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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…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
In the past decade, many Bayesian shrinkage models have been developed for linear regression problems where the number of covariates, $p$, is large. Computing the intractable posterior are often done with three-block Gibbs samplers (3BG),…
This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…
We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
Approximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets for problems with intractable or {unavailable} likelihood function. It uses synthetic data drawn from the simulation model to approximate the…
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…
In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…
We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…