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Bayesian symbolic regression via posterior sampling.

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Summary
This summary is machine-generated.

This study introduces a robust Bayesian symbolic regression (SR) framework using sequential Monte Carlo (SMC) to discover equations from noisy data. The method enhances accuracy and interpretability, improving scientific discovery.

Keywords:
Bayesian inferencesequential Monte Carlosymbolic regression

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Area of Science:

  • Physical Sciences
  • Data Science
  • Machine Learning

Background:

  • Symbolic regression (SR) discovers governing equations from data but struggles with noisy datasets.
  • Existing methods like genetic programming are sensitive to noise, limiting their application.
  • Uncertainty quantification in SR is crucial for reliable scientific discovery.

Purpose of the Study:

  • To develop a robust Bayesian symbolic regression framework using sequential Monte Carlo (SMC).
  • To enhance SR's performance in the presence of noise and enable uncertainty quantification.
  • To improve the discovery of accurate, interpretable, and generalizable equations from scientific data.

Main Methods:

  • A sequential Monte Carlo (SMC) framework for Bayesian symbolic regression.
  • Probabilistic selection and adaptive tempering for efficient exploration of symbolic expression space.
  • Normalized marginal likelihood (NML) for model selection and parsimony.

Main Results:

  • The SMC-based SR method demonstrates enhanced robustness against noise in benchmark datasets.
  • Achieved improved generalization and reduced overfitting compared to standard genetic programming.
  • Successfully discovered accurate and interpretable symbolic expressions from noisy data.

Conclusions:

  • The proposed SMC framework offers a more reliable approach to symbolic regression in noisy scientific data.
  • This method facilitates robust equation discovery, advancing applications in physical sciences and engineering.
  • Enables uncertainty quantification, crucial for trustworthy scientific insights and design.