Inference problems, typically posed as the computation of summarizing statistics (e.g., marginals, modes, means, likelihoods), arise in a variety of scientific fields and engineering applications. Probabilistic graphical models provide a scalable framework for developing efficient inference methods, such as message-passing algorithms that exploit the conditional independencies encoded by the given graph. Conceptually, this framework extends naturally to a distributed network setting: by associating to each node and edge in the graph a distinct sensor and communication link, respectively, the iterative message-passing algorithms are equivalent to a sequence of purely-local computations and nearest-neighbor communications. Practically, modern sensor networks can also involve distributed resource constraints beyond those satisfied by existing message-passing algorithms, including e.g., a fixed small number of iterations, the presence of low-rate or unreliable links, or a communication topology that differs from the probabilistic graph. The principal focus of this thesis is to augment the optimization problems from which existing message-passing algorithms are derived, explicitly taking into account that there may be decision-driven processing objectives as well as constraints or costs on available network resources. The resulting problems continue to be NP-hard, in general, but under certain conditions become amenable to an established team-theoretic relaxation technique by which a new class of efficient message-passing algorithms can be derived. From the academic perspective, this thesis marks the intersection of two lines of active research, namely approximate inference methods for graphical models and decentralized Bayesian methods for multi-sensor detection.
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