# PSPU: Enhanced Positive and Unlabeled Learning by Leveraging Pseudo Supervision

arXiv: https://arxiv.org/abs/2407.06698 · HTML: https://mlsanity.com/paper/2407.06698/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 16 of 16)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Semi-Supervised AUC Optimization based on Positive-Unlabeled Learning](https://mlsanity.com/paper/1705.01708/) (2017)
- [Instance-Dependent PU Learning by Bayesian Optimal Relabeling](https://mlsanity.com/paper/1808.02180/) (2018)
- [Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trends](https://mlsanity.com/paper/2310.04078/) (2023)
- [A Robust Ensemble Approach to Learn From Positive and Unlabeled Data Using SVM Base Models](https://mlsanity.com/paper/1402.3144/) (2014)
- [Split-PU: Hardness-aware Training Strategy for Positive-Unlabeled Learning](https://mlsanity.com/paper/2211.16756/) (2022)

## Built on by (most cited first, 3 of 3)

- [Dual-Interrelated Diffusion Model for Few-Shot Anomaly Image Generation](https://mlsanity.com/paper/2408.13509/) (2024)
- [Real-IAD D3: A Real-World 2D/Pseudo-3D/3D Dataset for Industrial Anomaly Detection](https://mlsanity.com/paper/2504.14221/) (2025)
- [Robust Self-Training with Closed-loop Label Correction for Learning from Noisy Labels](https://mlsanity.com/paper/2603.13894/) (2026)

## Abstract (arXiv)

Positive and Unlabeled (PU) learning, a binary classification model trained with only positive and unlabeled data, generally suffers from overfitted risk estimation due to inconsistent data distributions. To address this, we introduce a pseudo-supervised PU learning framework (PSPU), in which we train the PU model first, use it to gather confident samples for the pseudo supervision, and then apply these supervision to correct the PU model's weights by leveraging non-PU objectives. We also incorporate an additional consistency loss to mitigate noisy sample effects. Our PSPU outperforms recent PU learning methods significantly on MNIST, CIFAR-10, CIFAR-100 in both balanced and imbalanced settings, and enjoys competitive performance on MVTecAD for industrial anomaly detection.