Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry

2009/06/18 by Bernd Sturmfels, Caroline Uhler, Sturmfels, Bernd +1 · 2 citations
Computer Science · Mathematics · #14Q10 #62H12 #90C25 #Advanced Statistical Methods and Models #Algebraic Geometry (math.AG) #Data Management and Algorithms #FOS: Mathematics #Optimization and Control (math.OC) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0906.3529

openalex publication_date 2009/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Lissajous Varieties
• Characteristic numbers of algebras

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