Individual Transition Label Noise Logistic Regression in Binary Classification for Incorrectly Labeled Data

We consider a binary classification problem in the case where some observations in the training data are incorrectly labeled. In the presence of such label noise, conventional classification fails to obtain a classifier to be generalized to a population. In this work, we investigate label noise logistic regression and explain how it works with noisy training data. We demonstrate that, when label transition probabilities are correctly provided, label noise logistic regression satisfies the Fisher consistency and enjoys the property of robustness. To accommodate various label noise mechanisms that occur in practice, we propose a flexible label noise model in a nonparametric way. We propose an efficient algorithm under the thresholding rule for individual parameter estimation. We demonstrate its performance under synthetic and real examples. We discuss the proposed flexible transition model is also useful for robust classification.