  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 modeling, and
environmental statistics. We establish an efficient polynomial-time algorithm
using Determinantal Point Process for approximating the optimal solution to the
problem. We demonstrate the advantages of our methods by presenting
computational results for both synthetic and real data sets.
