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On Multiple Hypothesis Testing with Rejection Option

Grigoryan, N.
Harutyunyan, A.
Published in IEEE Information Theory Workshop (ITW). Paraty (Brazil) - 16-20 Oct. 2011 - . 2011, p. 75-79
Abstract We study the problem of multiple hypothesis testing (HT) in view of a rejection option. That model of HT has many different applications. Errors in testing of M hypotheses regarding the source distribution with an option of rejecting all those hypotheses are considered. The source is discrete and arbitrarily varying (AVS). The tradeoffs among error probability exponents/reliabilities associated with false acceptance of rejection decision and false rejection of true distribution are investigated, the optimal decision strategies are outlined. The special case of discrete memoryless source (DMS) is also discussed. An interesting insight that the analysis implies is the phenomenon (comprehensible in terms of supervised/unsupervised learning) that in optimal discrimination within M hypothetical distributions one permits always lower error than in deciding to decline the set of hypotheses. Geometric interpretations of the optimal decision schemes and bounds in multi-HT for AVS's are given.
Keywords decision theoryerror statisticssource codingstatistical distributions
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Research groups Computer Vision and Multimedia Laboratory
Stochastic Information Processing Group
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GRIGORYAN, N. et al. On Multiple Hypothesis Testing with Rejection Option. In: IEEE Information Theory Workshop (ITW). Paraty (Brazil). [s.l.] : [s.n.], 2011. p. 75-79. doi: 10.1109/ITW.2011.6089531 https://archive-ouverte.unige.ch/unige:47623

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Deposited on : 2015-03-06

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