Related papers: A new hierarchical distribution on arbitrary spars…

Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…

We show how to perform sparse approximate Gaussian elimination for Laplacian matrices. We present a simple, nearly linear time algorithm that approximates a Laplacian by a matrix with a sparse Cholesky factorization, the version of Gaussian…

We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…

Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…

We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…

In this paper an approach for finding a sparse incomplete Cholesky factor through an incomplete orthogonal factorization with Givens rotations is discussed and applied to Gaussian Markov random fields (GMRFs). The incomplete Cholesky factor…

Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…

In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…

In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of…

Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…

We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the…

Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…

In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…

In the last two decades, the linear model of coregionalization (LMC) has been widely used to model multivariate spatial processes. However, it can be a challenging task to conduct likelihood-based inference for such models because of the…

This paper presents a new algorithm for generating random inverse-Wishart matrices that directly generates the Cholesky factor of the matrix without computing the factorization. Whenever parameterized in terms of a precision matrix…

We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced…