  Noisy PN learning is the problem of binary classification when training
examples may be mislabeled (flipped) uniformly with noise rate rho1 for
positive examples and rho0 for negative examples. We propose Rank Pruning (RP)
to solve noisy PN learning and the open problem of estimating the noise rates,
i.e. the fraction of wrong positive and negative labels. Unlike prior
solutions, RP is time-efficient and general, requiring O(T) for any
unrestricted choice of probabilistic classifier with T fitting time. We prove
RP has consistent noise estimation and equivalent expected risk as learning
with uncorrupted labels in ideal conditions, and derive closed-form solutions
when conditions are non-ideal. RP achieves state-of-the-art noise estimation
and F1, error, and AUC-PR for both MNIST and CIFAR datasets, regardless of the
amount of noise and performs similarly impressively when a large portion of
training examples are noise drawn from a third distribution. To highlight, RP
with a CNN classifier can predict if an MNIST digit is a "one"or "not" with
only 0.25% error, and 0.46 error across all digits, even when 50% of positive
examples are mislabeled and 50% of observed positive labels are mislabeled
negative examples.
