Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry

Preprint

18 June 2009

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0906.3529

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.

Keywords

MAXIMUM LIKELIHOOD ESTIMATION
CONVEX ALGEBRAIC GEOMETRY
MULTIVARIATE GAUSSIANS
SEMIDEFINITE MATRIX
MATRIX COMPLETION
IMAGE

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Version 1, 2009-06-18, ArXiv

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