Bayesian symbolic regression: automated equation discovery from a physicist's perspective.

Area of Science:

• * Computational Physics
• * Machine Learning
• * Information Theory

Background:

• * Symbolic regression aims to discover closed-form mathematical models from data.
• * Current methods often use heuristics for model selection, regularization, and exploration.
• * These heuristic approaches lack performance guarantees.

Purpose of the Study:

• * To introduce and discuss the probabilistic approach to symbolic regression.
• * To highlight its advantages over heuristic methods in model discovery.
• * To explore its connections to information theory and statistical physics.

Main Methods:

• * Utilizing a probabilistic framework for symbolic regression.
• * Establishing model plausibility through fundamental considerations and approximations.
• * Connecting the approach to information theory and statistical physics principles.

Main Results:

• * The probabilistic approach provides performance guarantees absent in heuristic methods.
• * It offers a principled way to assess model plausibility.
• * The framework naturally leads to the consideration of model ensembles.

Conclusions:

• * The probabilistic approach offers a robust and theoretically grounded alternative for symbolic regression.
• * It enhances the reliability and interpretability of discovered mathematical models.
• * This methodology is particularly relevant for applications in the physical sciences.