# Rare anomalies require large datasets: About proving the existence of anomalies

arXiv: https://arxiv.org/abs/2508.09894 · HTML: https://mlsanity.com/paper/2508.09894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Self-Supervised Anomaly Detection in Computer Vision and Beyond: A Survey and Outlook](https://mlsanity.com/paper/2205.05173/) (2022)
- [Autoencoding Binary Classifiers for Supervised Anomaly Detection](https://mlsanity.com/paper/1903.10709/) (2019)
- [Online-compatible Unsupervised Non-resonant Anomaly Detection](https://mlsanity.com/paper/2111.06417/) (2021)
- [Periodicity Detection of Outlier Sequences Using Constraint Based Pattern Tree with MAD](https://mlsanity.com/paper/1507.01685/) (2015)
- [Locally Interpretable One-Class Anomaly Detection for Credit Card Fraud Detection](https://mlsanity.com/paper/2108.02501/) (2021)
- [Deep Transductive Outlier Detection](https://mlsanity.com/paper/2404.03495/) (2024)

## Abstract (arXiv)

Detecting whether any anomalies exist within a dataset is crucial for effective anomaly detection, yet it remains surprisingly underexplored in anomaly detection literature. This paper presents a comprehensive study that addresses the fundamental question: When can we conclusively determine that anomalies are present? Through extensive experimentation involving over three million statistical tests across various anomaly detection tasks and algorithms, we identify a relationship between the dataset size, contamination rate, and an algorithm-dependent constant  αalgo . Our results demonstrate that, for an unlabeled dataset of size  N  and contamination rate  nu , the condition  N ≥ fracαalgonu2  represents a lower bound on the number of samples required to confirm anomaly existence. This threshold implies a limit to how rare anomalies can be before proving their existence becomes infeasible.