Can We Predict Anomaly Detection Performance from Embedding-Space Geometry?

Anomaly detection systems are often trained using normal data alone, while model selection and evaluation typically require labeled anomalies. We study whether anomaly detection performance can be predicted without access to anomalous data. For kNN-based detectors, we derive a lower bound on the area under the ROC curve (AUC) that relates detection performance to the separation between inlier and outlier scores and to their respective variances. Under a local scaling model, we use this bound to characterize how density variation, intrinsic-dimensional heterogeneity, and cross-domain mismatch contribute to score variability. We then investigate anomaly-free model selection and show that inlier score variance alone does not reliably predict performance across different representations. To address this limitation, we introduce simple pseudo-anomaly probes that provide a reference for estimating relative score separation. Experiments on the DCASE 2022-2025 benchmarks, spanning four embedding models and 208 candidate systems, show that pseudo-anomaly-based estimators substantially improve anomaly-free model selection. In particular, diverse pseudo-anomalies enable anomaly-free model selection to outperform conventional development-set selection under domain shift. These results show that embedding-space geometry contains predictive information about anomaly detection performance while also highlighting the representation-dependent nature of inlier-only performance estimates.