  Suppose we have a sample of instances paired with binary labels corrupted by
arbitrary instance- and label-dependent noise. With sufficiently many such
samples, can we optimally classify and rank instances with respect to the
noise-free distribution? We provide a theoretical analysis of this question,
with three main contributions. First, we prove that for instance-dependent
noise, any algorithm that is consistent for classification on the noisy
distribution is also consistent on the clean distribution. Second, we prove
that for a broad class of instance- and label-dependent noise, a similar
consistency result holds for the area under the ROC curve. Third, for the
latter noise model, when the noise-free class-probability function belongs to
the generalised linear model family, we show that the Isotron can efficiently
and provably learn from the corrupted sample.
