# Learning from Label Proportions by Learning with Label Noise

arXiv: https://arxiv.org/abs/2203.02496 · HTML: https://mlsanity.com/paper/2203.02496/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [On Learning from Label Proportions](https://mlsanity.com/paper/1402.5902/) (2014)
- [Learning from Label Proportions with Consistency Regularization](https://mlsanity.com/paper/1910.13188/) (2019)
- [Deep multi-class learning from label proportions](https://mlsanity.com/paper/1905.12909/) (2019)
- [Co-training for Demographic Classification Using Deep Learning from Label Proportions](https://mlsanity.com/paper/1709.04108/) (2017)
- [Learning from Label Proportions with Generative Adversarial Networks](https://mlsanity.com/paper/1909.02180/) (2019)
- [Weakly Supervised Classification in High Energy Physics](https://mlsanity.com/paper/1702.00414/) (2017)
- [Two-stage Training for Learning from Label Proportions](https://mlsanity.com/paper/2105.10635/) (2021)
- [Deep Learning from Label Proportions for Emphysema Quantification](https://mlsanity.com/paper/1807.08601/) (2018)
- [Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classification](https://mlsanity.com/paper/2102.00678/) (2021)
- [Label Propagation for Learning with Label Proportions](https://mlsanity.com/paper/1810.10328/) (2018)

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

- [Easy Learning from Label Proportions](https://mlsanity.com/paper/2302.03115/) (2023)
- [Enhanced H-Consistency Bounds](https://mlsanity.com/paper/2407.13722/) (2024)
- [In-Context Example Ordering Guided by Label Distributions](https://mlsanity.com/paper/2402.11447/) (2024)
- [Unsupervised Learning under Latent Label Shift](https://mlsanity.com/paper/2207.13179/) (2022)
- [Label Noise: Ignorance Is Bliss](https://mlsanity.com/paper/2411.00079/) (2024)
- [Evaluating AI systems under uncertain ground truth: a case study in dermatology](https://mlsanity.com/paper/2307.02191/) (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)
- [LLP-Bench: A Large Scale Tabular Benchmark for Learning from Label Proportions](https://mlsanity.com/paper/2310.10096/) (2023)
- [Optimistic Rates for Learning from Label Proportions](https://mlsanity.com/paper/2406.00487/) (2024)
- [Nearly Optimal Sample Complexity for Learning with Label Proportions](https://mlsanity.com/paper/2505.05355/) (2025)
- [A Practical Theory of Generalization in Selectivity Learning](https://mlsanity.com/paper/2409.07014/) (2024)
- [Meta-Statistical Learning: Supervised Learning of Statistical Estimators](https://mlsanity.com/paper/2502.12088/) (2025)
- [Learning from Label Proportions with Instance-wise Consistency](https://mlsanity.com/paper/2203.12836/) (2022)
- [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)
- [Weakly-Supervised Domain Adaptation with Proportion-Constrained Pseudo-Labeling](https://mlsanity.com/paper/2506.22301/) (2025)
- [Kernel Density Matrices for Probabilistic Deep Learning](https://mlsanity.com/paper/2305.18204/) (2023)
- [Label Differential Privacy via Aggregation](https://mlsanity.com/paper/2310.10092/) (2023)
- [Optimal Learning from Label Proportions with General Loss Functions](https://mlsanity.com/paper/2509.15145/) (2025)
- [FRACTAL: Fine-Grained Scoring from Aggregate Text Labels](https://mlsanity.com/paper/2404.04817/) (2024)
- [Class-aware and Augmentation-free Contrastive Learning from Label Proportion](https://mlsanity.com/paper/2408.06743/) (2024)
- [Weak to Strong Learning from Aggregate Labels](https://mlsanity.com/paper/2411.06200/) (2024)
- [Learning from Label Proportions and Covariate-shifted Instances](https://mlsanity.com/paper/2411.12334/) (2024)
- [Neuro-symbolic Weak Supervision: Theory and Semantics](https://mlsanity.com/paper/2503.18509/) (2025)
- [Towards Privacy-Preserving Fine-Grained Visual Classification via Hierarchical Learning from Label Proportions](https://mlsanity.com/paper/2505.23031/) (2025)
- [Statistical Learning from Attribution Sets](https://mlsanity.com/paper/2602.06276/) (2026)
- [FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning](https://mlsanity.com/paper/2603.00517/) (2026)
- [Learning from Label Proportions with Dual-proportion Constraints](https://mlsanity.com/paper/2603.21153/) (2026)

## Abstract (arXiv)

Learning from label proportions (LLP) is a weakly supervised classification problem where data points are grouped into bags, and the label proportions within each bag are observed instead of the instance-level labels. The task is to learn a classifier to predict the individual labels of future individual instances. Prior work on LLP for multi-class data has yet to develop a theoretically grounded algorithm. In this work, we provide a theoretically grounded approach to LLP based on a reduction to learning with label noise, using the forward correction (FC) loss of citetPatrini2017MakingDN. We establish an excess risk bound and generalization error analysis for our approach, while also extending the theory of the FC loss which may be of independent interest. Our approach demonstrates improved empirical performance in deep learning scenarios across multiple datasets and architectures, compared to the leading existing methods.