# Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weighting

arXiv: https://arxiv.org/abs/2505.04733 · HTML: https://mlsanity.com/paper/2505.04733/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 59 references that are in the map.
- First posted on arXiv 7 May 2025.

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluation](https://mlsanity.com/paper/2106.03907/) (2021)
- [Achieving Risk Control in Online Learning Settings](https://mlsanity.com/paper/2205.09095/) (2022)
- [Conformal prediction under ambiguous ground truth](https://mlsanity.com/paper/2307.09302/) (2023)
- [Conformal Prediction with Missing Values](https://mlsanity.com/paper/2306.02732/) (2023)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [Conformalized survival analysis with adaptive cutoffs](https://mlsanity.com/paper/2211.01227/) (2022)
- [Toward Understanding Privileged Features Distillation in Learning-to-Rank](https://mlsanity.com/paper/2209.08754/) (2022)
- [Robust Yet Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2407.09165/) (2024)
- [Transfer and Marginalize: Explaining Away Label Noise with Privileged Information](https://mlsanity.com/paper/2202.09244/) (2022)
- [Group-Weighted Conformal Prediction](https://mlsanity.com/paper/2401.17452/) (2024)
- [A Conformal Prediction Score that is Robust to Label Noise](https://mlsanity.com/paper/2405.02648/) (2024)
- [Assessing Treatment Effect Variation in Observational Studies: Results from a Data Challenge](https://mlsanity.com/paper/1907.07592/) (2019)
- [Robust Conformal Outlier Detection under Contaminated Reference Data](https://mlsanity.com/paper/2502.04807/) (2025)
- [When does Privileged Information Explain Away Label Noise?](https://mlsanity.com/paper/2303.01806/) (2023)
- [RFCDE: Random Forests for Conditional Density Estimation](https://mlsanity.com/paper/1804.05753/) (2018)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)

## Built on by (most cited first, 3 of 3)

- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Online Conformal Prediction with Corrupted Feedback](https://mlsanity.com/paper/2605.20515/) (2026)

## Abstract (arXiv)

We introduce a framework for robust uncertainty quantification in situations where labeled training data are corrupted, through noisy or missing labels. We build on conformal prediction, a statistical tool for generating prediction sets that cover the test label with a pre-specified probability. The validity of conformal prediction, however, holds under the i.i.d assumption, which does not hold in our setting due to the corruptions in the data. To account for this distribution shift, the privileged conformal prediction (PCP) method proposed leveraging privileged information (PI) -- additional features available only during training -- to re-weight the data distribution, yielding valid prediction sets under the assumption that the weights are accurate. In this work, we analyze the robustness of PCP to inaccuracies in the weights. Our analysis indicates that PCP can still yield valid uncertainty estimates even when the weights are poorly estimated. Furthermore, we introduce uncertain imputation (UI), a new conformal method that does not rely on weight estimation. Instead, we impute corrupted labels in a way that preserves their uncertainty. Our approach is supported by theoretical guarantees and validated empirically on both synthetic and real benchmarks. Finally, we show that these techniques can be integrated into a triply robust framework, ensuring statistically valid predictions as long as at least one underlying method is valid.