In label-noise learning, estimating the transition matrix plays an important role in building statistically consistent classifier.

In label-noise learning, the \textit{noise transition matrix}, denoting the probabilities that clean labels flip into noisy labels, plays a central role in building \textit{statistically consistent classifiers}. Existing theories have shown that the transition matrix can be learned by exploiting \textit{anchor points} (i.e., data points that belong to a specific class almost surely). However, when there are no anchor points, the transition matrix will be poorly learned, and those previously consistent classifiers will significantly degenerate. In this paper, without employing anchor points, we propose a \textit{transition-revision} ($T$-Revision) method to effectively learn transition matrices, leading to better classifiers. Specifically, to learn a transition matrix, we first initialize it by exploiting data points that are similar to anchor points, having high \textit{noisy class posterior probabilities}. Then, we modify the initialized matrix by adding a \textit{slack variable}, which can be learned and validated together with the classifier by using noisy data. Empirical results on benchmark-simulated and real-world label-noise datasets demonstrate that without using exact anchor points, the proposed method is superior to state-of-the-art label-noise learning methods.

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 because of 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-estimated transition matrices. We term the proposed method as 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.

Specifically, we estimate the occurrence probability of two noisy labels to get noisy label correlations.

In label-noise learning, estimating the transition matrix plays an important role in building statistically consistent classifier.

Weaknesses: 1) The justification and explanation of equation 3 (which is a central point of the paper) is not clear. Here's how I interpret the approach proposed by the authors based on Algorithm 1. The elements of the Dual T-estimator transition matrix are computed as follows: \hat{T}_{ij} \sum_l \hat{P}(\bar{Y} j Y' l) \hat{P}(Y' l Y_i) The second element in the sum is obtained using equation 1, which is the same equation used to compute the T-estimator of the transition matrix. The first element in the sum is estimated using equation 4 which determines the number of examples belonging to the noisy class j which were incorrectly labeled as belonging to the noisy class l divided by the number of examples labeled as belonging to the noisy class l. This ratio is basically used to revise / correct the T-estimator of the transition matrix (and hence mitigate the effect of overfitting the noise in the training set).

In label-noise learning, the noise transition matrix, bridging the class posterior for noisy and clean data, has been widely exploited to learn statistically consistent classifiers. The effectiveness of these algorithms relies heavily on estimating the transition matrix. Recently, the problem of label-noise learning in multi-label classification has received increasing attention, and these consistent algorithms can be applied in multi-label cases. However, the estimation of transition matrices in noisy multi-label learning has not been studied and remains challenging, since most of the existing estimators in noisy multi-class learning depend on the existence of anchor points and the accurate fitting of noisy class posterior. To address this problem, in this paper, we first study the identifiability problem of the class-dependent transition matrix in noisy multi-label learning, and then inspired by the identifiability results, we propose a new estimator by exploiting label correlations without neither anchor points nor accurate fitting of noisy class posterior.

Noisy labels are both inevitable and problematic in machine learning methods, as they negatively impact models' generalization ability by causing overfitting. In the context of learning with noise, the transition matrix plays a crucial role in the design of statistically consistent algorithms. However, the transition matrix is often considered unidentifiable. One strand of methods typically addresses this problem by assuming that the transition matrix is instance-independent; that is, the probability of mislabeling a particular instance is not influenced by its characteristics or attributes. This assumption is clearly invalid in complex real-world scenarios. To better understand the transition relationship and relax this assumption, we propose to study the data generation process of noisy labels from a causal perspective. We discover that an unobservable latent variable can affect either the instance itself, the label annotation procedure, or both, which complicates the identification of the transition matrix. To address various scenarios, we have unified these observations within a new causal graph. In this graph, the input instance is divided into a noise-resistant component and a noise-sensitive component based on whether they are affected by the latent variable. These two components contribute to identifying the ``causal transition matrix'', which approximates the true transition matrix with theoretical guarantee. In line with this, we have designed a novel training framework that explicitly models this causal relationship and, as a result, achieves a more accurate model for inferring the clean label.