# Conformalized Unconditional Quantile Regression

arXiv: https://arxiv.org/abs/2304.01426 · HTML: https://mlsanity.com/paper/2304.01426/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 17 of 17)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [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)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Efficient and Differentiable Conformal Prediction with General Function Classes](https://mlsanity.com/paper/2202.11091/) (2022)
- [Conformal prediction with localization](https://mlsanity.com/paper/1908.08558/) (2019)
- [Variational Gaussian Dropout is not Bayesian](https://mlsanity.com/paper/1711.02989/) (2017)

## Built on by (most cited first, 8 of 8)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Efficient Conformal Prediction under Data Heterogeneity](https://mlsanity.com/paper/2312.15799/) (2023)
- [Conformalized Multimodal Uncertainty Regression and Reasoning](https://mlsanity.com/paper/2309.11018/) (2023)
- [Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methods](https://mlsanity.com/paper/2305.12283/) (2023)
- [Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better](https://mlsanity.com/paper/2601.21455/) (2026)
- [Generative Score Inference for Multimodal Data](https://mlsanity.com/paper/2603.26349/) (2026)

## Abstract (arXiv)

We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the quantile functional over input covariates. Unlike the more widely-known conditional QR, unconditional QR explicitly captures the impact of changes in covariate distribution on the quantiles of the marginal distribution of outcomes. Leveraging this property, our procedure issues adaptive predictive intervals with localized frequentist coverage guarantees. It operates by fitting a machine learning model for the RIFs using training data, and then applying the CP procedure for any test covariate with respect to a ``hypothetical'' covariate distribution localized around the new instance. Experiments show that our procedure is adaptive to heteroscedasticity, provides transparent coverage guarantees that are relevant to the test instance at hand, and performs competitively with existing methods in terms of efficiency.