Related papers: Covariance Structure Estimation with Laplace Appro…
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…
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…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
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…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…
We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
In this paper, we aim to estimate block-diagonal covariance matrices for Gaussian data in high dimension and in fixed dimension. We first estimate the block-diagonal structure of the covariance matrix by theoretical and practical estimators…
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…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…