  Modeling noise transition matrix is a kind of promising method for learning
with label noise. Based on the estimated noise transition matrix and the noisy
posterior probabilities, the clean posterior probabilities, which are jointly
called Label Distribution (LD) in this paper, can be calculated as the
supervision. To reliably estimate the noise transition matrix, some methods
assume that anchor points are available during training. Nonetheless, if anchor
points are invalid, the noise transition matrix might be poorly learned,
resulting in poor performance. Consequently, other methods treat reliable data
points, extracted from training data, as pseudo anchor points. However, from a
statistical point of view, the noise transition matrix can be inferred from
data with noisy labels under the clean-label-domination assumption. Therefore,
we aim to estimate the noise transition matrix without (pseudo) anchor points.
There is evidence showing that samples are more likely to be mislabeled as
other similar class labels, which means the mislabeling probability is highly
correlated with the inter-class correlation. Inspired by this observation, we
propose an instance-specific Label Distribution Regularization (LDR), in which
the instance-specific LD is estimated as the supervision, to prevent DCNNs from
memorizing noisy labels. Specifically, we estimate the noisy posterior under
the supervision of noisy labels, and approximate the batch-level noise
transition matrix by estimating the inter-class correlation matrix with neither
anchor points nor pseudo anchor points. Experimental results on two synthetic
noisy datasets and two real-world noisy datasets demonstrate that our LDR
outperforms existing methods.
