Contemporary Symbolic Regression Methods and their Relative Performance

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.