Geometry of maximum likelihood estimation in Gaussian graphical models

DOI10.1214/11-AOS957zbMath1246.62140arXiv1012.2643MaRDI QIDQ450030

Caroline Uhler

Publication date: 3 September 2012

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2643

zbMATH Keywords

dualitytreewidthbipartite graphssufficient statisticsalgebraic varietyalgebraic statisticsmatrix completion problemselimination idealML degreenumber of observations

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Applications of graph theory (05C90) Computational aspects in algebraic geometry (14Q99)

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Uses Software

• Macaulay2
• CVX
• gRc

Cites Work

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• Estimation of means in graphical Gaussian models with symmetries
• Positive definite completions of partial Hermitian matrices
• Lectures on algebraic statistics
• The real positive definite completion problem for a simple cycle
• Basicness of semialgebraic sets
• Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
• The real positive definite completion problem: cycle completability

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