Universal sequential outlier hypothesis testing

Yun Li, Sirin Nitinawarat, Venugopal V. Veeravalli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are generated by an 'outlier' distribution, distinct from a common 'typical' distribution governing the majority of the sequences. Apart from being distinct, the outlier and typical distributions can be arbitrarily close. The goal is to design a universal test to best discern all the outlier sequences. A universal test with the flavor of the repeated significance test is proposed and its asymptotic performance is characterized under various universal settings. The proposed test is shown to be universally consistent. For the model with identical outliers, the test is shown to be asymptotically optimal universally when the number of outliers is the largest possible and with the typical distribution being known, and its asymptotic performance otherwise is also characterized. An extension of the findings to the model with multiple distinct outliers is also discussed. In all cases, it is shown that the asymptotic performance guarantees for the proposed test when neither the outlier nor typical distribution is known converge to those when the typical distribution is known.

Original languageEnglish (US)
Title of host publicationConference Record of the 48th Asilomar Conference on Signals, Systems and Computers
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages281-285
Number of pages5
ISBN (Electronic)9781479982974
DOIs
StatePublished - Apr 24 2015
Event48th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 - Pacific Grove, United States
Duration: Nov 2 2014Nov 5 2014

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2015-April
ISSN (Print)1058-6393

Other

Other48th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
CountryUnited States
CityPacific Grove
Period11/2/1411/5/14

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ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

Cite this

Li, Y., Nitinawarat, S., & Veeravalli, V. V. (2015). Universal sequential outlier hypothesis testing. In M. B. Matthews (Ed.), Conference Record of the 48th Asilomar Conference on Signals, Systems and Computers (pp. 281-285). [7094445] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2015-April). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2014.7094445