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.
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