# On Learning from Label Proportions

arXiv: https://arxiv.org/abs/1402.5902 · HTML: https://mlsanity.com/paper/1402.5902/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2014.

## Built on by (most cited first, 30 of 38)

- [Learning from Label Proportions by Learning with Label Noise](https://mlsanity.com/paper/2203.02496/) (2022)
- [Federated Learning from Only Unlabeled Data with Class-Conditional-Sharing Clients](https://mlsanity.com/paper/2204.03304/) (2022)
- [Easy Learning from Label Proportions](https://mlsanity.com/paper/2302.03115/) (2023)
- [Two-stage Training for Learning from Label Proportions](https://mlsanity.com/paper/2105.10635/) (2021)
- [Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classification](https://mlsanity.com/paper/2102.00678/) (2021)
- [In-Context Example Ordering Guided by Label Distributions](https://mlsanity.com/paper/2402.11447/) (2024)
- [Learning from Aggregated Data: Curated Bags versus Random Bags](https://mlsanity.com/paper/2305.09557/) (2023)
- [Challenges and approaches to privacy preserving post-click conversion prediction](https://mlsanity.com/paper/2201.12666/) (2022)
- [PAC Learning Linear Thresholds from Label Proportions](https://mlsanity.com/paper/2310.10098/) (2023)
- [A Unified Approach to Count-Based Weakly-Supervised Learning](https://mlsanity.com/paper/2311.13718/) (2023)
- [Learning from Label Proportions: Bootstrapping Supervised Learners via Belief Propagation](https://mlsanity.com/paper/2310.08056/) (2023)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Multi-class Classification from Multiple Unlabeled Datasets with Partial Risk Regularization](https://mlsanity.com/paper/2207.01555/) (2022)
- [Fast learning from label proportions with small bags](https://mlsanity.com/paper/2110.03426/) (2021)
- [Learning crop type mapping from regional label proportions in large-scale SAR and optical imagery](https://mlsanity.com/paper/2208.11607/) (2022)
- [A Universal Unbiased Method for Classification from Aggregate Observations](https://mlsanity.com/paper/2306.11343/) (2023)
- [Local Differential Privacy in Graph Neural Networks: a Reconstruction Approach](https://mlsanity.com/paper/2309.08569/) (2023)
- [Optimistic Rates for Learning from Label Proportions](https://mlsanity.com/paper/2406.00487/) (2024)
- [Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervision](https://mlsanity.com/paper/2306.07036/) (2023)
- [The Tensor Data Platform: Towards an AI-centric Database System](https://mlsanity.com/paper/2211.02753/) (2022)
- [Learning from Label Proportions with Instance-wise Consistency](https://mlsanity.com/paper/2203.12836/) (2022)
- [Learning from Aggregate responses: Instance Level versus Bag Level Loss Functions](https://mlsanity.com/paper/2401.11081/) (2024)
- [PriorBoost: An Adaptive Algorithm for Learning from Aggregate Responses](https://mlsanity.com/paper/2402.04987/) (2024)
- [Theoretical Proportion Label Perturbation for Learning from Label Proportions in Large Bags](https://mlsanity.com/paper/2408.14130/) (2024)
- [Forming Auxiliary High-confident Instance-level Loss to Promote Learning from Label Proportions](https://mlsanity.com/paper/2411.10364/) (2024)
- [Semantic Segmentation by Semantic Proportions](https://mlsanity.com/paper/2305.15608/) (2023)
- [Label Differential Privacy via Aggregation](https://mlsanity.com/paper/2310.10092/) (2023)
- [AUC Optimization from Multiple Unlabeled Datasets](https://mlsanity.com/paper/2305.15776/) (2023)
- [Evaluating LLP Methods: Challenges and Approaches](https://mlsanity.com/paper/2310.19065/) (2023)
- [Hardness of Learning Boolean Functions from Label Proportions](https://mlsanity.com/paper/2403.19401/) (2024)

## Abstract (arXiv)

Learning from Label Proportions (LLP) is a learning setting, where the training data is provided in groups, or "bags", and only the proportion of each class in each bag is known. The task is to learn a model to predict the class labels of the individual instances. LLP has broad applications in political science, marketing, healthcare, and computer vision. This work answers the fundamental question, when and why LLP is possible, by introducing a general framework, Empirical Proportion Risk Minimization (EPRM). EPRM learns an instance label classifier to match the given label proportions on the training data. Our result is based on a two-step analysis. First, we provide a VC bound on the generalization error of the bag proportions. We show that the bag sample complexity is only mildly sensitive to the bag size. Second, we show that under some mild assumptions, good bag proportion prediction guarantees good instance label prediction. The results together provide a formal guarantee that the individual labels can indeed be learned in the LLP setting. We discuss applications of the analysis, including justification of LLP algorithms, learning with population proportions, and a paradigm for learning algorithms with privacy guarantees. We also demonstrate the feasibility of LLP based on a case study in real-world setting: predicting income based on census data.