Provable Hierarchical Martingale-based Testing for Visual Anomaly Detection

Existing visual anomaly detection approaches primarily focus on designing robust score functions but often neglect investigating the decision-making process, which plays a key role in reliable and safety-critical applications. Currently, the decision-making process suffers from two key challenges: distribution shift and theoretical guarantee. To address these issues, this paper proposes a novel approach called Hierarchical Martingale-based Testing framework (HiMT). Specifically, our approach leverages martingale theory to mitigate distribution shift issue and employs a hierarchical multiple testing procedure to rigorously control decision errors at both image level and pixel level. Extensive experimental results verify the superior decision-making capabilities of our proposed HiMT framework at both image level and pixel level.