# Classification from Positive, Unlabeled and Biased Negative Data

arXiv: https://arxiv.org/abs/1810.00846 · HTML: https://mlsanity.com/paper/1810.00846/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2018.

## Built on by (most cited first, 30 of 34)

- ["This is my unicorn, Fluffy": Personalizing frozen vision-language representations](https://mlsanity.com/paper/2204.01694/) (2022)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Positive-Unlabeled Reward Learning](https://mlsanity.com/paper/1911.00459/) (2019)
- [Distantly Supervised Named Entity Recognition via Confidence-Based Multi-Class Positive and Unlabeled Learning](https://mlsanity.com/paper/2204.09589/) (2022)
- [Decoupling the Class Label and the Target Concept in Machine Unlearning](https://mlsanity.com/paper/2406.08288/) (2024)
- [Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trends](https://mlsanity.com/paper/2310.04078/) (2023)
- [Harmfully Manipulated Images Matter in Multimodal Misinformation Detection](https://mlsanity.com/paper/2407.19192/) (2024)
- [Is Gradient Ascent Really Necessary? Memorize to Forget for Machine Unlearning](https://mlsanity.com/paper/2602.06441/) (2026)
- [PAUSE: Positive and Annealed Unlabeled Sentence Embedding](https://mlsanity.com/paper/2109.03155/) (2021)
- [Robust Positive-Unlabeled Learning via Noise Negative Sample Self-correction](https://mlsanity.com/paper/2308.00279/) (2023)
- [Dens-PU: PU Learning with Density-Based Positive Labeled Augmentation](https://mlsanity.com/paper/2303.11848/) (2023)
- [Positive-Unlabeled Node Classification with Structure-aware Graph Learning](https://mlsanity.com/paper/2310.13538/) (2023)
- [Uncertainty-aware Pseudo-label Selection for Positive-Unlabeled Learning](https://mlsanity.com/paper/2201.13192/) (2022)
- [Positive-Unlabeled Domain Adaptation](https://mlsanity.com/paper/2202.05695/) (2022)
- [Split-PU: Hardness-aware Training Strategy for Positive-Unlabeled Learning](https://mlsanity.com/paper/2211.16756/) (2022)
- [Anomaly detection with semi-supervised classification based on risk estimators](https://mlsanity.com/paper/2309.00379/) (2023)
- [Meta-learning for Positive-unlabeled Classification](https://mlsanity.com/paper/2406.03680/) (2024)
- [Forming Auxiliary High-confident Instance-level Loss to Promote Learning from Label Proportions](https://mlsanity.com/paper/2411.10364/) (2024)
- [A Novel Perspective for Positive-Unlabeled Learning via Noisy Labels](https://mlsanity.com/paper/2103.04685/) (2021)
- [A Semi-supervised Multi-task Learning Approach to Classify Customer Contact Intents](https://mlsanity.com/paper/2106.07381/) (2021)
- [A Positive/Unlabeled Approach for the Segmentation of Medical Sequences using Point-Wise Supervision](https://mlsanity.com/paper/2107.08394/) (2021)
- [Automatic Debiased Learning from Positive, Unlabeled, and Exposure Data](https://mlsanity.com/paper/2303.04797/) (2023)
- [Few Dimensions are Enough: Fine-tuning BERT with Selected Dimensions Revealed Its Redundant Nature](https://mlsanity.com/paper/2504.04966/) (2025)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [Classification from Positive and Biased Negative Data with Skewed Labeled Posterior Probability](https://mlsanity.com/paper/2203.05749/) (2022)
- [A Boosting Algorithm for Positive-Unlabeled Learning](https://mlsanity.com/paper/2205.09485/) (2022)
- [Robust and Efficient Imbalanced Positive-Unlabeled Learning with Self-supervision](https://mlsanity.com/paper/2209.02459/) (2022)
- [Leveraging Structure for Improved Classification of Grouped Biased Data](https://mlsanity.com/paper/2212.03697/) (2022)
- [Detecting Scarce and Sparse Anomalous: Solving Dual Imbalance in Multi-Instance Learning](https://mlsanity.com/paper/2503.13562/) (2025)

## Abstract (arXiv)

In binary classification, there are situations where negative (N) data are too diverse to be fully labeled and we often resort to positive-unlabeled (PU) learning in these scenarios. However, collecting a non-representative N set that contains only a small portion of all possible N data can often be much easier in practice. This paper studies a novel classification framework which incorporates such biased N (bN) data in PU learning. We provide a method based on empirical risk minimization to address this PUbN classification problem. Our approach can be regarded as a novel example-weighting algorithm, with the weight of each example computed through a preliminary step that draws inspiration from PU learning. We also derive an estimation error bound for the proposed method. Experimental results demonstrate the effectiveness of our algorithm in not only PUbN learning scenarios but also ordinary PU learning scenarios on several benchmark datasets.