Rethinking Thresholding as a Neglected Frontier in Anomaly Detection

Anomaly detection aims to identify data samples that deviate from expected patterns and is widely applied across domains. In practice, it consists of two stages: (i) computing continuous anomaly scores; and (ii) converting these scores into binary decisions via thresholding. While extensive research has focused on scoring mechanisms, thresholding is often treated as a minor detail, despite being essential for evaluation, comparison, and deployment. Over half of studies and libraries select thresholds using supervision, introducing oracle knowledge that conflicts with the unsupervised setting. Through a diagnostic study of 38 thresholding methods and 8 scaling strategies across three data modalities–time-series from TSB-AD, and tabular and image data from ADBench benchmarks–we show that violations of common parametric assumptions cause complete thresholding failures on one-third of datasets. Score normality, for example, holds in fewer than 2% of empirical distributions. Thresholding choices alone can also reverse detector rankings. To address these limitations, we propose the **Energy-Based Adaptive Boundary (EAB)**, a nonparametric, parameter-free method that partitions anomaly scores using a Gini-mean-difference-calibrated two-sample energy distance. Centroid aggregation over the energy landscape provides robustness to autocorrelation, while a prefix-sum reformulation reduces naive cubic computation to $O(n\log n)$ time and $O(n)$ space. Compared with the nine strongest unsupervised baselines, EAB achieves statistically significant F1 improvements against every baseline, with gains of up to 17.7% on time-series data and 16.2% on tabular and image data, confirmed by Wilcoxon signed-rank tests. These results establish EAB as an efficient, modality-agnostic framework for unsupervised anomaly thresholding.