Gaussian Covariance faithful Markov Trees

@article{Malouche2009GaussianCF,
  title={Gaussian Covariance faithful Markov Trees},
  author={Dhafer Malouche and Bala Rajaratnam},
  journal={arXiv: Probability},
  year={2009}
}
A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge between any pair of variables implies marginal independence between these two variables. Covariance graph models have recently received much attention in the literature and constitute a sub-family of graphical models. Though they are conceptually simple to… 

Figures from this paper

Gaussian Faithful Markov Trees
TLDR
Gaussian Markov trees are necessarily faithful to their concentration and covariance graph, which means that Gaussian distributions that have trees as concentration graphs are necessarily Faithful.
Reading dependencies from covariance graphs
Duality in Graphical Models
TLDR
This paper demonstrates how duality between undirected and bidirected models can be used to transport results for one class of graphical models to the dual model in a transparent manner, and applies the dualization method to understand the implications of faithfulness.
Reading dependencies from covariance graphs
  • J. Peña
  • Mathematics, Computer Science
    Int. J. Approx. Reason.
  • 2013
Unfaithful K-separable Gaussian Graphical Models
TLDR
This paper provides a characterization of faithful relations and an algorithm to test faithfulness based only on knowledge of other conditional relations of the form Xi ⊥ Xj | XS and introduces algorithms to learn the topologies of weakly K- separable and strongly K-separable Gaussian graphical models with Ω(K log p) sample complexity.
Testing Unfaithful Gaussian Graphical Models
TLDR
This paper provides a characterization of faithful relations and then provides an algorithm to test faithfulness based only on knowledge of other conditional relations of the form Xi ⊥ Xj | XS.
LIST OF CITATIONS
Learning Unfaithful $K$-separable Gaussian Graphical Models

References

SHOWING 1-10 OF 34 REFERENCES
Determining full conditional independence by low-order conditioning
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices
Wishart distributions for decomposable covariance graph models
TLDR
This paper constructs on the cone P G a family of Wishart distributions which serve a similar purpose in the covariance graph setting as those constructed by Letac and Massam and proves convergence of this block Gibbs sampler and establishes hyper-Markov properties for this class of priors.
Covariance decomposition in undirected Gaussian graphical models
The covariance between two variables in a multivariate Gaussian distribution is decomposed into a sum of path weights for all paths connecting the two variables in an undirected independence graph.
On a dualization of graphical Gaussian models
TLDR
Parameter estimation in graphical models with marginal indepen- dence interpretation is achieved by the dual likelihood concept, which shows interesting relations to results available for maximum likelihood estimation in graphs showing the marginal independence structure in graphical Gaussian models for conditional independence.
FLEXIBLE COVARIANCE ESTIMATION IN GRAPHICAL GAUSSIAN MODELS
In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the W PG family defined by
Probabilistic conditional independence structures
  • M. Studený
  • Computer Science
    Information science and statistics
  • 2005
TLDR
The author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence.
Perfect Tree-like Markovian Distributions
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence
Graphical Models in Applied Multivariate Statistics.
TLDR
This introduction to the use of graphical models in the description and modeling of multivariate systems covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition.
Hidden Markov Random Fields
TLDR
It is shown that hidden Markov models are dense among essentially all finitestate discrete-time stationary processes and finite-state lattice-based stationary random fields, and to a consistent non-parametric estimator.
Linear Dependencies Represented by Chain Graphs
Various special linear structures connected with covariance matrices are reviewed and graphical methods for their representation introduced, involving in particular two different kinds of edge
...
1
2
3
4
...