A Closer Look at Generalized BH Algorithm for Out-of-Distribution Detection

Out-of-distribution (OOD) detection is a crucial task in reliable and safety-critical applications. Previous studies primarily focus on developing score functions while neglecting the design of decision rules based on these scores. A recent work (Ma et al., 2024) is the first to highlight this issue and proposes the generalized BH (g-BH) algorithm to address it. The g-BH algorithm relies on empirical p-values, with the calibrated set playing a central role in their computation. However, the impact of calibrated set on the performance of g-BH algorithm has not been thoroughly investigated. This paper aims to uncover the underlying mechanisms between them. Theoretically, we demonstrate that conditional expectation of true positive rate (TPR) on calibrated set for the g-BH algorithm follows a beta distribution, which depends on the prescribed level and size of calibrated set. This indicates that a small calibrated set tends to degrade the performance of g-BH algorithm. To address the limitation of g-BH algorithm on small calibrated set, we propose a novel ensemble g-BH (eg-BH) algorithm which integrates various empirical p-values for making decisions. Finally, extensive experimental results validate the effectiveness of our theoretical findings and demonstrate the superiority of our method over g-BH algorithm on small calibrated set.

This paper focuses on studying the impact of calibrated set on the g-BH algorithm and proposes a novel eg-BH algorithm to tackle the problem caused by the small calibrated set.