Anomaly Detection with Variance Stabilized Density Estimation

Density estimation based anomaly detection schemes typically model anomalies as examples that reside in low-density regions. We propose a modified density estimation problem and demonstrate its effectiveness for anomaly detection. Specifically, we assume the density function of normal samples is uniform in some compact domain. This assumption implies the density function is more stable (with lower variance) around normal samples than anomalies. We first corroborate this assumption empirically using a wide range of real-world data. Then, we design a variance stabilized density estimation problem for maximizing the likelihood of the observed samples while minimizing the variance of the density around normal samples. We introduce an ensemble of autoregressive models to learn the variance stabilized distribution. Finally, we perform an extensive benchmark with 52 datasets demonstrating that our method leads to state-of-the-art results while alleviating the need for data-specific hyperparameter tuning.