GESR:一个象征回归的几何演化模型
1School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China cszhitongma@mail.scut.edu.cn.
Evolutionary computation
|October 31, 2025
概括
几何进化符号回归 (GESR) 通过发现可解释的方程来增强机器学习. 这种新的算法通过利用几何语义来提高复杂数据集的准确性,以获得更好的近似.
科学领域:
- 机器学习 机器学习
- 人工智能的人工智能
- 计算数学 计算数学 计算数学
背景情况:
- 符号回归 (SR) 旨在从数据中自动发现可解释的数学方程.
- 现有的SR方法面临着包含复杂数学表达式的数据集的挑战.
- 当前方法的局限性阻碍了准确和可理解模型的发现.
研究的目的:
- 提出一种新的算法,即几何演变符号回归 (GESR),以解决符号回归的局限性.
- 增强从有限和复杂的数据中发现高度可解释的数学方程.
- 为了提高复杂的数学表达式的符号回归的准确性和效率.
主要方法:
- 介绍了一种新的几何进化符号回归 (GESR) 算法.
- 将符号回归转化为使用几何语义在n维语义空间中的近似问题.
- 开发了三个关键模块:一个新的语义梯度概念,一个几何语义搜索运算符,以及带有L1规范化的Levenberg-Marquardt算法.
主要成果:
- 提出的语义渐变概念可以提高语义空间的探索和准确性.
- 几何语义搜索运算符在尺寸限制下有效地找到准确的,可解释的解决方案.
- 在SRSD基准数据集上,GESR实现了最先进的准确性表现.
结论:
- 在符号回归方面,GESR提供了显著的进步,特别是在复杂的数据集中.
- 几何语义和新型算法模块的整合提高了模型的解释性和准确性.
- 开发的方法为自动发现复杂的数学表达式提供了强大的解决方案.
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