Bayesian Symbolic Regression via Posterior Sampling

TL;DR

This paper presents a Bayesian symbolic regression method using Sequential Monte Carlo that improves robustness to noise, provides uncertainty quantification, and outperforms traditional genetic programming approaches in noisy data scenarios.

Contribution

It introduces a novel SMC-based Bayesian framework for symbolic regression, enhancing noise robustness and interpretability over existing methods.

Findings

Better handling of noisy datasets compared to genetic programming

Produces more parsimonious and generalizable symbolic expressions

Reduces overfitting and improves discovery of accurate equations

Abstract

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian symbolic regression that approximates the posterior distribution over symbolic expressions, enhancing robustness and enabling uncertainty quantification for symbolic regression in the presence of noise. Differing from traditional genetic programming approaches, the SMC-based algorithm combines probabilistic selection, adaptive tempering, and the use of normalized marginal likelihood to efficiently explore the search space of symbolic expressions, yielding parsimonious expressions with improved generalization. When compared to standard genetic programming baselines, the proposed method better deals with challenging, noisy benchmark datasets. The reduced tendency to overfit and enhanced ability to discover accurate and interpretable equations paves the way for more robust symbolic regression in scientific discovery and engineering design applications.