  Learning with noisy labels, which aims to reduce expensive labors on accurate
annotations, has become imperative in the Big Data era. Previous noise
transition based method has achieved promising results and presented a
theoretical guarantee on performance in the case of class-conditional noise.
However, this type of approaches critically depend on an accurate
pre-estimation of the noise transition, which is usually impractical.
Subsequent improvement adapts the pre-estimation along with the training
progress via a Softmax layer. However, the parameters in the Softmax layer are
highly tweaked for the fragile performance due to the ill-posed stochastic
approximation. To address these issues, we propose a Latent Class-Conditional
Noise model (LCCN) that naturally embeds the noise transition under a Bayesian
framework. By projecting the noise transition into a Dirichlet-distributed
space, the learning is constrained on a simplex based on the whole dataset,
instead of some ad-hoc parametric space. We then deduce a dynamic label
regression method for LCCN to iteratively infer the latent labels, to
stochastically train the classifier and to model the noise. Our approach
safeguards the bounded update of the noise transition, which avoids previous
arbitrarily tuning via a batch of samples. We further generalize LCCN for
open-set noisy labels and the semi-supervised setting. We perform extensive
experiments with the controllable noise data sets, CIFAR-10 and CIFAR-100, and
the agnostic noise data sets, Clothing1M and WebVision17. The experimental
results have demonstrated that the proposed model outperforms several
state-of-the-art methods.
