Minimum probability of error of list M-ary hypothesis testing

Kangarshahi, Ehsan Asadi; Guillén i Fábregas, A. (Albert)

doi:http://dx.doi.org/10.1093/imaiai/iaad001

Minimum probability of error of list M-ary hypothesis testing

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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

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.