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We study the problem of selecting most informative subset of a largeobservation set to enable accurate estimation of unknown parameters. Thisproblem arises in a variety of settings in machine learning and signalprocessing including feature selection, phase retrieval, and targetlocalization. Since for quadratic measurement models the moment matrix of theoptimal estimator is generally unknown, majority of prior work resorts toapproximation techniques such as linearization of the observation model tooptimize 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 therelational structure of the observation model. We further show that undercertain conditions on parameters of the problem these optimality criteria aremonotone and (weak) submodular set functions. These results enable us todevelop an efficient greedy observation selection algorithm uniquely tailoredfor quadratic models, and provide theoretical bounds on its achievable utility.

Submodular Observation Selection and Information Gathering for Quadratic Models