Compressed Anomaly Detection with Multiple Mixed Observations

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 meaNatalie Durgin Spiceworks Austin, TX, 78746. e-mail: [email protected] Rachel Grotheer Goucher College Baltimore, MD 21204. Chenxi Huang Yale University New Haven, CT 06511. e-mail: [email protected] Shuang Li Colorado School of Mines Golden, CO 80401. Anna Ma Claremont Graduate University Claremont, CA 91711. Deanna Needell University of California, Los Angeles Los Angeles, CA 90095. Jing Qin Montana State University Bozeman, MT 59717. 1 ar X iv :1 80 1. 10 26 4v 1 [ cs .I T ] 3 1 Ja n 20 18 2 Durgin, Grotheer, Huang, Li, Ma, Needell, Qin surement 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.