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

arXiv: https://arxiv.org/abs/2506.03602 · HTML: https://mlsanity.com/paper/2506.03602/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 72 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Model Based Explanations of Concept Drift](https://mlsanity.com/paper/2303.09331/) (2023)
- [Autoencoding with a Classifier System](https://mlsanity.com/paper/1910.10579/) (2019)
- [Ockham's Razor in Memetic Computing: Three Stage Optimal Memetic Exploration](https://mlsanity.com/paper/1810.08669/) (2018)
- [Fuzzy-UCS Revisited: Self-Adaptation of Rule Representations in Michigan-Style Learning Fuzzy-Classifier Systems](https://mlsanity.com/paper/2505.06017/) (2025)
- [Bayesian inference for a flexible class of bivariate beta distributions](https://mlsanity.com/paper/1402.1782/) (2014)

## Built on by (most cited first, 1 of 1)

- [Kolmogorov-Arnold Classifier Systems as Universal Approximators](https://mlsanity.com/paper/2609.37958/) (2026)

## Abstract (arXiv)

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.