Generalized Out-of-distribution (OOD) detection task plays the key role in reliable and safety-critical applications. Existing researches mainly devote to designing or training the powerful score function but overlook investigating the decision rule based on the proposed score function. Different from previous work, this paper aims to design a decision rule with rigorous theoretical guarantee and well empirical performance. Specifically, we provide a new insight for the OOD detection task from a hypothesis testing perspective and propose a novel generalized Benjamini Hochberg (g-BH) procedure to solve the testing problem. Theoretically, the g-BH procedure controls false discovery rate (FDR) under pre-specified level without the consideration of dependence for the p-values. Furthermore, we derive an upper bound and a lower bound of the expectation of false positive rate (FPR) for the g-BH procedure based on the tailed generalized Gaussian distribution family, indicating that the FPR of g-BH procedure converges to zero in probability. Finally, the extensive experimental results verify the superiority of g-BH procedure over the traditional threshold-based decision rule on several generalized OOD detection benchmarks.

Out-of-distribution (OOD) detection task is significant in reliable and safety-critical applications. Existing approaches primarily focus on developing the powerful score function, but overlook the design of decision-making rules based on these score function. In contrast to prior studies, we rethink the OOD detection task from an perspective of online multiple hypothesis testing. We then propose a novel generalized LOND (g-LOND) algorithm to solve the above problem. Theoretically, the g-LOND algorithm controls false discovery rate (FDR) at pre-specified level without the consideration for the dependence between the p-values. Furthermore, we prove that the false positive rate (FPR) of the g-LOND algorithm converges to zero in probability based on the generalized Gaussian-like distribution family. Finally, the extensive experimental results verify the effectiveness of g-LOND algorithm for OOD 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.

Visual anomaly detection is significant in safety-critical and reliability-sensitive scenarios. Prior studies mainly emphasize the design and training of scoring functions, while little effort has been devoted to constructing decision rules based on these score functions. A recent work Ma et al. (2025b) highlights this issue and proposes the SAC-BL algorithm to address it. This method consists of a strong anomaly constraint (SAC) network and a betting-like (BL) algorithm serving as the decision rule. The SAC-BL algorithm can control the false discovery rate (FDR). However the performance of SAC-BL algorithm on anomalous examples, or its false positive rate (FPR), has not been thoroughly investigated. This paper provides a deeper analysis of this problem and explores how to theoretically reduce its FPR. First, we show that as the number of testing examples tends to infinity, the SAC-BL algorithm performs well on abnormal data if the scores follow the generalized Gaussian-like distribution family. But such conditions about the number of testing examples and the distribution of scores are overly restrictive for the real-world applications. So, we attempt to decrease the FPR of the SAC-BL algorithm under the condition of finite samples for practical anomaly detection. To this end, we redesign the BL algorithm by incorporating a randomization strategy and propose a novel stochastic BL (SBL) algorithm. The combination of the SAC network and the SBL algorithm yields our method, SAC-SBL. Theoretical results show that the SAC-SBL algorithm can achieve smaller FPR than SAC-BL algorithm while controlling its FDR. Finally, extensive experimental results demonstrate the superiority of our method over SAC-BL algorithm on multiple visual anomaly detection benchmarks.

Out-of-distribution (OOD) detection task plays the key role in reliable and safety-critical applications. Existing researches mainly devote to designing or training the powerful score function but overlook investigating the decision rule based on the proposed score function. Different from previous work, this paper aims to design a decision rule with rigorous theoretical guarantee and well empirical performance. Specifically, we provide a new insight for the OOD detection task from a hypothesis testing perspective and propose a novel generalized Benjamini Hochberg (g-BH) procedure with empirical p-values to solve the testing problem. Theoretically, the g-BH procedure controls false discovery rate (FDR) at pre-specified level. Furthermore, we derive an upper bound of the expectation of false positive rate (FPR) for the g-BH procedure based on the tailed generalized Gaussian distribution family, indicating that the FPR of g-BH procedure converges to zero in probability. Finally, the extensive experimental results verify the superiority of g-BH procedure over the traditional threshold-based decision rule on several OOD detection benchmarks.

A critical element of learning with noisy labels is noisy label detection. Notably, numerous previous works assume that no source of labels can be clean in a noisy label detection context. In this work, we relax this assumption and assume that a small subset of the training data is clean, which enables substantial noisy label detection performance gains. Specifically, we propose a novel framework that leverages clean data by framing the problem of noisy label detection with clean data as a multiple hypothesis testing problem. Moreover, we propose BHN, a simple yet effective approach for noisy label detection that integrates the Benjamini-Hochberg (BH) procedure into deep neural networks. BHN achieves $\textit{state-of-the-art}$ performance and outperforms baselines by $\textbf{28.48}$% in terms of false discovery rate (FDR) and by $\textbf{18.99}$% in terms of F1 on CIFAR-10. Extensive ablation studies further demonstrate the superiority of BHN. Our code is available at https://github.com/ChenglinYu/BHN.

Interestingly, recent experimental results [2, 26, 22] have identified a robust fairness phenomenon in adversarial training (AT), namely that a robust model well-trained by AT exhibits a remarkable disparity of standard accuracy and robust accuracy among different classes compared with natural training. However, the effect of different perturbation radii in AT on robust fairness has not been studied, and one natural question is raised: does a tradeoff exist between average robustness and robust fairness? Our extensive experimental results provide an affirmative answer to this question: with an increasing perturbation radius, stronger AT will lead to a larger class-wise disparity of robust accuracy. Theoretically, we analyze the class-wise performance of adversarially trained linear models with mixture Gaussian distribution. Our theoretical results support our observations. Moreover, our theory shows that adversarial training easily leads to more serious robust fairness issue than natural training. Motivated by theoretical results, we propose a fairly adversarial training (FAT) method to mitigate the tradeoff between average robustness and robust fairness. Experimental results validate the effectiveness of our proposed method.