Minimum probability of error of list M-ary hypothesis testing

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• dc.contributor.author Kangarshahi, Ehsan Asadi
• dc.contributor.author Guillén i Fábregas, A. (Albert)
• dc.date.accessioned 2023-07-04T06:40:34Z
• dc.date.available 2023-07-04T06:40:34Z
• dc.date.issued 2023
• dc.description.abstract We study a variation of Bayesian M-ary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an error is defined as the event where the true hypothesis is not in the list output by the test. We derive two exact expressions of the minimum probability or error. The first is expressed as the error probability of a certain non-Bayesian binary hypothesis test and is reminiscent of the meta-converse bound by Polyanskiy, Poor and Verdú (2010). The second, is expressed as the tail probability of the likelihood ratio between the two distributions involved in the aforementioned non-Bayesian binary hypothesis test. Hypothesis testing, error probability, information theory.
• dc.description.sponsorship European Research Council (Grant 725411); Spanish Ministry of Economy and Competitiveness (Grant PID2020-116683GB-C22).
• dc.format.mimetype application/pdf
• dc.identifier.citation Kangarshahi EA, Guillén i Fàbregas A. Minimum probability of error of list M-ary hypothesis testing. Inf inference. 2023;12(3):iaad001. DOI: 10.1093/imaiai/iaad001
• dc.identifier.doi http://dx.doi.org/10.1093/imaiai/iaad001
• dc.identifier.issn 2049-8764
• dc.identifier.uri http://hdl.handle.net/10230/57446
• dc.language.iso eng
• dc.publisher Oxford University Press
• dc.relation.ispartof Information and Inference: A Journal of the IMA. 2023;12(3):iaad001.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/725411
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PID2020-116683GB-C22
• dc.rights © The Author(s) 2023. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword hypothesis testing
• dc.subject.keyword error probability
• dc.subject.keyword information theory
• dc.title Minimum probability of error of list M-ary hypothesis testing
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion