The Histogram-Based Outlier Score (HBOS) is a widely used outlier detection method due to its computational efficiency and simplicity. However, because it assumes independence between features, its ability to detect outliers in datasets where feature interactions are significant is limited. In this paper, we propose the Extended Histogram-Based Outlier Score (EHBOS), an enhancement of HBOS that incorporates two-dimensional histograms to capture dependencies between feature pairs. This extension enables EHBOS to identify contextual and dependency-based anomalies that HBOS fails to detect. Using 17 benchmark datasets, we evaluate the effectiveness and robustness of EHBOS in various anomaly detection scenarios. EHBOS outperforms HBOS on several datasets where feature interactions are crucial for defining the anomaly structure, achieving significant improvements in ROC AUC. These results demonstrate that EHBOS can be a valuable extension of HBOS for modeling complex feature dependencies. Especially in datasets where contextual or relational anomalies play a significant role, EHBOS provides a powerful new anomaly detection tool.
