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arXiv · 2508.09894

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

Simon Klüttermann·Emmanuel Müller
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Abstract

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 $ \alpha_{\text{algo}} $. Our results demonstrate that, for an unlabeled dataset of size $ N $ and contamination rate $ \nu $, the condition $ N \ge \frac{\alpha_{\text{algo}}}{\nu^2} $ 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.

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Simon Klüttermann, Emmanuel Müller. 2025-08-13. Rare anomalies require large datasets: About proving the existence of anomalies. https://arxiv.org/abs/2508.09894

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