# Conformal Prediction with Partially Labeled Data

arXiv: https://arxiv.org/abs/2306.01191 · HTML: https://mlsanity.com/paper/2306.01191/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2110.12911/) (2021)
- [Structured Prediction with Partial Labelling through the Infimum Loss](https://mlsanity.com/paper/2003.00920/) (2020)
- [Disambiguation of weak supervision with exponential convergence rates](https://mlsanity.com/paper/2102.02789/) (2021)
- [Conservative Inference Rule for Uncertain Reasoning under Incompleteness](https://mlsanity.com/paper/1401.3471/) (2014)

## Built on by (most cited first, 5 of 5)

- [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)
- [Conformal Prediction Regions are Imprecise Highest Density Regions](https://mlsanity.com/paper/2502.06331/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Partial-Label Learning with Conformal Candidate Cleaning](https://mlsanity.com/paper/2502.07661/) (2025)

## Abstract (arXiv)

While the predictions produced by conformal prediction are set-valued, the data used for training and calibration is supposed to be precise. In the setting of superset learning or learning from partial labels, a variant of weakly supervised learning, it is exactly the other way around: training data is possibly imprecise (set-valued), but the model induced from this data yields precise predictions. In this paper, we combine the two settings by making conformal prediction amenable to set-valued training data. We propose a generalization of the conformal prediction procedure that can be applied to set-valued training and calibration data. We prove the validity of the proposed method and present experimental studies in which it compares favorably to natural baselines.