Related papers: A Loss-Based Prior for Gaussian Graphical Models
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 model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…
Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
This paper describes a decision theoretic formulation of learning the graphical structure of a Bayesian Belief Network from data. This framework subsumes the standard Bayesian approach of choosing the model with the largest posterior…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem.…
In this paper we present a loss-based approach to change point analysis. In particular, we look at the problem from two perspectives. The first focuses on the definition of a prior when the number of change points is known a priori. The…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…
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…
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…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
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…