Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression

arXiv cs.LG Papers

Summary

A comprehensive survey on uncertainty quantification in symbolic regression, reviewing frequentist, Bayesian, and model selection approaches to address the lack of reliability support in real-world decision processes.

arXiv:2606.06567v1 Announce Type: new Abstract: 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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# Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression
Source: [https://arxiv.org/abs/2606.06567](https://arxiv.org/abs/2606.06567)
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> Abstract: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\.

## Submission history

From: Julia Reuter \[[view email](https://arxiv.org/show-email/9bf85f8e/2606.06567)\] **\[v1\]**Thu, 4 Jun 2026 17:29:56 UTC \(187 KB\)

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