Submodular Observation Selection and Information Gathering for Quadratic Models

Understand

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.