Multi-Label Noise Transition Matrix Estimation with Label Correlations:
  Theory and Algorithm
Shikun Li Xiaobo Xia Hansong Zhang Shiming Ge Tongliang Liu
Noisy multi-label learning has garnered increasing attention due to the
challenges posed by collecting large-scale accurate labels, making noisy labels
a more practical alternative. Motivated by noisy multi-class learning, the
introduction of transition matrices can help model multi-label noise and enable
the development of statistically consistent algorithms for noisy multi-label
learning. However, estimating multi-label noise transition matrices remains a
challenging task, as most existing estimators in noisy multi-class learning
rely on anchor points and accurate fitting of noisy class posteriors, which is
hard to satisfy in noisy multi-label learning. In this paper, we address this
problem by first investigating the identifiability of class-dependent
transition matrices in noisy multi-label learning. Building upon the
identifiability results, we propose a novel estimator that leverages label
correlations without the need for anchor points or precise fitting of noisy
class posteriors. Specifically, we first estimate the occurrence probability of
two noisy labels to capture noisy label correlations. Subsequently, we employ
sample selection techniques to extract information implying clean label
correlations, which are then used to estimate the occurrence probability of one
noisy label when a certain clean label appears. By exploiting the mismatches in
label correlations implied by these occurrence probabilities, we demonstrate
that the transition matrix becomes identifiable and can be acquired by solving
a bilinear decomposition problem. Theoretically, we establish an estimation
error bound for our multi-label transition matrix estimator and derive a
generalization error bound for our statistically consistent algorithm.
Empirically, we validate the effectiveness of our estimator in estimating
multi-label noise transition matrices, leading to excellent classification
performance.