# Anomaly detection with semi-supervised classification based on risk estimators

arXiv: https://arxiv.org/abs/2309.00379 · HTML: https://mlsanity.com/paper/2309.00379/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 1 Sep 2023.

## Builds on (most cited first, 17 of 17)

- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [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)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [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)
- [MAD-GAN: Multivariate Anomaly Detection for Time Series Data with Generative Adversarial Networks](https://mlsanity.com/paper/1901.04997/) (2019)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Anomaly Detection using One-Class Neural Networks](https://mlsanity.com/paper/1802.06360/) (2018)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [One-Class Classification: Taxonomy of Study and Review of Techniques](https://mlsanity.com/paper/1312.0049/) (2013)
- [GODS: Generalized One-class Discriminative Subspaces for Anomaly Detection](https://mlsanity.com/paper/1908.05884/) (2019)
- [Latent Outlier Exposure for Anomaly Detection with Contaminated Data](https://mlsanity.com/paper/2202.08088/) (2022)
- [An overview of deep learning based methods for unsupervised and semi-supervised anomaly detection in videos](https://mlsanity.com/paper/1801.03149/) (2018)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Classification from Positive, Unlabeled and Biased Negative Data](https://mlsanity.com/paper/1810.00846/) (2018)

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

- [An Evidence-Based Post-Hoc Adjustment Framework for Anomaly Detection Under Data Contamination](https://mlsanity.com/paper/2510.21296/) (2025)
- [Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite](https://mlsanity.com/paper/2607.11947/) (2026)

## Abstract (arXiv)

A significant limitation of one-class classification anomaly detection methods is their reliance on the assumption that unlabeled training data only contains normal instances. To overcome this impractical assumption, we propose two novel classification-based anomaly detection methods. Firstly, we introduce a semi-supervised shallow anomaly detection method based on an unbiased risk estimator. Secondly, we present a semi-supervised deep anomaly detection method utilizing a nonnegative (biased) risk estimator. We establish estimation error bounds and excess risk bounds for both risk minimizers. Additionally, we propose techniques to select appropriate regularization parameters that ensure the nonnegativity of the empirical risk in the shallow model under specific loss functions. Our extensive experiments provide strong evidence of the effectiveness of the risk-based anomaly detection methods.