# Conditional validity of heteroskedastic conformal regression

arXiv: https://arxiv.org/abs/2309.08313 · HTML: https://mlsanity.com/paper/2309.08313/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 44 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)

## Built on by (most cited first, 4 of 4)

- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Conformalized Regression for Continuous Bounded Outcomes](https://mlsanity.com/paper/2507.14023/) (2025)
- [Conformal Prediction for Compositional Data](https://mlsanity.com/paper/2511.18141/) (2025)
- [Conformal Prediction for Uncertainty Estimation in Drug-Target Interaction Prediction](https://mlsanity.com/paper/2505.18890/) (2025)

## Abstract (arXiv)

Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can produce state-of-the-art prediction intervals when focusing on marginal coverage, i.e. on a calibration dataset the method produces on average prediction intervals that contain the ground truth with a predefined coverage level. However, such intervals are often not adaptive, which can be problematic for regression problems with heteroskedastic noise. This paper tries to shed new light on how prediction intervals can be constructed, using methods such as normalized and Mondrian conformal prediction, in such a way that they adapt to the heteroskedasticity of the underlying process. Theoretical and experimental results are presented in which these methods are compared in a systematic way. In particular, it is shown how the conditional validity of a chosen conformal predictor can be related to (implicit) assumptions about the data-generating distribution.