arXiv:2506.19626cs.LG2025-06IJCAI被引 8

通过系统搜索小表达式,提升符号回归的准确性和抗噪能力。

Scaling Up Unbiased Search-based Symbolic Regression

  • 聚焦小表达式空间,系统搜索而非依赖结构假设。
  • 在基准数据集上恢复真实表达式的成功率显著优于现有方法。
  • 适合需要高可解释性与鲁棒性的科学建模场景。

在回归任务中,目标是从带标签数据学习函数以预测新数据点的标签,追求低预测误差。符号回归的目标更进一步:学习一个可解释且误差小的函数。这一额外目标排除了传统回归中通过优化基函数展开参数的方法。相反,符号回归需在符号表达式空间中搜索最优解。为应对庞大的搜索空间,多数方法隐含或明确假设其结构。本文认为,搜索空间唯一明显的结构是包含小表达式——即能分解为少数子表达式的表达式。我们证明,系统搜索小表达式空间能获得比当前顶尖符号回归方法更准确、更具抗噪性的解。特别是在标准基准数据集上,系统搜索在恢复真实底层符号表达式方面表现更优。

原文摘要 · Abstract (English)

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.

符号回归可解释性搜索算法

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。