# Structured Prediction with Partial Labelling through the Infimum Loss

arXiv: https://arxiv.org/abs/2003.00920 · HTML: https://mlsanity.com/paper/2003.00920/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2020.

## Built on by (most cited first, 30 of 34)

- [Leveraged Weighted Loss for Partial Label Learning](https://mlsanity.com/paper/2106.05731/) (2021)
- [Efficient Algorithms for Learning from Coarse Labels](https://mlsanity.com/paper/2108.09805/) (2021)
- [On the Robustness of Average Losses for Partial-Label Learning](https://mlsanity.com/paper/2106.06152/) (2021)
- [Credal Self-Supervised Learning](https://mlsanity.com/paper/2106.11853/) (2021)
- [Learning from Multiple Noisy Partial Labelers](https://mlsanity.com/paper/2106.04530/) (2021)
- [Differentiable Clustering with Perturbed Spanning Forests](https://mlsanity.com/paper/2305.16358/) (2023)
- [Predictive Inference with Weak Supervision](https://mlsanity.com/paper/2201.08315/) (2022)
- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [Fast rates in structured prediction](https://mlsanity.com/paper/2102.00760/) (2021)
- [Active Learning for Semantic Segmentation with Multi-class Label Query](https://mlsanity.com/paper/2309.09319/) (2023)
- [Resolving label uncertainty with implicit posterior models](https://mlsanity.com/paper/2202.14000/) (2022)
- [Conformal Credal Self-Supervised Learning](https://mlsanity.com/paper/2205.15239/) (2022)
- [Online Structured Prediction with Fenchel--Young Losses and Improved Surrogate Regret for Online Multiclass Classification with Logistic Loss](https://mlsanity.com/paper/2402.08180/) (2024)
- [Conformal Prediction with Partially Labeled Data](https://mlsanity.com/paper/2306.01191/) (2023)
- [Disambiguation of weak supervision with exponential convergence rates](https://mlsanity.com/paper/2102.02789/) (2021)
- [Active Labeling: Streaming Stochastic Gradients](https://mlsanity.com/paper/2205.13255/) (2022)
- [On Regularization and Inference with Label Constraints](https://mlsanity.com/paper/2307.03886/) (2023)
- [Partial-Label Learning with a Reject Option](https://mlsanity.com/paper/2402.00592/) (2024)
- [Handling Long-Tail Queries with Slice-Aware Conversational Systems](https://mlsanity.com/paper/2104.13216/) (2021)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)
- [Tuning the Right Foundation Models is What you Need for Partial Label Learning](https://mlsanity.com/paper/2506.05027/) (2025)
- [A Convex Loss Function for Set Prediction with Optimal Trade-offs Between Size and Conditional Coverage](https://mlsanity.com/paper/2512.19142/) (2025)
- [Lower-Bounded Proper Losses for Weakly Supervised Classification](https://mlsanity.com/paper/2103.02893/) (2021)
- [DistrictNet: Decision-aware learning for geographical districting](https://mlsanity.com/paper/2412.08287/) (2024)
- [Robust Partial-Label Learning by Leveraging Class Activation Values](https://mlsanity.com/paper/2502.11743/) (2025)
- [On Improving Neurosymbolic Learning by Exploiting the Representation Space](https://mlsanity.com/paper/2602.07973/) (2026)
- [From Weakly Supervised Learning to Active Learning](https://mlsanity.com/paper/2209.11629/) (2022)
- [In all LikelihoodS: How to Reliably Select Pseudo-Labeled Data for Self-Training in Semi-Supervised Learning](https://mlsanity.com/paper/2303.01117/) (2023)
- [Augmented prediction of a true class for Positive Unlabeled data under selection bias](https://mlsanity.com/paper/2407.10309/) (2024)
- [Neuro-symbolic Weak Supervision: Theory and Semantics](https://mlsanity.com/paper/2503.18509/) (2025)

## Abstract (arXiv)

Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial labelling. This is a type of incomplete annotation where, for each datapoint, supervision is cast as a set of labels containing the real one. The problem of supervised learning with partial labelling has been studied for specific instances such as classification, multi-label, ranking or segmentation, but a general framework is still missing. This paper provides a unified framework based on structured prediction and on the concept of infimum loss to deal with partial labelling over a wide family of learning problems and loss functions. The framework leads naturally to explicit algorithms that can be easily implemented and for which proved statistical consistency and learning rates. Experiments confirm the superiority of the proposed approach over commonly used baselines.