# Distributional conformal prediction

arXiv: https://arxiv.org/abs/1909.07889 · HTML: https://mlsanity.com/paper/1909.07889/

## Key facts

- Cited by 105 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 30 of 105)

- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [A Large-Scale Study of Probabilistic Calibration in Neural Network Regression](https://mlsanity.com/paper/2306.02738/) (2023)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Probabilistic Conformal Prediction with Approximate Conditional Validity](https://mlsanity.com/paper/2407.01794/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Improving Adaptive Conformal Prediction Using Self-Supervised Learning](https://mlsanity.com/paper/2302.12238/) (2023)
- [Integrating Uncertainty Awareness into Conformalized Quantile Regression](https://mlsanity.com/paper/2306.08693/) (2023)
- [Simulator-Based Inference with Waldo: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems](https://mlsanity.com/paper/2205.15680/) (2022)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [Neural Conditional Probability for Uncertainty Quantification](https://mlsanity.com/paper/2407.01171/) (2024)

## Abstract (arXiv)

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.