# Towards the Identifiability in Noisy Label Learning: A Multinomial Mixture Modelling Approach

arXiv: https://arxiv.org/abs/2301.01405 · HTML: https://mlsanity.com/paper/2301.01405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 73 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [Learning with Feature-Dependent Label Noise: A Progressive Approach](https://mlsanity.com/paper/2103.07756/) (2021)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Multi-Objective Interpolation Training for Robustness to Label Noise](https://mlsanity.com/paper/2012.04462/) (2020)
- [FINE Samples for Learning with Noisy Labels](https://mlsanity.com/paper/2102.11628/) (2021)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)

## Built on by (most cited first, 1 of 1)

- [Neural Bayesian Anomaly Mitigation: A Robust Loss that Doubles as an Unsupervised Contamination Classifier](https://mlsanity.com/paper/2606.16524/) (2026)

## Abstract (arXiv)

Learning from noisy labels (LNL) is crucial in deep learning, in which one of the approaches is to identify clean-label samples from poorly-annotated datasets. Such an identification is challenging because the conventional LNL problem, which assumes only one noisy label per instance, is non-identifiable, i.e., clean labels cannot be estimated theoretically without additional heuristics. This paper presents a novel data-driven approach that addresses this issue without requiring any heuristics about clean samples. We discover that the LNL problem becomes identifiable if there are at least 2C - 1 i.i.d. noisy labels per instance, where C is the number of classes. Our finding relies on the assumption of i.i.d. noisy labels and multinomial mixture modelling, making it easier to interpret than previous studies that require full-rank noisy-label transition matrices. To fulfil this condition without additional manual annotations, we propose a method that automatically generates additional i.i.d. noisy labels through nearest neighbours. These noisy labels are then used in the Expectation-Maximisation algorithm to infer clean labels. Our method demonstrably estimates clean labels accurately across various label noise benchmarks, including synthetic, web-controlled, and real-world datasets. Furthermore, the model trained with our method performs competitively with many state-of-the-art methods.