Abstract

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix that characterizes the chosen subset. This problem arises in many domains, such as experimental designs, regression modelling, and environmental statistics. However, finding the exact solution to this optimization problem is shown to be computationally intractable for large datasets. In this paper, we establish an efficient polynomial-time algorithm using the determinantal point process to approximate the optimal solution to the problem. We demonstrate the advantages of our methods by presenting examples from D-optimal designs of experiemnts for regression modelling and maximum entropy based designs for spatial monitoring networks.

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