Confidence-Based PU Learning With Instance-Dependent Label Noise

Positive and unlabeled (PU) learning, which trains binary classifiers using only PU data, has gained vast attentions in recent years. Traditional PU learning often assumes that all the positive samples are labeled accurately. Nevertheless, due to the reasons such as sample ambiguity and insufficient algorithms, label noise is almost unavoidable in this scenario. Current PU algorithms neglect the label noise issue in the positive set, which is often biased toward certain instances rather than being uniformly distributed in practical applications. We define this important but understudied problem as PU learning with instance-dependent label noise (PUIDN). To eliminate the adverse impact of IDN, we leverage confidence scores for each instance in the positive set, which establish the connection between samples and labels without any assumption on noise distribution. Then, we propose an unbiased estimator for classification risk considering both label and confidence information, which can be computed immediately from PUIDN data along with their confidence scores. Moreover, our classification framework integrates an optimization strategy of alternating iteration based on the correlation between different confidence information, thereby alleviating the additional requirement for training data. Theoretically, we derive a generalization error bound for our proposed method. Experimentally, the effectiveness of our approach is demonstrated through various types of numerical results.