发现作为关键数据挖掘任务，能生成人类可理解的规则，兼具透明性与可解释性。本文提出最优模式检测树（OPDT），一种基于新型混合整数规划的规则学习模型，通过二分类任务发现单一最优模式。为融入先验知识与合规要求，进一步提出分支结构约束（BSC）框架，使决策者可直接将领域知识与约束编码至模型中。该优化方法在存在隐含模式时，识别出覆盖度高且误报率最低的最优规则。计算实验表明，OPDT可在合理运行时间内对中等规模数据集实现具有最优性保证的模式发现。
原文摘要 · Abstract (English)
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.
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