首篇系统梳理符号回归中不确定性量化方法的综述
Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression
- 从频率派、贝叶斯和模型选择三方面梳理不确定性量化方法
- 揭示符号回归中不确定性量化仍处于早期探索阶段
- 适合关注模型可靠性与决策可信度的研究者阅读
符号回归（Symbolic Regression, SR）是一类系统探索数学函数空间以发现准确捕捉数据潜在关系模型的方法。尽管该领域近年取得进展，但缺乏不确定性量化（Uncertainty Quantification, UQ）支持，限制了其在真实决策过程中的应用。在回归分析中，UQ 提供模型可靠性的重要信息，有助于避免过拟合并为决策提供依据。本文是首个明确针对此问题的综述，旨在介绍关键的不确定性量化概念，并系统回顾当前关于符号回归中不确定性量化的文献，研究可归纳为三大方向：频率派、贝叶斯方法与模型选择。尽管其重要性显著，符号回归中的不确定性量化仍处于未充分探索状态，亟需进一步研究可靠的方法。
原文摘要 · Abstract (English)
Symbolic regression (SR) is a class of methods that systematically explore the space of mathematical functions to discover models that accurately capture the underlying relationships in a dataset. Despite recent advances in the field, a lack of support for uncertainty quantification (UQ) limits its adoption in real-world decision processes. In regression analysis, UQ provides important information about the model reliability, which can both help to avoid overfitting by accounting for uncertainty in the data, and provide insights for decision-making. This survey is the first to clearly address this issue, with the objective of introducing essential UQ concepts and reviewing the current literature on UQ in SR, which can be broadly organized into three research directions: frequentist, Bayesian, and model selection. Despite its importance, UQ in SR is still underexplored, which motivates further research into reliable UQ methods for SR.
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