# Conformalized Regression for Continuous Bounded Outcomes

arXiv: https://arxiv.org/abs/2507.14023 · HTML: https://mlsanity.com/paper/2507.14023/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 41 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Optimal Conformal Prediction for Small Areas](https://mlsanity.com/paper/2204.08122/) (2022)
- [Conditional validity of heteroskedastic conformal regression](https://mlsanity.com/paper/2309.08313/) (2023)
- [Scalable and robust regression models for continuous proportional data](https://mlsanity.com/paper/2504.15269/) (2025)

## Built on by (most cited first, 2 of 2)

- [Conformal Prediction for Compositional Data](https://mlsanity.com/paper/2511.18141/) (2025)
- [Conformalized Super Learner](https://mlsanity.com/paper/2604.22391/) (2026)

## Abstract (arXiv)

Regression problems with continuous bounded outcomes frequently arise in statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting the response at a new covariate value. Most of the existing literature has focused either on point prediction or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes within the framework of transformation regression models, encompassing widely used models such as beta regression and logit-normal regression. We construct non-conformity scores based on model-aligned residuals and identify a quantile-residual score that is particularly well suited to bounded outcomes, bridging normalized conformal prediction and distributional conformal prediction. This score accounts for both the heteroscedasticity inherent in such data and the asymmetry that emerges near the boundaries of the response space. We establish marginal validity and asymptotic conditional validity for both full and split conformal prediction, holding under model misspecification. A comprehensive simulation study confirms that both methods empirically attain valid finite-sample coverage, including cases under model misspecification. A real-data application demonstrates their practical performance against bootstrap-based alternatives.