Related papers: An empirical $G$-Wishart prior for sparse high-dim…
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 present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the…
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…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
When considering a graphical Gaussian model ${\mathcal{N}}_G$ Markov with respect to a decomposable graph $G$, the parameter space of interest for the precision parameter is the cone $P_G$ of positive definite matrices with fixed zeros…
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
Sparse graphical modelling has attained widespread attention across various academic fields. We propose two new graphical model approaches, Gslope and Tslope, which provide sparse estimates of the precision matrix by penalizing its sorted…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
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…
Learning a suitable graph is an important precursor to many graph signal processing (GSP) pipelines, such as graph spectral signal compression and denoising. Previous graph learning algorithms either i) make some assumptions on connectivity…
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…
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…
In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known…
Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based…