Related papers: Bayesian Analysis of High-dimensional Discrete Gra…

Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…

Latent class analysis is used to perform model based clustering for multivariate categorical responses. Selection of the variables most relevant for clustering is an important task which can affect the quality of clustering considerably.…

Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…

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…

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for…

This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…

Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…

Estimating the probability density of a population while preserving the privacy of individuals in that population is an important and challenging problem that has received considerable attention in recent years. While the previous…

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart…

Variable selection for structured covariates lying on an underlying known graph is a problem motivated by practical applications, and has been a topic of increasing interest. However, most of the existing methods may not be scalable to high…

This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…