Tighten The Lasso: A Convex Hull Volume-based Anomaly Detection Method

Detecting out-of-distribution (OOD) data is a critical task for maintaining model reliability and robustness. In this study, we propose a novel anomaly detection algorithm that leverages the convex hull (CH) property of a dataset by exploiting the observation that OOD samples marginally increase the CH's volume compared to in-distribution samples. Thus, we establish a decision boundary between OOD and in-distribution data by iteratively computing the CH's volume as samples are removed, stopping when such removal does not significantly alter the CH's volume. The proposed algorithm is evaluated against seven widely used anomaly detection methods across ten datasets, demonstrating performance comparable to state-of-the-art (SOTA) techniques. Furthermore, we introduce a computationally efficient criterion for identifying datasets where the proposed method outperforms existing SOTA approaches.