Individual transition label noise logistic regression in binary classification for incorrectly-labeled data

We consider binary classification problem in the case where some observations in training data are incorrectly labeled. In presence of such label noise, conventional classification fails to obtain a classifier to be generalized to 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 Fisher consistency and enjoys robustness property. To accommodate various label noise mechanisms occurred in practice, we propose a flexible label noise model in a nonparametric way. An efficient algorithm is proposed under 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.