# Symbolic Quantile Regression for the Interpretable Prediction of Conditional Quantiles

arXiv: https://arxiv.org/abs/2508.08080 · HTML: https://mlsanity.com/paper/2508.08080/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 16 of 16)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Conformal Prediction: a Unified Review of Theory and New Challenges](https://mlsanity.com/paper/2005.07972/) (2020)
- [A Comparative Analysis of XGBoost](https://mlsanity.com/paper/1911.01914/) (2019)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy](https://mlsanity.com/paper/2201.09932/) (2022)
- [Predicting Friction System Performance with Symbolic Regression and Genetic Programming with Factor Variables](https://mlsanity.com/paper/2107.09484/) (2021)
- [Explainable Fraud Detection with Deep Symbolic Classification](https://mlsanity.com/paper/2312.00586/) (2023)
- [Symbolic Regression for Space Applications: Differentiable Cartesian Genetic Programming Powered by Multi-objective Memetic Algorithms](https://mlsanity.com/paper/2206.06213/) (2022)

## Built on by (most cited first, 1 of 1)

- [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 (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently not well understood how it can be used to estimate the relationship between variables at other points in the distribution of the target variable. Such estimates of e.g. the median or an extreme value provide a fuller picture of how predictive variables affect the outcome and are necessary in high-stakes, safety-critical application domains. This study introduces Symbolic Quantile Regression (SQR), an approach to predict conditional quantiles with SR. In an extensive evaluation, we find that SQR outperforms transparent models and performs comparably to a strong black-box baseline without compromising transparency. We also show how SQR can be used to explain differences in the target distribution by comparing models that predict extreme and central outcomes in an airline fuel usage case study. We conclude that SQR is suitable for predicting conditional quantiles and understanding interesting feature influences at varying quantiles.