ROPU: A robust online positive-unlabeled learning algorithm

Positive-unlabeled (PU) learning aims to train classifiers using positive and unlabeled samples. Most methods assume a selected completely at random labeling scenario, which may not reflect real-world PU learning conditions. Our investigation across multiple peptide spectrum match datasets reveals a nonuniform distribution of labeled positive samples, concentrated in specific subsets. To address this, we propose a “missing in a subset area” labeling assumption and analyze resulting model biases. Furthermore, we introduce nonconvex loss functions and develop a robust online positive-unlabeled (ROPU)classification algorithm using gradient descent. Theoretically, ROPU achieves sublinear nonstationary regret bounds under mild conditions. Experimental results demonstrate the effectiveness of ROPU across various simulated and practical PU learning datasets. The source code is available at https://github.com/Isaac-QiXing/ROPU.