  In label-noise learning, the transition matrix plays a key role in building
statistically consistent classifiers. Existing consistent estimators for the
transition matrix have been developed by exploiting anchor points. However, the
anchor-point assumption is not always satisfied in real scenarios. In this
paper, we propose an end-to-end framework for solving label-noise learning
without anchor points, in which we simultaneously minimize two objectives: the
discrepancy between the distribution learned by the neural network and the
noisy class-posterior distribution, and the volume of the simplex formed by the
columns of the transition matrix. Our proposed framework can identify the
transition matrix if the clean class-posterior probabilities are sufficiently
scattered. This is by far the mildest assumption under which the transition
matrix is provably identifiable and the learned classifier is statistically
consistent. Experimental results on benchmark datasets demonstrate the
effectiveness and robustness of the proposed method.
