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Active Learning and Hypothesis Testing

  • Author(s): Naghshvar, Mohammad
  • et al.
Abstract

This dissertation considers a generalization of the classical hypothesis testing problem. Suppose there are M hypotheses of interest among which only one is true. A Bayesian decision maker is responsible to collect observation samples so as to enhance his information about the true hypothesis in a speedy manner while accounting for the penalty of wrong declaration. In contrast to the classical hypothesis testing problem, at any given time, the decision maker can choose one of the available sensing actions and hence, exert some control over the collected samples' "information content." This generalization, referred to as the active hypothesis testing, naturally arises in a broad spectrum of applications such as medical diagnosis, cognition, communication, sensor management, image inspection, generalized search, and group testing. The first part of the dissertation provides a theoretical analysis of the problem of active hypothesis testing. Using results in sequential analysis and dynamic programming, lower bounds for the optimal performance are established. The lower bounds are complementary for various values of the parameters of the problem, and characterize the fundamental limits on the maximum achievable information acquisition rate and the optimal reliability. Moreover, upper bounds are obtained via an analysis of the proposed heuristic policies for dynamic selection of actions. From the obtained bounds, sufficient conditions are provided under which the maximum information acquisition rate and reliability are achieved, establishing the asymptotic optimality of the proposed heuristics. The second part of the dissertation investigates the applications of the first part for three important special cases of the active hypothesis testing. Chapter 5 considers the problem of conveying a message over discrete memoryless channels with noiseless feedback. Chapter 6 studies the problem of two-dimensional search to locate a target in an image against a background of distractors. Finally, in Chapter 7, the problem of active learning for multiclass classification is investigated where the outcomes of label queries are corrupted by noise. In each of these chapters, the results in the first part of the dissertation are specialized, new results are obtained, and many of the known results are recovered with concise proofs

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