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Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…

We explore the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. The particular generalized t distribution we adopt is a…

Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…

Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…