Universal outlier hypothesis testing

Yun Li, Sirin Nitinawarat, Venugopal V. Veeravalli

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


The following outlier hypothesis testing problem is studied in a universal setting. Vector observations are collected each with M ≥ 3 coordinates. When a given coordinate is the outlier, the observations in that coordinate are assumed to be distributed according to the 'outlier' distribution, distinct from the common 'typical' distribution governing the observations in all the other coordinates. Nothing is known about the outlier and the typical distributions except that they are distinct and have full supports. The goal is to design a universal test to best discern the outlier coordinate. A universal test based on the generalized likelihood principle is proposed and is shown to be universally exponentially consistent, and a single-letter characterization of the error exponent achievable by the test is derived. It is shown that as the number of coordinates approaches infinity, our universal test is asymptotically efficient. Specifically, it achieves a limiting error exponent that is equal to the largest achievable error exponent when the outlier and typical distributions are both known.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Number of pages5
StatePublished - 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

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


Other2013 IEEE International Symposium on Information Theory, ISIT 2013

ASJC Scopus subject areas

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


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