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Contemporary Symbolic Regression Methods and their Relative Performance.

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This study introduces a reproducible benchmarking platform for symbolic regression, evaluating 14 methods on 252 problems. Best methods for real-world data combine genetic algorithms with parameter estimation or semantic search.

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Area of Science:

  • Computer Science
  • Machine Learning
  • Data Science

Background:

  • Symbolic regression (SR) lacks standardized benchmarking, hindering progress.
  • Existing SR methods require robust evaluation on diverse problems.
  • Transparent and reproducible benchmarks are crucial for advancing SR.

Purpose of the Study:

  • Introduce an open-source, reproducible benchmarking platform for symbolic regression.
  • Provide a standardized evaluation framework for SR methods.
  • Facilitate collaborative development and improvement of SR techniques.

Main Methods:

  • Assessed 14 symbolic regression (SR) methods and 7 machine learning (ML) methods.
  • Utilized a benchmark suite of 252 diverse regression problems, including real-world and synthetic datasets.
  • Evaluated methods on model accuracy, complexity, and ability to recover exact equations under noise.

Main Results:

  • For real-world datasets, SR methods combining genetic algorithms with parameter estimation or semantic search performed best.
  • On synthetic problems with noise, several methods showed similar performance in recovering exact equations.
  • The developed platform allows for reproducible assessment and comparison of SR algorithms.

Conclusions:

  • A standardized, open-source benchmarking platform is essential for symbolic regression research.
  • Hybrid approaches (genetic algorithms + parameter estimation/semantic search) are effective for real-world SR.
  • Further collaboration is encouraged to develop a living benchmark for symbolic regression.