Learning with Bounded Instance- and Label-dependent Label Noise

Instance- and label-dependent label noise (ILN) is widely existed in real-world datasets but has been rarely studied. In this paper, we focus on a particular case of ILN where the label noise rates, representing the probabilities that the true labels of examples flip into the corrupted labels, have upper bounds. We propose to handle this bounded instance- and label-dependent label noise under two different conditions. First, theoretically, we prove that when the marginal distributions $P(X|Y=+1)$ and $P(X|Y=-1)$ have non-overlapping supports, we can recover every noisy example's true label and perform supervised learning directly on the cleansed examples. Second, for the overlapping situation, we propose a novel approach to learn a well-performing classifier which needs only a few noisy examples to be labeled manually. Experimental results demonstrate that our method works well on both synthetic and real-world datasets.