# Robust Learning under Hybrid Noise

arXiv: https://arxiv.org/abs/2407.04029 · HTML: https://mlsanity.com/paper/2407.04029/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 4 Jul 2024.

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

- [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)
- [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)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [PU Learning for Matrix Completion](https://mlsanity.com/paper/1411.6081/) (2014)
- [Beyond Images: Label Noise Transition Matrix Estimation for Tasks with Lower-Quality Features](https://mlsanity.com/paper/2202.01273/) (2022)
- [Loss factorization, weakly supervised learning and label noise robustness](https://mlsanity.com/paper/1602.02450/) (2016)
- [Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes](https://mlsanity.com/paper/1405.1207/) (2014)
- [Labeling Chaos to Learning Harmony: Federated Learning with Noisy Labels](https://mlsanity.com/paper/2208.09378/) (2022)
- [Learning to Rectify for Robust Learning with Noisy Labels](https://mlsanity.com/paper/2111.04239/) (2021)
- [Dynamics-Aware Loss for Learning with Label Noise](https://mlsanity.com/paper/2303.11562/) (2023)
- [Beyond Pretrained Features: Noisy Image Modeling Provides Adversarial Defense](https://mlsanity.com/paper/2302.01056/) (2023)
- [Learning with Inadequate and Incorrect Supervision](https://mlsanity.com/paper/1902.07429/) (2019)

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

- [QuAIL: Quality-Aware Inertial Learning for Robust Training under Data Corruption](https://mlsanity.com/paper/2602.03686/) (2026)

## Abstract (arXiv)

Feature noise and label noise are ubiquitous in practical scenarios, which pose great challenges for training a robust machine learning model. Most previous approaches usually deal with only a single problem of either feature noise or label noise. However, in real-world applications, hybrid noise, which contains both feature noise and label noise, is very common due to the unreliable data collection and annotation processes. Although some results have been achieved by a few representation learning based attempts, this issue is still far from being addressed with promising performance and guaranteed theoretical analyses. To address the challenge, we propose a novel unified learning framework called "Feature and Label Recovery" (FLR) to combat the hybrid noise from the perspective of data recovery, where we concurrently reconstruct both the feature matrix and the label matrix of input data. Specifically, the clean feature matrix is discovered by the low-rank approximation, and the ground-truth label matrix is embedded based on the recovered features with a nuclear norm regularization. Meanwhile, the feature noise and label noise are characterized by their respective adaptive matrix norms to satisfy the corresponding maximum likelihood. As this framework leads to a non-convex optimization problem, we develop the non-convex Alternating Direction Method of Multipliers (ADMM) with the convergence guarantee to solve our learning objective. We also provide the theoretical analysis to show that the generalization error of FLR can be upper-bounded in the presence of hybrid noise. Experimental results on several typical benchmark datasets clearly demonstrate the superiority of our proposed method over the state-of-the-art robust learning approaches for various noises.