PURIST: PU Refinement via Iterative Soft-Label Training

Positive–unlabeled (PU) learning trains classifiers from trusted positives and mixed unlabeled examples. Existing methods compensate for missing negatives through different assumptions, but their effectiveness varies across data types and labeling conditions. We investigate which design principles transfer across heterogeneous PU problems. PURIST builds on two structural properties: under selected completely at random (SCAR) labeling, population-optimal P–U binary cross-entropy preserves optimal ranking at any fixed sampling ratio; label noise is confined to unlabeled examples. It combines balanced P:U optimization with Self-Adaptive EMA soft labels (SAEM), balancing training on trusted positives and noisy unlabeled examples while refining only unlabeled targets. Factorial ablations reveal a significant positive interaction between balancing and target refinement. Training dynamics further show that balancing improves target quality early, providing a more reliable starting point for subsequent temporal refinement. The method uses one model without a supplied class prior or data augmentation. Under selected at random (SAR) labeling, we analyze ranking preservation, AUC-regret bounds under anti-monotone selection, and non-identifiability under zero-correlation selection. Across 21 SCAR datasets from six source-data types, PURIST achieves an average AUC of 0.919 and the best average rank of 5.0 among 25 methods; it also ranks best on average under three proxy-defined SAR constructions on 14 datasets.