# Conformal Prediction with Missing Values

arXiv: https://arxiv.org/abs/2306.02732 · HTML: https://mlsanity.com/paper/2306.02732/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [Linear predictor on linearly-generated data with missing values: non consistency and solutions](https://mlsanity.com/paper/2002.00658/) (2020)
- [The Missing Indicator Method: From Low to High Dimensions](https://mlsanity.com/paper/2211.09259/) (2022)
- [R-miss-tastic: a unified platform for missing values methods and workflows](https://mlsanity.com/paper/1908.04822/) (2019)

## Built on by (most cited first, 25 of 25)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Prediction for Class-wise Coverage via Augmented Label Rank Calibration](https://mlsanity.com/paper/2406.06818/) (2024)
- [Equal Opportunity of Coverage in Fair Regression](https://mlsanity.com/paper/2311.02243/) (2023)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Uncertainty quantification for probabilistic machine learning in earth observation using conformal prediction](https://mlsanity.com/paper/2401.06421/) (2024)
- [Robust Conformal Prediction Using Privileged Information](https://mlsanity.com/paper/2406.05405/) (2024)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weighting](https://mlsanity.com/paper/2505.04733/) (2025)
- [Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approaches](https://mlsanity.com/paper/2506.01696/) (2025)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Risk-Sensitive Diffusion: Robustly Optimizing Diffusion Models with Noisy Samples](https://mlsanity.com/paper/2402.02081/) (2024)
- [Denoising ESG: quantifying data uncertainty from missing data with Machine Learning and prediction intervals](https://mlsanity.com/paper/2407.20047/) (2024)
- [A Kernel Nonconformity Score for Multivariate Conformal Prediction](https://mlsanity.com/paper/2604.21595/) (2026)
- [Learning from Uncertain Data: From Possible Worlds to Possible Models](https://mlsanity.com/paper/2405.18549/) (2024)
- [Learning from Complementary Features](https://mlsanity.com/paper/2408.14788/) (2024)
- [Online Conformal Anomaly Detection with Prediction-Powered Data Acquisition](https://mlsanity.com/paper/2505.01783/) (2025)
- [Weighted Conformal Prediction Provides Adaptive and Valid Mask-Conditional Coverage for General Missing Data Mechanisms](https://mlsanity.com/paper/2512.14221/) (2025)
- [Handling Covariate Mismatch in Collaborative Linear Prediction](https://mlsanity.com/paper/2602.02083/) (2026)
- [Robust Bayes-Assisted Conformal Prediction](https://mlsanity.com/paper/2607.04236/) (2026)
- [Conformal Fusion Under Missing Modalities](https://mlsanity.com/paper/2608.07183/) (2026)
- [Missingness-Aware Conformal Prediction Under Cross-Hospital Distribution Shift](https://mlsanity.com/paper/2609.30781/) (2026)
- [Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure](https://mlsanity.com/paper/2610.13588/) (2026)

## Abstract (arXiv)

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.