# Integrating Uncertainty Awareness into Conformalized Quantile Regression

arXiv: https://arxiv.org/abs/2306.08693 · HTML: https://mlsanity.com/paper/2306.08693/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 14 Jun 2023.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [DeepGlobe 2018: A Challenge to Parse the Earth through Satellite Images](https://mlsanity.com/paper/1805.06561/) (2018)
- [Why do tree-based models still outperform deep learning on tabular data?](https://mlsanity.com/paper/2207.08815/) (2022)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)

## Built on by (most cited first, 17 of 17)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Position: Epistemic uncertainty estimation methods are fundamentally incomplete](https://mlsanity.com/paper/2505.23506/) (2025)
- [Entropy Reweighted Conformal Classification](https://mlsanity.com/paper/2407.17377/) (2024)
- [Adapting Prediction Sets to Distribution Shifts Without Labels](https://mlsanity.com/paper/2406.01416/) (2024)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [Adaptive Uncertainty Quantification for Generative AI](https://mlsanity.com/paper/2408.08990/) (2024)
- [Conformal Prediction in Hierarchical Classification with Constrained Representation Complexity](https://mlsanity.com/paper/2501.19038/) (2025)
- [Optimal Conformal Prediction under Epistemic Uncertainty](https://mlsanity.com/paper/2505.19033/) (2025)
- [Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning](https://mlsanity.com/paper/2607.14817/) (2026)
- [Improving Coverage in Combined Prediction Sets with Weighted p-values](https://mlsanity.com/paper/2505.11785/) (2025)
- [Calibrated uncertainty quantification for prosumer flexibility aggregation in ancillary service markets](https://mlsanity.com/paper/2601.14663/) (2026)
- [Leverage-Weighted Conformal Prediction](https://mlsanity.com/paper/2602.12693/) (2026)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)
- [ConformaDecompose: Explaining Uncertainty via Calibration Localization](https://mlsanity.com/paper/2604.27149/) (2026)

## Abstract (arXiv)

Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response Y given covariates X, without making distributional assumptions. However, existing constructions of CQR can be ineffective for problems where the quantile regressors perform better in certain parts of the feature space than others. The reason is that the prediction intervals of CQR do not distinguish between two forms of uncertainty: first, the variability of the conditional distribution of Y given X (i.e., aleatoric uncertainty), and second, our uncertainty in estimating this conditional distribution (i.e., epistemic uncertainty). This can lead to intervals that are overly narrow in regions where epistemic uncertainty is high. To address this, we propose a new variant of the CQR methodology, Uncertainty-Aware CQR (UACQR), that explicitly separates these two sources of uncertainty to adjust quantile regressors differentially across the feature space. Compared to CQR, our methods enjoy the same distribution-free theoretical coverage guarantees, while demonstrating in our experiments stronger conditional coverage properties in simulated settings and real-world data sets alike.