# Partial-Label Regression

arXiv: https://arxiv.org/abs/2306.08968 · HTML: https://mlsanity.com/paper/2306.08968/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Leveraged Weighted Loss for Partial Label Learning](https://mlsanity.com/paper/2106.05731/) (2021)
- [Complementary-Label Learning for Arbitrary Losses and Models](https://mlsanity.com/paper/1810.04327/) (2018)
- [Partial Label Learning with Self-Guided Retraining](https://mlsanity.com/paper/1902.03045/) (2019)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Learning from Ambiguously Labeled Face Images](https://mlsanity.com/paper/1702.04455/) (2017)
- [A Regularization Approach for Instance-Based Superset Label Learning](https://mlsanity.com/paper/1904.02832/) (2019)

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

- [Robust Representation Learning for Unreliable Partial Label Learning](https://mlsanity.com/paper/2308.16718/) (2023)
- [Learning from Interval Targets](https://mlsanity.com/paper/2510.20925/) (2025)
- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)

## Abstract (arXiv)

Partial-label learning is a popular weakly supervised learning setting that allows each training example to be annotated with a set of candidate labels. Previous studies on partial-label learning only focused on the classification setting where candidate labels are all discrete, which cannot handle continuous labels with real values. In this paper, we provide the first attempt to investigate partial-label regression, where each training example is annotated with a set of real-valued candidate labels. To solve this problem, we first propose a simple baseline method that takes the average loss incurred by candidate labels as the predictive loss. The drawback of this method lies in that the loss incurred by the true label may be overwhelmed by other false labels. To overcome this drawback, we propose an identification method that takes the least loss incurred by candidate labels as the predictive loss. We further improve it by proposing a progressive identification method to differentiate candidate labels using progressively updated weights for incurred losses. We prove that the latter two methods are model-consistent and provide convergence analyses. Our proposed methods are theoretically grounded and can be compatible with any models, optimizers, and losses. Experiments validate the effectiveness of our proposed methods.