Related papers: Bayesian inference for Gaussian graphical models b…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and…

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…

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…

In learned image compression, probabilistic models play an essential role in characterizing the distribution of latent variables. The Gaussian model with mean and scale parameters has been widely used for its simplicity and effectiveness.…

Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…

Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…

Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…

We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…

In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…

Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…

We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several…

Gaussian Boson Sampling (GBS) generate random samples of photon-click patterns from a class of probability distributions that are hard for a classical computer to sample from. Despite heroic demonstrations for quantum supremacy using GBS,…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

In this paper, we present the Bayesian inference procedures for the parameters of the multivariate random effects model derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the…

Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization…

Bayesian model selection, with precedents in George and McCulloch (1993) and Abramovich et al. (1998), support credibility measures that relate model uncertainty, but computation can be costly when sparse priors are approximate. We design…