Submodular Observation Selection and Information Gathering for Quadratic Models
Submodular Observation Selection and Information Gathering for Quadratic Models
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发表时间：
2019-05
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通讯作者：
Abolfazl Hashemi;Mahsa Ghasemi;H. Vikalo;U. Topcu
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作者：
Abolfazl Hashemi;Mahsa Ghasemi;H. Vikalo;U. Topcu
我们研究了在一个大的观测集中选择信息量最大的子集的问题，以便对未知参数进行准确的估计。这个问题出现在机器学习和信号处理的各种设置中，包括特征选择、相位检索和目标定位。由于对于二次测量模型，最优估计量的矩矩阵通常是未知的，因此大多数先前的工作都采用近似技术，如观测模型的线性化，以优化近似矩矩阵的字母最优性准则。相反，通过利用与经典范树不等式的联系，我们在不扭曲观察模型的关系结构的情况下推导出新的字母最优性准则。进一步证明了在问题参数的一定条件下，这些最优性准则是单调的（弱）次模集函数。这些结果使我们能够开发出一种高效的贪婪观测选择算法，该算法是为二次模型量身定制的，并为其可实现的效用提供了理论界限。
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.