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Noisy PN learning is the problem of binary classification when trainingexamples may be mislabeled (flipped) uniformly with noise rate rho1 forpositive 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 priorsolutions, RP is time-efficient and general, requiring O(T) for anyunrestricted choice of probabilistic classifier with T fitting time. We proveRP has consistent noise estimation and equivalent expected risk as learningwith uncorrupted labels in ideal conditions, and derive closed-form solutionswhen conditions are non-ideal. RP achieves state-of-the-art noise estimationand F1, error, and AUC-PR for both MNIST and CIFAR datasets, regardless of theamount of noise and performs similarly impressively when a large portion oftraining examples are noise drawn from a third distribution. To highlight, RPwith a CNN classifier can predict if an MNIST digit is a "one"or "not" withonly 0.25% error, and 0.46 error across all digits, even when 50% of positiveexamples are mislabeled and 50% of observed positive labels are mislabelednegative examples.

Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels