# Learning Causal Transition Matrix for Instance-dependent Label Noise

arXiv: https://arxiv.org/abs/2412.13516 · HTML: https://mlsanity.com/paper/2412.13516/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 50 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (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)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [Does label smoothing mitigate label noise?](https://mlsanity.com/paper/2003.02819/) (2020)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Learning to Learn from Noisy Labeled Data](https://mlsanity.com/paper/1812.05214/) (2018)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [Debiased Learning from Naturally Imbalanced Pseudo-Labels](https://mlsanity.com/paper/2201.01490/) (2022)
- [Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks](https://mlsanity.com/paper/1706.00038/) (2017)
- [A Topological Filter for Learning with Label Noise](https://mlsanity.com/paper/2012.04835/) (2020)
- [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)
- [Classification with Rejection Based on Cost-sensitive Classification](https://mlsanity.com/paper/2010.11748/) (2020)
- [Instance-dependent Label-noise Learning under a Structural Causal Model](https://mlsanity.com/paper/2109.02986/) (2021)
- [ProMix: Combating Label Noise via Maximizing Clean Sample Utility](https://mlsanity.com/paper/2207.10276/) (2022)

## Built on by (most cited first, 3 of 3)

- [Mitigating Instance Entanglement in Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2603.04825/) (2026)
- [GAMR: Geometric-Aware Manifold Regularization with Virtual Outlier Synthesis for Learning with Noisy Labels](https://mlsanity.com/paper/2605.20727/) (2026)
- [SLT: Robust Quantum Neural Networks for Noisy-Label Medical Image Classification via Supermartingale-based Label Transition](https://mlsanity.com/paper/2607.16293/) (2026)

## Abstract (arXiv)

Noisy labels are both inevitable and problematic in machine learning methods, as they negatively impact models' generalization ability by causing overfitting. In the context of learning with noise, the transition matrix plays a crucial role in the design of statistically consistent algorithms. However, the transition matrix is often considered unidentifiable. One strand of methods typically addresses this problem by assuming that the transition matrix is instance-independent; that is, the probability of mislabeling a particular instance is not influenced by its characteristics or attributes. This assumption is clearly invalid in complex real-world scenarios. To better understand the transition relationship and relax this assumption, we propose to study the data generation process of noisy labels from a causal perspective. We discover that an unobservable latent variable can affect either the instance itself, the label annotation procedure, or both, which complicates the identification of the transition matrix. To address various scenarios, we have unified these observations within a new causal graph. In this graph, the input instance is divided into a noise-resistant component and a noise-sensitive component based on whether they are affected by the latent variable. These two components contribute to identifying the ``causal transition matrix'', which approximates the true transition matrix with theoretical guarantee. In line with this, we have designed a novel training framework that explicitly models this causal relationship and, as a result, achieves a more accurate model for inferring the clean label.