# Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Data

arXiv: https://arxiv.org/abs/2405.18929 · HTML: https://mlsanity.com/paper/2405.18929/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 81 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [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)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Catching Both Gray and Black Swans: Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2203.14506/) (2022)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Deep Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/1910.13601/) (2019)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)
- [Deep Learning in Bioinformatics](https://mlsanity.com/paper/1603.06430/) (2016)
- [Latent Outlier Exposure for Anomaly Detection with Contaminated Data](https://mlsanity.com/paper/2202.08088/) (2022)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Toward Deep Supervised Anomaly Detection: Reinforcement Learning from Partially Labeled Anomaly Data](https://mlsanity.com/paper/2009.06847/) (2020)
- [Feature Encoding with AutoEncoders for Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/2105.10500/) (2021)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)

## Built on by (most cited first, 2 of 2)

- [Positive-Unlabeled Diffusion Models for Preventing Sensitive Data Generation](https://mlsanity.com/paper/2503.03789/) (2025)
- [From Local Geometry to Global Pseudo Labeling for Robust Positive Unlabeled Learning under Covariate Shift](https://mlsanity.com/paper/2605.31187/) (2026)

## Abstract (arXiv)

Semi-supervised anomaly detection, which aims to improve the anomaly detection performance by using a small amount of labeled anomaly data in addition to unlabeled data, has attracted attention. Existing semi-supervised approaches assume that most unlabeled data are normal, and train anomaly detectors by minimizing the anomaly scores for the unlabeled data while maximizing those for the labeled anomaly data. However, in practice, the unlabeled data are often contaminated with anomalies. This weakens the effect of maximizing the anomaly scores for anomalies, and prevents us from improving the detection performance. To solve this, we propose the deep positive-unlabeled anomaly detection framework, which integrates positive-unlabeled learning with deep anomaly detection models such as autoencoders and deep support vector data descriptions. Our approach enables the approximation of anomaly scores for normal data using the unlabeled data and the labeled anomaly data. Therefore, without labeled normal data, our approach can train anomaly detectors by minimizing the anomaly scores for normal data while maximizing those for the labeled anomaly data. We also provide a theoretical analysis establishing a generalization error bound for the proposed objective, guaranteeing that the empirical minimizer converges asymptotically to the ideal minimizer. Our approach achieves better detection performance than existing approaches on various datasets.