  Many weakly supervised classification methods employ a noise transition
matrix to capture the class-conditional label corruption. To estimate the
transition matrix from noisy data, existing methods often need to estimate the
noisy class-posterior, which could be unreliable due to the overconfidence of
neural networks. In this work, we propose a theoretically grounded method that
can estimate the noise transition matrix and learn a classifier simultaneously,
without relying on the error-prone noisy class-posterior estimation.
Concretely, inspired by the characteristics of the stochastic label corruption
process, we propose total variation regularization, which encourages the
predicted probabilities to be more distinguishable from each other. Under mild
assumptions, the proposed method yields a consistent estimator of the
transition matrix. We show the effectiveness of the proposed method through
experiments on benchmark and real-world datasets.
