Estimating Noise Transition Matrix with Label Correlations for Noisy Multi-Label Learning

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.