Active hypothesis testing on a tree: Anomaly detection under hierarchical observations

Chao Wang, Kobi Cohen, Qing Zhao

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

Abstract

The problem of detecting a few anomalous processes among a large number of M processes is considered. At each time, aggregated observations can be taken from a chosen subset of processes, where the chosen subset conforms to a given binary tree structure. The random observations are i.i.d. over time with a general distribution that may depend on the size of the chosen subset and the number of anomalous processes in the subset. The objective is a sequential search strategy that minimizes the sample complexity (i.e., the expected number of observations which represents detection delay) subject to a reliability constraint. A sequential test that results in a biased random walk on the tree is developed and is shown to be asymptotically optimal in terms of detection accuracy. Furthermore, it achieves the optimal logarithmic-order sample complexity in M provided that the Kullback-Liebler divergence between aggregated observations in the presence and the absence of anomalous processes are bounded away from zero at all levels of the tree structure as M approaches infinity. Sufficient conditions on the decaying rate of the aggregated observations to pure noise under which a sublinear scaling in M is preserved are also identified for the Bernoulli case.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages993-997
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - 9 Aug 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

Keywords

  • Active hypothesis testing
  • Anomaly detection
  • Noisy group testing
  • Random walk
  • Sequential design of experiments

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Active hypothesis testing on a tree: Anomaly detection under hierarchical observations'. Together they form a unique fingerprint.

Cite this