# Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles

arXiv: https://arxiv.org/abs/2209.06454 · HTML: https://mlsanity.com/paper/2209.06454/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge](https://mlsanity.com/paper/2103.15624/) (2021)
- [Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication](https://mlsanity.com/paper/2109.13895/) (2021)
- [Automated Learning of Interpretable Models with Quantified Uncertainty](https://mlsanity.com/paper/2205.01626/) (2022)
- [Transformation-Interaction-Rational Representation for Symbolic Regression](https://mlsanity.com/paper/2205.06807/) (2022)
- [Local Optimization Often is Ill-conditioned in Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2209.00942/) (2022)

## Built on by (most cited first, 3 of 3)

- [Learning from Uncertain Data: From Possible Worlds to Possible Models](https://mlsanity.com/paper/2405.18549/) (2024)
- [Exploring Multi-view Symbolic Regression methods in physical sciences](https://mlsanity.com/paper/2509.10500/) (2025)
- [Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression](https://mlsanity.com/paper/2606.06567/) (2026)

## Abstract (arXiv)

Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of models and for decision making. The linear approximation and so-called likelihood profiles are well-known possibilities for the calculation of confidence and prediction intervals for nonlinear regression models. These simple and effective techniques have been completely ignored so far in the genetic programming literature. In this work we describe the calculation of likelihood profiles in details and also provide some illustrative examples with models created with three different symbolic regression algorithms on two different datasets. The examples highlight the importance of the likelihood profiles to understand the limitations of symbolic regression models and to help the user taking an informed post-prediction decision.