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

arXiv: https://arxiv.org/abs/2606.06567 · HTML: https://mlsanity.com/paper/2606.06567/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Priors for symbolic regression](https://mlsanity.com/paper/2304.06333/) (2023)
- [Automated Learning of Interpretable Models with Quantified Uncertainty](https://mlsanity.com/paper/2205.01626/) (2022)
- [The Inefficiency of Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2404.17292/) (2024)
- [Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles](https://mlsanity.com/paper/2209.06454/) (2022)
- [Bayesian Symbolic Regression via Posterior Sampling](https://mlsanity.com/paper/2512.10849/) (2025)
- [Marginalised Normal Regression: Unbiased curve fitting in the presence of x-errors](https://mlsanity.com/paper/2309.00948/) (2023)
- [Symbolic Quantile Regression for the Interpretable Prediction of Conditional Quantiles](https://mlsanity.com/paper/2508.08080/) (2025)
- [Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests](https://mlsanity.com/paper/2509.19710/) (2025)
- [VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees](https://mlsanity.com/paper/2602.23561/) (2026)

## Abstract (arXiv)

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.