Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning

Abstract

The transition matrix, denoting the transition relationship from clean labels to noisy labels, is essential to build statistically consistent classifiers in label-noise learning. Existing methods for estimating the transition matrix rely heavily on estimating the noisy class posterior. However, the estimation error for noisy class posterior could be large due to the randomness of label noise. The estimation error would lead the transition matrix to be poorly estimated. Therefore, in this paper, we aim to solve this problem by exploiting the divide-and-conquer paradigm. Specifically, we introduce an intermediate class to avoid directly estimating the noisy class posterior. By this intermediate class, the original transition matrix can then be factorized into the product of two easy-to-estimate transition matrices. We term the proposed method the dual T -estimator. Both theoretical analyses and empirical results illustrate the effectiveness of the dual T -estimator for estimating transition matrices, leading to better classification performances.

Do We Need to Penalize Variance of Losses for Learning with Label Noise?

“…T-Revision [44] proposes a method to ne-tune the estimated transition matrix to improve the classi cation performance; 6). Dual T [49] improves the estimation of the transition matrix by introducing an intermediate class, and then factorizes the transition matrix into the product of two easy-to-estimate transition matrices; 7). VolMinNet [25] is an end-to-end label-noise learning method, which can learn the transition matrix and the classi er simultaneously; 8).…”

“…However, the estimated transition matrix could contain a large estimation error. One reason is that the transition matrix can be hard to accurately estimate when sample size is limited [49]. Another reason is that the assumptions [33,25] used to identify the transition matrix may not be held.…”

Contrast to Divide: Self-Supervised Pre-Training for Learning with Noisy Labels

“…Existing methods for LNL can be divided into two broad categories: loss modification and noise detection. The former group includes techniques that account for noise distribution [41,53,60]. Alternatively, the loss itself may be replaced by a more robust version, such as mean absolute error [12], generalized cross-entropy [68 mutual information [58], or a meta-learning objective [28].…”

Identifiability of Label Noise Transition Matrix

“…The literature has provided discussions of the identifiability of T under the mixture proportion estimation setup (Scott, 2015), and has identified a reducibility condition for inferring the inverse noise rate. Later works have developed a sequence of solutions to estimate T under a variety of assumptions, including irreducibility (Scott, 2015), anchor points (Liu & Tao, 2016;Xia et al, 2019;Yao et al, 2020a), separability (Cheng et al, 2020b), rankability (Northcutt et al, 2017;2021), redundant labels (Liu et al, 2020), clusterability (Zhu et al, 2021c), among others (Zhang et al, 2021;Li et al, 2021).…”