(Exhaustive) symbolic regression and model selection by minimum description length

Area of Science:

• Machine learning
• Physical sciences
• Astrophysics

Background:

• Traditional symbolic regression (SR) algorithms face challenges in reliably finding accurate functions.
• Existing methods exhibit ambiguity and poorly justified assumptions in function selection.

Purpose of the Study:

• To address limitations in traditional SR algorithms.
• To develop a robust methodology for learning functions from data.

Main Methods:

• An exhaustive search strategy combined with model selection using the minimum description length (MDL) principle.
• The MDL principle allows direct trade-offs between model accuracy and complexity measured in information units.

Main Results:

• The developed Exhaustive Symbolic Regression (ESR) algorithm was applied to three astrophysics problems.
• ESR identified numerous functions superior to current literature standards for the universe's expansion history, galactic gravity, and inflaton field potential.

Conclusions:

• The proposed SR methodology offers a general-purpose approach for scientific discovery.
• This method has the potential for widespread application across various scientific domains and beyond.