On composite binary hypothesis testing with training data

Michael Bell, Yuval Kochman

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

3 Scopus citations

Abstract

Motivated by an outlier detection problem, we consider the problem of testing between a known i.i.d. distribution over a finite alphabet, and a composite hypothesis consisting of all other i.i.d. distributions over the same alphabet. We wish to quantify the loss with respect to simple hypothesis testing, and further to find how much of it can be re-gained using a training sequence that is known to come from the unknown distribution. To that end, we present new optimality criteria, universal minimax with and without a training sequence. We show that under our criteria, the acceptance region of the optimal tests takes the simple form of a 'sphere of types', where the center is shifted to be 'antipodal' to the type of the training sequence (if such a sequence is present). Further, noting that universality has no cost in the exponential sense, we turn to the second-order regime of fixed error probabilities, where we define a figure of merit that we call resolution tradeoff. In this regime we solve Gaussian hypothesis testing problems, that are asymptotically equivalent to the original ones, in order to derive the resolution tradeoffs with and without training sequence.

Original languageAmerican English
Title of host publication55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1026-1033
Number of pages8
ISBN (Electronic)9781538632666
DOIs
StatePublished - 1 Jul 2017
Event55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 - Monticello, United States
Duration: 3 Oct 20176 Oct 2017

Publication series

Name55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
Volume2018-January

Conference

Conference55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017
Country/TerritoryUnited States
CityMonticello
Period3/10/176/10/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

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