Related papers: Bayesian Estimation of Gaussian Graphical Models w…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…
Several statistical models used in genome-wide prediction assume independence of marker allele substitution effects, but it is known that these effects might be correlated. In statistics, graphical models have been identified as a useful…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…