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GESR: A Geometric Evolution Model for Symbolic Regression.

Zhitong Ma1, Jinghui Zhong2

  • 1School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China cszhitongma@mail.scut.edu.cn.

Evolutionary Computation
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Summary
This summary is machine-generated.

Geometric Evolution Symbolic Regression (GESR) enhances machine learning by discovering interpretable equations. This novel algorithm improves accuracy on complex datasets by leveraging geometric semantics for better approximation.

Keywords:
Genetic Programming (GP)Geometric Semantic OperatorSemantic GradientSymbolic Regression

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Computational Mathematics

Background:

  • Symbolic regression (SR) aims to automatically discover interpretable mathematical equations from data.
  • Existing SR methods face challenges with datasets containing intricate mathematical expressions.
  • Limitations in current approaches hinder the discovery of accurate and understandable models.

Purpose of the Study:

  • To propose a novel algorithm, Geometric Evolution Symbolic Regression (GESR), to address limitations in symbolic regression.
  • To enhance the discovery of highly interpretable mathematical equations from limited and complex data.
  • To improve the accuracy and efficiency of symbolic regression for intricate mathematical expressions.

Main Methods:

  • Introduced a novel Geometric Evolution Symbolic Regression (GESR) algorithm.
  • Transformed symbolic regression into an approximation problem in n-dimensional semantic space using geometric semantics.
  • Developed three key modules: a new semantic gradient concept, a geometric semantic search operator, and the Levenberg-Marquardt algorithm with L1 regularization.

Main Results:

  • The proposed semantic gradient concept improves exploration and accuracy in semantic space.
  • The geometric semantic search operator efficiently finds accurate, interpretable solutions under size constraints.
  • GESR achieved state-of-the-art accuracy performance on the SRSD benchmark datasets.

Conclusions:

  • GESR offers a significant advancement in symbolic regression, particularly for complex datasets.
  • The integration of geometric semantics and novel algorithmic modules enhances model interpretability and accuracy.
  • The developed approach provides a robust solution for discovering intricate mathematical expressions automatically.