# A Second-Order Approach to Learning with Instance-Dependent Label Noise

arXiv: https://arxiv.org/abs/2012.11854 · HTML: https://mlsanity.com/paper/2012.11854/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2020.

## Built on by (most cited first, 30 of 90)

- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Open-Vocabulary Instance Segmentation via Robust Cross-Modal Pseudo-Labeling](https://mlsanity.com/paper/2111.12698/) (2021)
- [To Smooth or Not? When Label Smoothing Meets Noisy Labels](https://mlsanity.com/paper/2106.04149/) (2021)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)
- [Detecting Corrupted Labels Without Training a Model to Predict](https://mlsanity.com/paper/2110.06283/) (2021)
- [Instance-dependent Label-noise Learning under a Structural Causal Model](https://mlsanity.com/paper/2109.02986/) (2021)
- [Instance-Dependent Label-Noise Learning with Manifold-Regularized Transition Matrix Estimation](https://mlsanity.com/paper/2206.02791/) (2022)
- [ProMix: Combating Label Noise via Maximizing Clean Sample Utility](https://mlsanity.com/paper/2207.10276/) (2022)
- [When Source-Free Domain Adaptation Meets Learning with Noisy Labels](https://mlsanity.com/paper/2301.13381/) (2023)
- [Mitigating Memorization of Noisy Labels by Clipping the Model Prediction](https://mlsanity.com/paper/2212.04055/) (2022)
- [Token Cleaning: Fine-Grained Data Selection for LLM Supervised Fine-Tuning](https://mlsanity.com/paper/2502.01968/) (2025)
- [Identifiability of Label Noise Transition Matrix](https://mlsanity.com/paper/2202.02016/) (2022)
- [Estimating Instance-dependent Bayes-label Transition Matrix using a Deep Neural Network](https://mlsanity.com/paper/2105.13001/) (2021)
- [To Aggregate or Not? Learning with Separate Noisy Labels](https://mlsanity.com/paper/2206.07181/) (2022)
- [The Rich Get Richer: Disparate Impact of Semi-Supervised Learning](https://mlsanity.com/paper/2110.06282/) (2021)
- [Beyond Images: Label Noise Transition Matrix Estimation for Tasks with Lower-Quality Features](https://mlsanity.com/paper/2202.01273/) (2022)
- [Mitigating Memorization of Noisy Labels via Regularization between Representations](https://mlsanity.com/paper/2110.09022/) (2021)
- [Unmasking and Improving Data Credibility: A Study with Datasets for Training Harmless Language Models](https://mlsanity.com/paper/2311.11202/) (2023)
- [Open-Sampling: Exploring Out-of-Distribution data for Re-balancing Long-tailed datasets](https://mlsanity.com/paper/2206.08802/) (2022)
- [Understanding Instance-Level Label Noise: Disparate Impacts and Treatments](https://mlsanity.com/paper/2102.05336/) (2021)
- [Learning on Graphs under Label Noise](https://mlsanity.com/paper/2306.08194/) (2023)
- [Adaptive Sample Selection for Robust Learning under Label Noise](https://mlsanity.com/paper/2106.15292/) (2021)
- [Learning with Noisy Labels by Efficient Transition Matrix Estimation to Combat Label Miscorrection](https://mlsanity.com/paper/2111.14932/) (2021)
- [RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies](https://mlsanity.com/paper/2402.02032/) (2024)
- [SimT: Handling Open-set Noise for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2203.15202/) (2022)
- [Instance-Dependent Noisy Label Learning via Graphical Modelling](https://mlsanity.com/paper/2209.00906/) (2022)
- [Weak Proxies are Sufficient and Preferable for Fairness with Missing Sensitive Attributes](https://mlsanity.com/paper/2210.03175/) (2022)
- [Centrality and Consistency: Two-Stage Clean Samples Identification for Learning with Instance-Dependent Noisy Labels](https://mlsanity.com/paper/2207.14476/) (2022)
- [Distributionally Robust Post-hoc Classifiers under Prior Shifts](https://mlsanity.com/paper/2309.08825/) (2023)

## Abstract (arXiv)

The presence of label noise often misleads the training of deep neural networks. Departing from the recent literature which largely assumes the label noise rate is only determined by the true label class, the errors in human-annotated labels are more likely to be dependent on the difficulty levels of tasks, resulting in settings with instance-dependent label noise. We first provide evidences that the heterogeneous instance-dependent label noise is effectively down-weighting the examples with higher noise rates in a non-uniform way and thus causes imbalances, rendering the strategy of directly applying methods for class-dependent label noise questionable. Built on a recent work peer loss [24], we then propose and study the potentials of a second-order approach that leverages the estimation of several covariance terms defined between the instance-dependent noise rates and the Bayes optimal label. We show that this set of second-order statistics successfully captures the induced imbalances. We further proceed to show that with the help of the estimated second-order statistics, we identify a new loss function whose expected risk of a classifier under instance-dependent label noise is equivalent to a new problem with only class-dependent label noise. This fact allows us to apply existing solutions to handle this better-studied setting. We provide an efficient procedure to estimate these second-order statistics without accessing either ground truth labels or prior knowledge of the noise rates. Experiments on CIFAR10 and CIFAR100 with synthetic instance-dependent label noise and Clothing1M with real-world human label noise verify our approach. Our implementation is available at https://github.com/UCSC-REAL/CAL.