Compressed Anomaly Detection with Multiple Mixed Observations
For researchers in anomaly detection and compressed sensing, this work provides a theoretical and empirical bridge between the two fields, though the results are incremental as they apply existing algorithms to a known problem.
The paper connects compressed anomaly detection with compressed sensing, showing that algorithms for recovering jointly sparse signals from multiple measurement vectors (MMVs) can effectively detect anomalies. Experiments on synthetic data explore the trade-off between the number of mixed observations per sample and the number of samples needed.
We consider a collection of independent random variables that are identically distributed, except for a small subset which follows a different, anomalous distribution. We study the problem of detecting which random variables in the collection are governed by the anomalous distribution. Recent work proposes to solve this problem by conducting hypothesis tests based on mixed observations (e.g. linear combinations) of the random variables. Recognizing the connection between taking mixed observations and compressed sensing, we view the problem as recovering the "support" (index set) of the anomalous random variables from multiple measurement vectors (MMVs). Many algorithms have been developed for recovering jointly sparse signals and their support from MMVs. We establish the theoretical and empirical effectiveness of these algorithms at detecting anomalies. We also extend the LASSO algorithm to an MMV version for our purpose. Further, we perform experiments on synthetic data, consisting of samples from the random variables, to explore the trade-off between the number of mixed observations per sample and the number of samples required to detect anomalies.