Maximum likelihood estimation in Gaussian models under total positivity

DOI10.1214/17-AOS1668zbMath1467.62092arXiv1702.04031WikidataQ127838243 ScholiaQ127838243MaRDI QIDQ2313271

Caroline Uhler, Piotr Zwiernik, Steffen L. Lauritzen

Publication date: 18 July 2019

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

Full work available at URL: https://arxiv.org/abs/1702.04031

zbMATH Keywords

Gaussian graphical modelultrametricinverse M-matrix\(\mathrm{MTP}_2\) distributionattractive Gaussian Markov random field (GMRF)nonfrustrated GRMF

Mathematics Subject Classification ID

Multivariate analysis (62H99) Estimation in multivariate analysis (62H12) Inequalities; stochastic orderings (60E15) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (15)

Total positivity in exponential families with application to binary variables ⋮ Universal inference ⋮ Tropical Gaussians: a brief survey ⋮ On Sidorenko's conjecture for determinants and Gaussian Markov random fields ⋮ A multitest procedure for testing MTP2 for Gaussian distributions ⋮ Optimal rates for estimation of two-dimensional totally positive distributions ⋮ Convolutions of totally positive distributions with applications to kernel density estimation ⋮ Nonlinear algebra and applications ⋮ Total positivity in multivariate extremes ⋮ Gaussian Markov random fields and totally positive matrices ⋮ Estimation of Monge matrices ⋮ Dependence in elliptical partial correlation graphs ⋮ The geometry of gaussoids ⋮ Bimonotone subdivisions of point configurations in the plane ⋮ Locally associated graphical models and mixed convex exponential families

Uses Software

• CVX

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inverse \(M\)-matrices and ultrametric matrices
• Geometry of maximum likelihood estimation in Gaussian graphical models
• Inverse \(M\)-matrices. II
• Covariance selection and multivariate dependence
• A general central limit theorem for FKG systems
• M-matrices as covariance matrices of multinormal distributions
• Gaussian Markov distributions over finite graphs
• Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions
• Total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities
• Correlation inequalities on some partially ordered sets
• On the convergence of the coordinate descent method for convex differentiable minimization
• A likelihood ratio test for \(\text{MTP}_ 2\) within binary variables.
• The completion problem for \(M\)-matrices and inverse \(M\)-matrices
• Total positivity in Markov structures
• Estimation of positive definite \(M\)-matrices and structure learning for attractive Gaussian Markov random fields
• The maximum likelihood threshold of a graph
• Some notions of multivariate positive dependence
• Über die Determinanten mit überwiegender Hauptdiagonale
• Graphical Models with R
• Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis
• Path product matrices
• A recursive algorithm for Markov random fields
• Learning Graphs With Monotone Topology Properties and Multiple Connected Components
• Exact sampling with coupled Markov chains and applications to statistical mechanics
• The correlation space of Gaussian latent tree models and model selection without fitting
• Learning Latent Tree Graphical Models
• High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion

This page was built for publication: Maximum likelihood estimation in Gaussian models under total positivity