Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
Statistics Theory
2009-06-22 v1 Algebraic Geometry
Optimization and Control
Statistics Theory
Abstract
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry.
Cite
@article{arxiv.0906.3529,
title = {Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry},
author = {Bernd Sturmfels and Caroline Uhler},
journal= {arXiv preprint arXiv:0906.3529},
year = {2009}
}