# Identifiability of Label Noise Transition Matrix

arXiv: https://arxiv.org/abs/2202.02016 · HTML: https://mlsanity.com/paper/2202.02016/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 70 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (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)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Learning with Instance-Dependent Label Noise: A Sample Sieve Approach](https://mlsanity.com/paper/2010.02347/) (2020)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Contrast to Divide: Self-Supervised Pre-Training for Learning with Noisy Labels](https://mlsanity.com/paper/2103.13646/) (2021)
- [Fair Classification with Group-Dependent Label Noise](https://mlsanity.com/paper/2011.00379/) (2020)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)
- [Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing](https://mlsanity.com/paper/1406.3824/) (2014)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)
- [Learning Noise Transition Matrix from Only Noisy Labels via Total Variation Regularization](https://mlsanity.com/paper/2102.02414/) (2021)
- [Learning with Bounded Instance- and Label-dependent Label Noise](https://mlsanity.com/paper/1709.03768/) (2017)
- [Deep k-NN for Noisy Labels](https://mlsanity.com/paper/2004.12289/) (2020)
- [Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels](https://mlsanity.com/paper/1705.01936/) (2017)
- [Instance-dependent Label-noise Learning under a Structural Causal Model](https://mlsanity.com/paper/2109.02986/) (2021)

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

- [Improving Data Efficiency via Curating LLM-Driven Rating Systems](https://mlsanity.com/paper/2410.10877/) (2024)
- [Unmasking and Improving Data Credibility: A Study with Datasets for Training Harmless Language Models](https://mlsanity.com/paper/2311.11202/) (2023)
- [Weak Proxies are Sufficient and Preferable for Fairness with Missing Sensitive Attributes](https://mlsanity.com/paper/2210.03175/) (2022)
- [InstanT: Semi-supervised Learning with Instance-dependent Thresholds](https://mlsanity.com/paper/2310.18910/) (2023)
- [Transferring Annotator- and Instance-dependent Transition Matrix for Learning from Crowds](https://mlsanity.com/paper/2306.03116/) (2023)
- [Regularly Truncated M-estimators for Learning with Noisy Labels](https://mlsanity.com/paper/2309.00894/) (2023)
- [Tackling Noisy Labels with Network Parameter Additive Decomposition](https://mlsanity.com/paper/2403.13241/) (2024)
- [Learning to Complement and to Defer to Multiple Users](https://mlsanity.com/paper/2407.07003/) (2024)
- [Learning to Complement with Multiple Humans](https://mlsanity.com/paper/2311.13172/) (2023)
- [Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation](https://mlsanity.com/paper/2305.19486/) (2023)
- [Dirichlet-based Per-Sample Weighting by Transition Matrix for Noisy Label Learning](https://mlsanity.com/paper/2403.02690/) (2024)
- [Improve Noise Tolerance of Robust Loss via Noise-Awareness](https://mlsanity.com/paper/2301.07306/) (2023)
- [Understanding and Mitigating Human-Labelling Errors in Supervised Contrastive Learning](https://mlsanity.com/paper/2403.06289/) (2024)
- [When Human Preferences Flip: An Instance-Dependent Robust Loss for RLHF](https://mlsanity.com/paper/2512.00709/) (2025)
- [LNL+K: Enhancing Learning with Noisy Labels Through Noise Source Knowledge Integration](https://mlsanity.com/paper/2306.11911/) (2023)
- [Elucidating and Overcoming the Challenges of Label Noise in Supervised Contrastive Learning](https://mlsanity.com/paper/2311.16481/) (2023)
- [Noise-Aware Generalization: Robustness to In-Domain Noise and Out-of-Domain Generalization](https://mlsanity.com/paper/2504.02996/) (2025)
- [Foundation Model Priors Enhance Object Focus in Feature Space for Source-Free Object Detection](https://mlsanity.com/paper/2512.17514/) (2025)
- [L2CU: Learning to Complement Unseen Users](https://mlsanity.com/paper/2601.06119/) (2026)
- [Towards the Identifiability in Noisy Label Learning: A Multinomial Mixture Modelling Approach](https://mlsanity.com/paper/2301.01405/) (2023)
- [Human-annotated label noise and their impact on ConvNets for remote sensing image scene classification](https://mlsanity.com/paper/2305.12106/) (2023)
- [Bridging Generative and Discriminative Noisy-Label Learning via Direction-Agnostic EM Formulation](https://mlsanity.com/paper/2308.01184/) (2023)
- [NoisyAG-News: A Benchmark for Addressing Instance-Dependent Noise in Text Classification](https://mlsanity.com/paper/2407.06579/) (2024)
- [Mislabeled examples detection viewed as probing machine learning models: concepts, survey and extensive benchmark](https://mlsanity.com/paper/2410.15772/) (2024)
- [Deconstructing the Failure of Ideal Noise Correction: A Three-Pillar Diagnosis](https://mlsanity.com/paper/2603.12997/) (2026)
- [MOLAR: Learning Multimodal Molecular Representations from Noisy Labels](https://mlsanity.com/paper/2606.18390/) (2026)
- [Multi-Label Noise Transition Matrix Estimation with Label Correlations: Theory and Algorithm](https://mlsanity.com/paper/2309.12706/) (2023)
- [Hypothesis Testing for Class-Conditional Noise Using Local Maximum Likelihood](https://mlsanity.com/paper/2312.10238/) (2023)
- [EchoAlign: Bridging Generative and Discriminative Learning under Noisy Labels](https://mlsanity.com/paper/2405.12969/) (2024)
- [The Majority Vote Paradigm Shift: When Popular Meets Optimal](https://mlsanity.com/paper/2502.12581/) (2025)

## Abstract (arXiv)

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on access to it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, the field lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result also reveals that disentangled features are helpful in the above identification task and we provide empirical evidence.