Related papers: Graphical Gaussian models associated to a homogene…
Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We…
Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this…
The covariance graph (aka bi-directed graph) of a probability distribution $p$ is the undirected graph $G$ where two nodes are adjacent iff their corresponding random variables are marginally dependent in $p$. In this paper, we present a…
We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
We study a random graph model which is a superposition of the bond percolation model on $Z^d$ with probability $p$ of an edge, and a classical random graph $G(n, c/n)$. We show that this model, being a {\it homogeneous} random graph, has a…
Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative…
This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…
This article is motivated by studying the interaction of magnetic moments in high entropy alloys (HEAs), which plays an important role in guiding HEA designs in materials science. While first principles simulations can capture magnetic…
This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction…
Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…
Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…
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…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class…