Title: Convex relaxation for the generalized maximum-entropy sampling problem

Abstract: The generalized maximum-entropy sampling problem (GMESP) is to select
an order-s principal submatrix from an order-n covariance matrix, to maximize
the product of its $t$ greatest eigenvalues, 0 < t <= s < n. Introduced more
than 25 years ago, GMESP is a natural generalization of two fundamental problems
in statistical design theory: (i) maximum-entropy sampling problem (MESP); (ii)
binary D-optimality (D-Opt). In the general case, it can be motivated by  a
selection problem in the context of principal component analysis (PCA). We
introduce the first convex-optimization based relaxation for GMESP, study its
behavior, compare it to an earlier spectral bound, and demonstrate its use in a
branch-and-bound scheme. We find that such an approach is practical when s-t is
very small. 

Marcia Fampa

(with Jon Lee and Gabriel Ponte)