# Efficient Training for Positive Unlabeled Learning

arXiv: https://arxiv.org/abs/1608.06807 · HTML: https://mlsanity.com/paper/1608.06807/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2016.

## Built on by (most cited first, 10 of 10)

- [Learning from Similarity-Confidence Data](https://mlsanity.com/paper/2102.06879/) (2021)
- [Semi-Supervised Disease Classification based on Limited Medical Image Data](https://mlsanity.com/paper/2405.04295/) (2024)
- [Unified Risk Analysis for Weakly Supervised Learning](https://mlsanity.com/paper/2309.08216/) (2023)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)
- [Double logistic regression approach to biased positive-unlabeled data](https://mlsanity.com/paper/2209.07787/) (2022)
- [Learning from Positive and Unlabeled Data with Augmented Classes](https://mlsanity.com/paper/2207.13274/) (2022)
- [Efficient Training of One Class Classification-SVMs](https://mlsanity.com/paper/2309.16745/) (2023)
- [Detecting Scarce and Sparse Anomalous: Solving Dual Imbalance in Multi-Instance Learning](https://mlsanity.com/paper/2503.13562/) (2025)
- [Learning from M-Tuple Dominant Positive and Unlabeled Data](https://mlsanity.com/paper/2506.15686/) (2025)
- [CEDL: Centre-Enhanced Discriminative Learning for Anomaly Detection](https://mlsanity.com/paper/2511.12388/) (2025)

## Abstract (arXiv)

Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes. The learning task can be formulated as an optimization problem under the framework of statistical learning theory. Recent studies have theoretically analyzed its properties and generalization performance, nevertheless, little effort has been made to consider the problem of scalability, especially when large sets of unlabeled data are available. In this work we propose a novel scalable PU learning algorithm that is theoretically proven to provide the optimal solution, while showing superior computational and memory performance. Experimental evaluation confirms the theoretical evidence and shows that the proposed method can be successfully applied to a large variety of real-world problems involving PU learning.