Compressed Anomaly Detection with Multiple Mixed Observations

Natalie Durgin, Rachel Grotheer, Chenxi Huang, Shuang Li, Anna Ma, Deanna Needell, Jing Qin

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations


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 in 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.

Original languageEnglish
Title of host publicationAssociation for Women in Mathematics Series
Number of pages27
StatePublished - 2019

Publication series

NameAssociation for Women in Mathematics Series
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

Bibliographical note

Publisher Copyright:
© 2019, The Author(s) and the Association for Women in Mathematics.

ASJC Scopus subject areas

  • Gender Studies
  • General Mathematics


Dive into the research topics of 'Compressed Anomaly Detection with Multiple Mixed Observations'. Together they form a unique fingerprint.

Cite this