Related papers: Bayesian Scalable Precision Factor Analysis for Ma…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
This paper introduces a multi-way tensor generalization of the Bigraphical Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal model for the precision matrix to parsimoniously model conditional dependence…
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…
This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…
Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
The sparse precision matrix plays an essential role in the Gaussian graphical model since a zero off-diagonal element indicates conditional independence of the corresponding two variables given others. In the Gaussian graphical model, many…
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…
There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. Firstly, we design a new prior model based on the singular-value-decomposition…