Related papers: Bayesian Covariate-Dependent Graph Learning with a…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and…

We introduce a Bayesian prior distribution, the Logit-Normal continuous analogue of the spike-and-slab (LN-CASS), which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG…

The graph structure of a Bayesian network (BN) can be learned from data using the well-known score-and-search approach. Previous work has shown that incorporating structured representations of the conditional probability distributions…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

This paper considers a novel problem, bi-level graphical modeling, in which multiple individual graphical models can be considered as variants of a common group-level graphical model and inference of both the group- and individual-level…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

In multivariate data analysis, it is often important to estimate a graph characterizing dependence among (p) variables. A popular strategy uses the non-zero entries in a (p\times p) covariance or precision matrix, typically requiring…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

The popularity of transfer learning stems from the fact that it can borrow information from useful auxiliary datasets. Existing statistical transfer learning methods usually adopt a global similarity measure between the source data and the…

High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…

We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic,…

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…