Scaling Up Unbiased Search-based Symbolic Regression
This work addresses the challenge of learning interpretable functions in regression tasks, offering a novel approach that could benefit fields requiring transparent models, though it appears incremental in improving existing symbolic regression techniques.
The authors tackled the problem of symbolic regression by systematically searching spaces of small expressions, resulting in more accurate and robust solutions that outperform state-of-the-art methods on benchmark datasets, with improved ability to recover true underlying symbolic expressions.
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.