Multiple Objects: Error Exponents in Hypotheses Testing and Identification

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 and the optimal decision strategies are outlined. The main result is specialized for discrete memoryless sources (DMS) and studied further. 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 are given for the current and known bounds in multi-HT for AVS's.

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“…According to [22] the authors claim to have obtained Theorem 4 independently. This means that discrimination is always easier than rejection.…”

Section: Results For Dmsmentioning

confidence: 99%

“…for N > max{N 0 (ε), N 1 (δ), N 2 (δ)} and for every m = 1, M . Now we have to proceed with the proof of (22). Suppose again…”

Section: Basic Propertiesmentioning

confidence: 99%

On multiple hypothesis testing with rejection option

Grigoryan¹,

Harutyunyan²,

Voloshynovskiy³

et al. 2011

2011 IEEE Information Theory Workshop

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“…Interesting is the case with multiple objects [cf. 21,24,26,27]. Significant are arbitrarily varying models with a sequence of states known to the decision maker [cf.…”

Section: Discussionmentioning

confidence: 99%

“…Neyman-Pearson criterion of multiple hypotheses testing for discrete random variables was explored in [25]. In publications [1], [24] and [26], many hypotheses logarithmically asymptotically optimal (LAO) testing for the models consisting of many independent objects was investigated. Following Birgé [3], we called the sequence of tests logarithmically asymptotically optimal (LAO), when for given values of some reliabilities (error probability exponents) the test ensures the best values for the rest of them.…”

Section: Introductionmentioning

confidence: 99%

A Neyman-Pearson Proper Way to Universal Testing of Multiple Hypotheses Formed by Groups of Distributions

Haroutunian

Yesayan

2020

Mathematical Problems of Computer Science

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The asymptotically optimal Neyman-Pearson procedures of detection for models characterized by M discrete probability distributions arranged into K, 2 ≤ K ≤ M groups considered as hypotheses are investigated. The sequence of tests based on a growing number of observations is logarithmically asymptotically optimal (LAO) when a certain part of the given error probability exponents (reliabilities) provides positives values for all other reliabilities. LAO tests sequences for some models of objects, including cases, when rejection of decision may be permitted, and when part, or all given error probabilities decrease subexponentially with an increase in the of number of experiments, are desined. For all reliabilities of such tests single-letter characterizations are obtained. A simple case with three distributions and two hypotheses is considered.

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