Related papers: On the Equivalence of Gaussian Graphical Models De…
For a specific class of sparse Gaussian graphical models, we provide a closed-form solution for the determinant of the covariance matrix. In our framework, the graphical interaction model (i.e., the covariance selection model) is equal to…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…
Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A…
We show that each perfect matching in a bipartite graph $G$ intersects at least half of the perfect matchings in $G$. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with…
The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence.…
Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain…
Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…
This paper propose a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a…