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 design, variable selection, 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 datasets.