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On cooperative and concurrent detection in distributed hypothesis testing

Abstract : Statistical inference plays a major role in the development of new technologies and inspires a large number of algorithms dedicated to detection, identification and estimation tasks. However, there is no theoretical guarantee for the performance of these algorithms. In this thesis we try to understand how sensors can best share their information in a network with communication constraints to detect the same or distinct events. We investigate different aspects of detector cooperation and how conflicting needs can best be met in the case of detection tasks. More specifically we study a hypothesis testing problem where each detector must maximize the decay exponent of the Type II error under a given Type I error constraint. As the detectors are interested in different information, a compromise between the achievable decay exponents of the Type II error appears. Our goal is to characterize the region of possible trade-offs between Type II error decay exponents. In massive sensor networks, the amount of information is often limited due to energy consumption and network saturation risks. We are therefore studying the case of the zero rate compression communication regime (i.e. the messages size increases sub-linearly with the number of observations). In this case we fully characterize the region of Type II error decay exponent. In configurations where the detectors have or do not have the same purposes. We also study the case of a network with positive compression rates (i.e. the messages size increases linearly with the number of observations). In this case we present subparts of the region of Type II error decay exponent. Finally, in the case of a single sensor single detector scenario with a positive compression rate, we propose a complete characterization of the optimal Type II error decay exponent for a family of Gaussian hypothesis testing problems.
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Pierre Escamilla. On cooperative and concurrent detection in distributed hypothesis testing. Information Theory [cs.IT]. Institut Polytechnique de Paris, 2019. English. ⟨NNT : 2019IPPAT007⟩. ⟨tel-02525159⟩

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