Best Principal Submatrix Selection for the Maximum Entropy Sampling Problem: Scalable Algorithms and Performance Guarantees

This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of prespecified size from covariance matrix. MESP is widely applied many areas, including healthcare, power systems, manufacturing, and data science. By investigating its Lagrangian dual primal characterization, we derive novel convex integer program for show that continuous relaxation yields near-optimal solution. The results motivate us study efficient approximation algorithms develop their bounds MESP, improves best known one in literature.