Related papers: Joint Bayesian Variable and DAG Selection Consiste…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
Quantitative genetic studies that model complex, multivariate phenotypes are important for both evolutionary prediction and artificial selection. For example, changes in gene expression can provide insight into developmental and…
A Bayesian network is a probabilistic graphical model that consists of a directed acyclic graph (DAG), where each node is a random variable and attached to each node is a conditional probability distribution (CPD). A Bayesian network can be…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…
A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number…
Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of…
Existing approaches to differentiable structure learning of directed acyclic graphs (DAGs) rely on strong identifiability assumptions in order to guarantee that global minimizers of the acyclicity-constrained optimization problem identifies…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant…
Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
The multiple-subject vector autoregression (multi-VAR) model captures heterogeneous network Granger causality across subjects by decomposing individual sparse VAR transition matrices into commonly shared and subject-unique paths. The model…
Causal Bayesian networks (CBN) are popular graphical probabilistic models that encode causal relations among variables. Learning their graphical structure from observational data has received a lot of attention in the literature. When there…
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The…
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The…
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…