Scaling Up Unbiased Search-based Symbolic Regression

TL;DR

This paper introduces a systematic search approach for symbolic regression focusing on small, decomposable expressions, leading to more accurate and noise-robust solutions compared to existing methods.

Contribution

It proposes a novel systematic search method emphasizing small expressions, improving accuracy and robustness over state-of-the-art symbolic regression techniques.

Findings

Systematic search outperforms existing methods in recovering true expressions.

Small, decomposable expressions lead to more accurate models.

The approach is more robust against noise in data.

Abstract

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable function that makes small prediction errors. This additional goal largely rules out the standard approach used in regression, that is, reducing the learning problem to learning parameters of an expansion of basis functions by optimization. Instead, symbolic regression methods search for a good solution in a space of symbolic expressions. To cope with the typically vast search space, most symbolic regression methods make implicit, or sometimes even explicit, assumptions about its structure. Here, we argue that the only obvious structure of the search space is that it contains small expressions, that is, expressions that can be decomposed into a few subexpressions. We show that systematically searching spaces of small expressions finds solutions that are more accurate and more robust against noise than those obtained by state-of-the-art symbolic regression methods. In particular, systematic search outperforms state-of-the-art symbolic regressors in terms of its ability to recover the true underlying symbolic expressions on established benchmark data sets.