Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems

2025-06-04

IEEE Transactions on Evolutionary Computation

AI Summary

To address the challenge of inflexible rule representation in Learning Classifier Systems (LCS) for multi-modal problem spaces, this paper proposes an adaptive rule representation based on the four-parameter Beta distribution—the first such integration in LCS. This representation enables automatic selection of diverse decision boundaries (e.g., rectangular, bell-shaped) across input subspaces, supporting continuous boundary shape adjustment and subspace-specific adaptation. Coupled with a generalization mechanism biased toward crisp, interpretable rules, it preserves classification accuracy while enhancing transparency. The approach is embedded within a fuzzy-style LCS architecture, featuring adaptive rule evolution and bi-objective optimization balancing accuracy and rule set simplicity. Empirical evaluation on real-world classification tasks demonstrates statistically significant improvements in test accuracy, alongside generation of more compact and human-interpretable rule sets. An open-source implementation is publicly available on GitHub.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models through evolutionary processes. However, it is very difficult to choose an appropriate rule representation for each problem. Additionally, some problems benefit from using different representations for different subspaces within the input space. Thus, an adaptive mechanism is needed to choose an appropriate rule representation for each rule in LCSs. This article introduces a flexible rule representation using a four-parameter beta distribution and integrates it into a fuzzy-style LCS. The four-parameter beta distribution can form various function shapes, and this flexibility enables our LCS to automatically select appropriate representations for different subspaces. Our rule representation can represent crisp/fuzzy decision boundaries in various boundary shapes, such as rectangles and bells, by controlling four parameters, compared to the standard representations such as trapezoidal ones. Leveraging this flexibility, our LCS is designed to adapt the appropriate rule representation for each subspace. Moreover, our LCS incorporates a generalization bias favoring crisp rules where feasible, enhancing model interpretability without compromising accuracy. Experimental results on real-world classification tasks show that our LCS achieves significantly superior test accuracy and produces more compact rule sets. Our implementation is available at https://github.com/YNU-NakataLab/Beta4-UCS. An extended abstract related to this work is available at https://doi.org/10.36227/techrxiv.174900805.59801248/v1.

Problem

• Adapting rule representation for Learning Classifier Systems (LCSs)
• Automatically selecting rule representations for different subspaces
• Enhancing model interpretability without compromising accuracy

Innovation

• Uses four-parameter beta distribution for rules
• Adapts rule representation per subspace
• Balances accuracy and interpretability effectively