Posterior graph selection and estimation consistency for high-dimensional Bayesian DAG models

DOI10.1214/18-AOS1689zbMath1417.62140arXiv1611.01205OpenAlexW2963846915MaRDI QIDQ1731759

Malay Ghosh, Xuan Cao, Kshitij Khare

Publication date: 14 March 2019

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01205

zbMATH Keywords

high-dimensional datacovariance estimationposterior consistencyBayesian DAG modelsgraph selectionhigh-dimensional multivariate datasets

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Bayesian inference (62F15)

Related Items

On the non-local priors for sparsity selection in high-dimensional Gaussian DAG models, Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach, Gaussian Bayesian network comparisons with graph ordering unknown, Bayesian joint inference for multiple directed acyclic graphs, A generalized likelihood-based Bayesian approach for scalable joint regression and covariance selection in high dimensions, Estimating Large Precision Matrices via Modified Cholesky Decomposition, A permutation-based Bayesian approach for inverse covariance estimation, Bayesian inference of causal effects from observational data in Gaussian graphical models, Bayesian group selection in logistic regression with application to MRI data analysis, A Bayesian Subset Specific Approach to Joint Selection of Multiple Graphical Models, Network Structure Learning Under Uncertain Interventions, Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures, Estimation of Gaussian directed acyclic graphs using partial ordering information with applications to DREAM3 networks and dairy cattle data, Densely connected sub-Gaussian linear structural equation model learning via \(\ell_1\)- and \(\ell_2\)-regularized regressions, Scalable Bayesian high-dimensional local dependence learning, Complexity analysis of Bayesian learning of high-dimensional DAG models and their equivalence classes, Joint variable selection and network modeling for detecting eQTLs, Consistent Bayesian sparsity selection for high-dimensional Gaussian DAG models with multiplicative and beta-mixture priors, Bayesian adaptive Lasso estimation of large graphical model based on modified Cholesky decomposition, Bayesian causal inference in probit graphical models, Bayesian graph selection consistency under model misspecification, Compatible priors for model selection of high-dimensional Gaussian DAGs, Bayesian bandwidth test and selection for high-dimensional banded precision matrices, Posterior graph selection and estimation consistency for high-dimensional Bayesian DAG models, Joint Bayesian Variable and DAG Selection Consistency for High-dimensional Regression Models with Network-structured Covariates, Minimax posterior convergence rates and model selection consistency in high-dimensional DAG models based on sparse Cholesky factors, Objective Bayes model selection of Gaussian interventional essential graphs for the identification of signaling pathways, Bayesian inference for high-dimensional decomposable graphs, High-dimensional posterior consistency for hierarchical non-local priors in regression, A review of Gaussian Markov models for conditional independence, A Gibbs sampler for learning DAG: a unification for discrete and Gaussian domains, Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo

Cites Work

• Unnamed Item
• Parameter priors for directed acyclic graphical models and the characterization of several probability distributions
• Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs
• Bayesian variable selection with shrinking and diffusing priors
• \(\ell_{0}\)-penalized maximum likelihood for sparse directed acyclic graphs
• Posterior convergence rates for estimating large precision matrices using graphical models
• Hanson-Wright inequality and sub-Gaussian concentration
• High dimensional posterior convergence rates for decomposable graphical models
• Spectrum estimation for large dimensional covariance matrices using random matrix theory
• Schur products and matrix completions
• Posterior graph selection and estimation consistency for high-dimensional Bayesian DAG models
• High dimensional sparse covariance estimation via directed acyclic graphs
• Bayesian structure learning in graphical models
• Regularized estimation of large covariance matrices
• Wishart distributions for decomposable graphs
• A new approach to Cholesky-based covariance regularization in high dimensions
• Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non‐Local Priors
• Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance Correlation Parameters
• Parsimonious Covariance Matrix Estimation for Longitudinal Data
• On the use of Non-Local Prior Densities in Bayesian Hypothesis Tests
• Bayesian Model Selection in High-Dimensional Settings
• Objective Bayes Covariate‐Adjusted Sparse Graphical Model Selection
• Learning Local Dependence In Ordered Data
• Covariance matrix selection and estimation via penalised normal likelihood