# Making Risk Minimization Tolerant to Label Noise

arXiv: https://arxiv.org/abs/1403.3610 · HTML: https://mlsanity.com/paper/1403.3610/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2014.

## Built on by (most cited first, 30 of 54)

- [Learning with Feature-Dependent Label Noise: A Progressive Approach](https://mlsanity.com/paper/2103.07756/) (2021)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [PolyLoss: A Polynomial Expansion Perspective of Classification Loss Functions](https://mlsanity.com/paper/2204.12511/) (2022)
- [Asymmetric Loss Functions for Learning with Noisy Labels](https://mlsanity.com/paper/2106.03110/) (2021)
- [Robust Contrastive Learning against Noisy Views](https://mlsanity.com/paper/2201.04309/) (2022)
- [Contrastive Learning Improves Model Robustness Under Label Noise](https://mlsanity.com/paper/2104.08984/) (2021)
- [Joint Negative and Positive Learning for Noisy Labels](https://mlsanity.com/paper/2104.06574/) (2021)
- [Benchmarking and Analyzing 3D Human Pose and Shape Estimation Beyond Algorithms](https://mlsanity.com/paper/2209.10529/) (2022)
- [On the Robustness of Average Losses for Partial-Label Learning](https://mlsanity.com/paper/2106.06152/) (2021)
- [Debiasing Multimodal Large Language Models via Noise-Aware Preference Optimization](https://mlsanity.com/paper/2503.17928/) (2025)
- [SSR: An Efficient and Robust Framework for Learning with Unknown Label Noise](https://mlsanity.com/paper/2111.11288/) (2021)
- [Stable-DiffCoder: Pushing the Frontier of Code Diffusion Large Language Model](https://mlsanity.com/paper/2601.15892/) (2026)
- [Boosting Facial Expression Recognition by A Semi-Supervised Progressive Teacher](https://mlsanity.com/paper/2205.14361/) (2022)
- [Robustness and Reliability When Training With Noisy Labels](https://mlsanity.com/paper/2110.03321/) (2021)
- [Label Noise: Ignorance Is Bliss](https://mlsanity.com/paper/2411.00079/) (2024)
- [Weak Adaptation Learning -- Addressing Cross-domain Data Insufficiency with Weak Annotator](https://mlsanity.com/paper/2102.07358/) (2021)
- [LLM-Powered Preference Elicitation in Combinatorial Assignment](https://mlsanity.com/paper/2502.10308/) (2025)
- [Self-paced Resistance Learning against Overfitting on Noisy Labels](https://mlsanity.com/paper/2105.03059/) (2021)
- [Your contrastive learning problem is secretly a distribution alignment problem](https://mlsanity.com/paper/2502.20141/) (2025)
- [Unbiased Loss Functions for Multilabel Classification with Missing Labels](https://mlsanity.com/paper/2109.11282/) (2021)
- [SelectMix: Enhancing Label Noise Robustness through Targeted Sample Mixing](https://mlsanity.com/paper/2509.11265/) (2025)
- [Learning to Combat Noisy Labels via Classification Margins](https://mlsanity.com/paper/2102.00751/) (2021)
- [Multiplicative Reweighting for Robust Neural Network Optimization](https://mlsanity.com/paper/2102.12192/) (2021)
- [Binary classification with corrupted labels](https://mlsanity.com/paper/2106.09136/) (2021)
- [Learning with Noisy Labels through Learnable Weighting and Centroid Similarity](https://mlsanity.com/paper/2303.09470/) (2023)
- [Cross-Video Contextual Knowledge Exploration and Exploitation for Ambiguity Reduction in Weakly Supervised Temporal Action Localization](https://mlsanity.com/paper/2308.12609/) (2023)
- [Do We Really Need Gold Samples for Sample Weighting Under Label Noise?](https://mlsanity.com/paper/2104.09045/) (2021)
- [Asymmetric error control under imperfect supervision: a label-noise-adjusted Neyman-Pearson umbrella algorithm](https://mlsanity.com/paper/2112.00314/) (2021)
- [Multi-class Label Noise Learning via Loss Decomposition and Centroid Estimation](https://mlsanity.com/paper/2203.10858/) (2022)
- [Improve Noise Tolerance of Robust Loss via Noise-Awareness](https://mlsanity.com/paper/2301.07306/) (2023)

## Abstract (arXiv)

In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the 0-1 loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the 0-1 loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm.