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POSITIVITY FOR GAUSSIAN GRAPHICAL MODELS
, 2012
"... Gaussian graphical models are parametric statistical models for jointly nor-mal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient condition in terms of the graph for when a subdeterminant is ..."
Abstract
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Gaussian graphical models are parametric statistical models for jointly nor-mal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient condition in terms of the graph for when a subdeterminant
Stratified Gaussian Graphical Models
"... Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide certain forms of context-specific independence that are natur ..."
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Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide certain forms of context-specific independence
On generalizing Gaussian graphical models
"... We explore elliptical graphical models as a generalization of Gaussian graphical models, that is, we allow the population distribution to be elliptical instead of normal. Towards a statis-tical theory for such graphical models, consisting of estimation, testing and model selection, we consider the p ..."
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We explore elliptical graphical models as a generalization of Gaussian graphical models, that is, we allow the population distribution to be elliptical instead of normal. Towards a statis-tical theory for such graphical models, consisting of estimation, testing and model selection, we consider
Multiscale Gaussian Graphical Models and . . .
, 2007
"... Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long ..."
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pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although
in penalized Gaussian graphical models
"... computationally fast alternative to cross-validation ..."
Approximate Inference in Gaussian Graphical Models
, 2008
"... The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high-d ..."
Abstract
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Cited by 5 (0 self)
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The focus of this thesis is approximate inference in Gaussian graphical models. A graphical model is a family of probability distributions in which the structure of interactions among the random variables is captured by a graph. Graphical models have become a powerful tool to describe complex high
TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS
- SUBMITTED TO THE ANNALS OF STATISTICS
, 2009
"... Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when su ..."
Abstract
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Cited by 11 (5 self)
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Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when
Model selection and estimation in the Gaussian graphical model
- BIOMETRIKA (2007), PP. 1–17
, 2007
"... ..."
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