# Extended T: Learning with Mixed Closed-set and Open-set Noisy Labels

arXiv: https://arxiv.org/abs/2012.00932 · HTML: https://mlsanity.com/paper/2012.00932/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [To Smooth or Not? When Label Smoothing Meets Noisy Labels](https://mlsanity.com/paper/2106.04149/) (2021)
- [Open-set Label Noise Can Improve Robustness Against Inherent Label Noise](https://mlsanity.com/paper/2106.10891/) (2021)
- [SimT: Handling Open-set Noise for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2203.15202/) (2022)
- [Centrality and Consistency: Two-Stage Clean Samples Identification for Learning with Instance-Dependent Noisy Labels](https://mlsanity.com/paper/2207.14476/) (2022)
- [Tackling Instance-Dependent Label Noise with Dynamic Distribution Calibration](https://mlsanity.com/paper/2210.05126/) (2022)

## Abstract (arXiv)

The label noise transition matrix T, reflecting the probabilities that true labels flip into noisy ones, is of vital importance to model label noise and design statistically consistent classifiers. The traditional transition matrix is limited to model closed-set label noise, where noisy training data has true class labels within the noisy label set. It is unfitted to employ such a transition matrix to model open-set label noise, where some true class labels are outside the noisy label set. Thus when considering a more realistic situation, i.e., both closed-set and open-set label noise occurs, existing methods will undesirably give biased solutions. Besides, the traditional transition matrix is limited to model instance-independent label noise, which may not perform well in practice. In this paper, we focus on learning under the mixed closed-set and open-set label noise. We address the aforementioned issues by extending the traditional transition matrix to be able to model mixed label noise, and further to the cluster-dependent transition matrix to better approximate the instance-dependent label noise in real-world applications. We term the proposed transition matrix as the cluster-dependent extended transition matrix. An unbiased estimator (i.e., extended T-estimator) has been designed to estimate the cluster-dependent extended transition matrix by only exploiting the noisy data. Comprehensive synthetic and real experiments validate that our method can better model the mixed label noise, following its more robust performance than the prior state-of-the-art label-noise learning methods.