Anomaly Detection in the Presence of Missing Values

Standard methods for anomaly detection assume that all features are observed at both learning time and prediction time. Such methods cannot process data containing missing values. This paper studies five strategies for handling missing values in test queries: (a) mean imputation, (b) MAP imputation, (c) reduction (reduced-dimension anomaly detectors via feature bagging), (d) marginalization (for density estimators only), and (e) proportional distribution (for tree-based methods only). Our analysis suggests that MAP imputation and proportional distribution should give better results than mean imputation, reduction, and marginalization. These hypotheses are largely confirmed by experimental studies on synthetic data and on anomaly detection benchmark data sets using the Isolation Forest (IF), LODA, and EGMM anomaly detection algorithms. However, marginalization worked surprisingly well for EGMM, and there are exceptions where reduction works well on some benchmark problems. We recommend proportional distribution for IF, MAP imputation for LODA, and marginalization for EGMM.