One such filter, the partitioned learned Bloom filter (PLBF), achieves excellent memory efficiency.

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/\epsilon^6)$ for finding a nearly $\epsilon$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms in training both linear models and deep neural networks for partial AUC maximization and sum of ranked range loss minimization.

Backdoor attack is a common threat to deep neural networks. During testing, samples embedded with a backdoor trigger will be misclassified as an adversarial target by a backdoored model, while samples without the backdoor trigger will be correctly classified. In this paper, we present the first certified backdoor detector (CBD), which is based on a novel, adjustable conformal prediction scheme based on our proposed statistic local dominant probability. For any classifier under inspection, CBD provides 1) a detection inference, 2) the condition under which the attacks are guaranteed to be detectable for the same classification domain, and 3) a probabilistic upper bound for the false positive rate. Our theoretical results show that attacks with triggers that are more resilient to test-time noise and have smaller perturbation magnitudes are more likely to be detected with guarantees. Moreover, we conduct extensive experiments on four benchmark datasets considering various backdoor types, such as BadNet, CB, and Blend. CBD achieves comparable or even higher detection accuracy than state-of-the-art detectors, and it in addition provides detection certification. Notably, for backdoor attacks with random perturbation triggers bounded by $\ell_2\leq0.75$

We frame novelty detection on path space as a hypothesis testing problem with signature-based test statistics. Using transportation-cost inequalities of Gasteratos and Jacquier (2023), we obtain tail bounds for false positive rates that extend beyond Gaussian measures to laws of RDE solutions with smooth bounded vector fields, yielding estimates of quantiles and p-values. Exploiting the shuffle product, we derive exact formulae for smooth surrogates of conditional value-at-risk (CVaR) in terms of expected signatures, leading to new one-class SVM algorithms optimising smooth CVaR objectives. We then establish lower bounds on type-$\mathrm{II}$ error for alternatives with finite first moment, giving general power bounds when the reference measure and the alternative are absolutely continuous with respect to each other. Finally, we evaluate numerically the type-$\mathrm{I}$ error and statistical power of signature-based test statistic, using synthetic anomalous diffusion data and real-world molecular biology data.

Deep unsupervised anomaly detection in brain magnetic resonance imaging offers a promising route to identify pathological deviations without requiring lesion-specific annotations. Yet, fragmented evaluations, heterogeneous datasets, and inconsistent metrics have hindered progress toward clinical translation. Here, we present a large-scale, multi-center benchmark of deep unsupervised anomaly detection for brain imaging. The training cohort comprised 2,976 T1 and 2,972 T2-weighted scans from healthy individuals across six scanners, with ages ranging from 6 to 89 years. Validation used 92 scans to tune hyperparameters and estimate unbiased thresholds. Testing encompassed 2,221 T1w and 1,262 T2w scans spanning healthy datasets and diverse clinical cohorts. Across all algorithms, the Dice-based segmentation performance varied between 0.03 and 0.65, indicating substantial variability. To assess robustness, we systematically evaluated the impact of different scanners, lesion types and sizes, as well as demographics (age, sex). Reconstruction-based methods, particularly diffusion-inspired approaches, achieved the strongest lesion segmentation performance, while feature-based methods showed greater robustness under distributional shifts. However, systematic biases, such as scanner-related effects, were observed for the majority of algorithms, including that small and low-contrast lesions were missed more often, and that false positives varied with age and sex. Increasing healthy training data yields only modest gains, underscoring that current unsupervised anomaly detection frameworks are limited algorithmically rather than by data availability. Our benchmark establishes a transparent foundation for future research and highlights priorities for clinical translation, including image native pretraining, principled deviation measures, fairness-aware modeling, and robust domain adaptation.