Bayesian symbolic regression: Automated equation discovery from a physicists' perspective

TL;DR

This paper discusses a probabilistic approach to symbolic regression that offers a principled alternative to heuristic methods, connecting model plausibility with information theory and statistical physics, and emphasizing the use of model ensembles.

Contribution

It introduces a probabilistic framework for symbolic regression that provides performance guarantees and encourages the use of model ensembles over single models.

Findings

Probabilistic approach links model plausibility to information theory.

Guarantees of performance are established for the probabilistic method.

Model ensembles are favored over single models in this framework.

Abstract

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic regularization, and heuristic exploration of model space. Here, we discuss the probabilistic approach to symbolic regression, an alternative to such heuristic approaches with direct connections to information theory and statistical physics. We show how the probabilistic approach establishes model plausibility from basic considerations and explicit approximations, and how it provides guarantees of performance that heuristic approaches lack. We also discuss how the probabilistic approach compels us to consider model ensembles, as opposed to single models.