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Submodular Observation Selection and Information Gathering for Quadratic Models
Abolfazl Hashemi · Mahsa Ghasemi · Haris Vikalo · Ufuk Topcu

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #167

We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees' inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.

Author Information

Abolfazl Hashemi (University of Texas at Austin)
Mahsa Ghasemi (The University of Texas at Austin)
Haris Vikalo (University of Texas at Austin)
Ufuk Topcu (University of Texas at Austin)

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