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This paper introduces the PUe framework, which enhances Positive-Unlabeled (PU) learning by addressing selection bias in label distributions through normalized propensity scores and normalized inverse probability weighting (NIPW). By reformulating the PU risk and providing theoretical analyses, PUe integrates with existing cost-sensitive methods and supports selectively labeled negative classes. Experiments on datasets like MNIST and CIFAR-10 show that PUe significantly outperforms traditional PU baselines, particularly in scenarios with non-uniform label distributions.
Selection bias in Positive-Unlabeled learning can be mitigated, leading to significant performance gains in real-world classification tasks.
Positive-Unlabeled (PU) learning aims to achieve high-accuracy binary classification with limited labeled positive examples and numerous unlabeled ones. Existing cost-sensitive-based methods often rely on strong assumptions that examples with an observed positive label were selected entirely at random. In fact, the uneven distribution of labels is prevalent in real-world PU problems, indicating that most actual positive and unlabeled data are subject to selection bias. Building on the SAR-PU propensity-weighted framework of Bekker et al., we study a PU learning enhancement (PUe) framework using normalized propensity scores and normalized inverse probability weighting (NIPW). PUe's main contributions are a normalized inverse-probability-weighted PU risk formulation; additional theoretical analyses of normalized sample-weight error and common PU estimators under biased labeling; regularized deep propensity-score estimation; integration with modern cost-sensitive PU methods; and support for selectively labeled negative classes. Experiments on MNIST, CIFAR-10, and ADNI demonstrate improvements over several PU baselines under non-uniform label distributions.
