PUe: Biased Positive-Unlabeled Learning Enhancement by Causal Inference

2026-07-15

AI Summary

This work addresses selection bias in positive-unlabeled (PU) learning caused by non-random labeling mechanisms by proposing PUe, a causal inference–based framework. PUe introduces normalized propensity scores and normalized inverse probability weighting (NIPW) to refine PU risk estimation, integrating regularized deep learning with cost-sensitive strategies to effectively handle biased annotations under non-uniform label distributions and enable the utilization of selectively labeled negative samples. Theoretical analysis elucidates how errors in sample weights propagate into estimation bias. Experimental results demonstrate that PUe significantly outperforms existing PU methods on MNIST, CIFAR-10, and ADNI datasets, with particularly pronounced gains under strong selection bias scenarios.

Abstract

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.

Problem

• Positive-Unlabeled learning
• selection bias
• label distribution
• biased labeling
• PU learning

Innovation

• Positive-Unlabeled Learning
• Selection Bias
• Causal Inference
• Normalized Inverse Probability Weighting
• Propensity Score