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Weakly Supervised Anomaly Detection via Dual-Tailed Kernel
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Proposes WSAD-DT, a weakly supervised anomaly detector that uses two latent centers with light-tailed (in-class) and heavy-tailed (out-of-class) kernels, a diversity regularizer, and a subset-split ensemble sharing labeled anomalies.
Problem
Anomaly detection with only a handful of labeled anomalies, where those labels fail to capture the diversity of abnormal behaviors and single-center or single-tail methods degrade.
Approach
Two latent centers (normal and anomaly) with a dual-tailed kernel separation loss that pairs a light-tailed kernel for the sample's own center with a heavy-tailed kernel for the opposite center, plus a kernel-based diversity term against collapse, and an ensemble where unlabeled data is split into disjoint subsets while all models share the same labeled anomalies.
Key results
- WSAD-DT achieves an average AUC-ROC rank of 1.27 across the benchmarks, ranking first on 23 datasets and second on 6 (vs. XGBOD 3.10, RoSAS 3.73, DeepSAD 3.43).
- On AUC-PR, WSAD-DT achieves average rank 1.70, ranking first on 15 datasets and second on 11, with significant Wilcoxon p-values against all compared methods.
- Example AUC-ROC on Vertebral: WSAD-DT 0.9051 vs. XGBOD 0.8125 and DeepSAD 0.7810.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use WSAD-DT instead of competing methods | Weakly supervised anomaly detection on AdBench datasets · AdBench datasets | AUC-ROC average rank: 1.27 vs. 3.10 | Helped |
| Use WSAD-DT instead of competing methods | Weakly supervised anomaly detection on AdBench datasets · AdBench datasets | AUC-PR average rank: 1.70 vs. 3.23 | Helped |
| Replace the dual-tailed design with a single kernel for in-class and out-of-class distances (ablation) | WSAD-DT · Anomaly detection benchmarks | anomaly detection performance | Hurt |
| Add the diversity term to the separation loss (ablation) | WSAD-DT · Anomaly detection benchmarks | anomaly detection performance | Helped |
| Use ensemble size M = 5 rather than smaller or larger ensembles (ablation) | WSAD-DT · Anomaly detection benchmarks | performance | Mixed |
Surprising findings
- The paper's Table 4 shows the light-tailed kernel yields smaller in-class distances than the heavy-tailed kernel, consistent with the theory, but the paper's own theoretical lemmas on gradient magnitudes are argued informally.
- Several baselines (e.g., GANomaly, FeaWAD) perform near chance on some datasets, such as GANomaly at 0.6041 AUC-ROC on Optdigits and 0.3618 on Vertebral.
Limitations
- Does not explicitly handle temporal or relational structures such as time series or graphs (stated as future work).
- Assumes unlabeled data is predominantly normal; performance under contamination is only analyzed in appendix.
- Some baselines fail to run within 12 hours or raise runtime errors, leaving missing entries in the comparison tables.
Experimental setup
Datasets: AdBench (Han et al., 2022) datasets: Optdigits, Lymphography, Pendigits, Vertebral, Wdbc, Cardiotocography, Wpbc, Stamps
Benchmarks: AdBench datasets (AUC-ROC, AUC-PR)
Metrics: AUC-ROC AUC-PR average rank Wilcoxon signed-rank p-value
Baselines: DeepSAD DevNet FeaWAD GANomaly PReNet RoSAS XGBOD
Builds on: DeepSAD DeepSVDD DevNet XGBOD
Closest papers by meaning
- Long-Tailed Anomaly Detection with Learnable Class Names (CVPR 2024 · similarity 0.87)
- TailedCore: Few-Shot Sampling for Unsupervised Long-Tail Noisy Anomaly Detection (CVPR 2025 · similarity 0.87)
- Beyond Normal References: Discriminative Few-Shot Anomaly Detection (NeurIPS 2026 · similarity 0.86)
- Anomaly Heterogeneity Learning for Open-set Supervised Anomaly Detection (CVPR 2024 · similarity 0.86)
- ResAD: A Simple Framework for Class Generalizable Anomaly Detection (NeurIPS 2024 · similarity 0.86)
- Normal-Abnormal Guided Generalist Anomaly Detection (NeurIPS 2025 · similarity 0.85)
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