Related papers: Bayesian Covariance Matrix Estimation using a Mixt…

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high dimensional features, in this case transcripts, collected from…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we…

This paper considers estimating a covariance matrix of $p$ variables from $n$ observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these…

A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

We propose a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

We propose a greedy variational method for decomposing a non-negative multivariate signal as a weighted sum of Gaussians, which, borrowing the terminology from statistics, we refer to as a Gaussian mixture model. Notably, our method has the…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model…

In recent years, Ising prior with the network information for the "in" or "out" binary random variable in Bayesian variable selections has received more and more attentions. In this paper, we discover that even without the informative prior…

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…

Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation…

In many inverse problems such as 3D X-ray Computed Tomography (CT), the estimation of an unknown quantity, such as a volume or an image, can be greatly enhanced, compared to maximum-likelihood techniques, by incorporating a prior model on…

Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…