Related papers: Robust and sparse Gaussian graphical modeling unde…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…
Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…
We consider a framework for determining and estimating the conditional pairwise relationships of variables when the observed samples are contaminated with measurement error in high dimensional settings. Assuming the true underlying…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
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…
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…
The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…
Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…
Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…