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New Framework Improves Biased Positive-Unlabeled Learning with Causal Inference.

Xutao Wang, Hanting Chen, Tianyu Guo, Yunhe Wang· July 16, 2026 View original

Key takeaways

  • Real-world PU learning often suffers from selection bias due to non-random label distributions.
  • The PUe framework uses causal inference and normalized weighting to correct for this bias.
  • It improves classification accuracy, especially with uneven label distributions and limited positive examples.
  • The framework offers theoretical grounding and practical integration with existing PU methods.

Who benefits

HealthcareFinanceE-commerceCybersecurityManufacturing

Summary

This paper introduces PUe, a framework enhancing Positive-Unlabeled (PU) learning by addressing selection bias in real-world datasets. It uses normalized propensity scores and inverse probability weighting to improve binary classification accuracy with limited positive labels.

Positive-Unlabeled (PU) learning is a machine learning technique used for binary classification when only a small number of positive examples are labeled, alongside a large pool of unlabeled data. A common challenge in these scenarios is selection bias, where the observed positive labels are not randomly distributed, leading to skewed datasets. Researchers have developed a new framework, PUe, which aims to mitigate this bias. Building on existing propensity-weighted methods, PUe incorporates normalized propensity scores and normalized inverse probability weighting to create a more robust risk formulation. The framework also includes theoretical analyses of sample-weight error under biased labeling, regularized deep propensity-score estimation, and integration with current cost-sensitive PU methods. Experimental results on standard datasets like MNIST and CIFAR-10 show that PUe significantly improves performance compared to baseline PU methods when dealing with non-uniform label distributions.

Why it matters

Professionals dealing with imbalanced datasets or limited labeled data can leverage this framework to build more accurate and reliable classification models, especially in domains where labeling is costly or difficult.

How to implement this in your domain

  1. 1Evaluate existing PU learning pipelines for potential selection bias in data labeling.
  2. 2Integrate propensity score estimation techniques to quantify and correct for bias in unlabeled data.
  3. 3Apply normalized inverse probability weighting within your PU learning objective function.
  4. 4Test the PUe framework's effectiveness on your specific datasets, comparing it against current baselines.
  5. 5Consider using deep learning for propensity score estimation to handle complex data distributions.

Original post by Xutao Wang, Hanting Chen, Tianyu Guo, Yunhe Wang

"arXiv:2607.13428v1 Announce Type: new 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 exa…"

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Originally posted by Xutao Wang, Hanting Chen, Tianyu Guo, Yunhe Wang on X · view source

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