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. Unlike prior solutions, RP is efficient and general, requiring O(T) for any unrestricted choice of probabilistic classifier with T fitting time. We prove RP achieves consistent noise estimation and equivalent empirical 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 rate estimation and F1, error, and AUC-PR on the MNIST and CIFAR datasets, regardless of noise rates. To highlight, RP with a CNN classifier can predict if a MNIST digit is a "1" or "not 1" 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.
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