Convergence rates of variational posterior distributions

DOI10.1214/19-AOS1883zbMath1471.62243arXiv1712.02519OpenAlexW3049347563MaRDI QIDQ2215731

Fengshuo Zhang, Chao Gao

Publication date: 14 December 2020

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

Full work available at URL: https://arxiv.org/abs/1712.02519

zbMATH Keywords

empirical Bayesdensity estimationposterior contractionGaussian sequence modelpiecewise constant modelmean-field variational inference

Mathematics Subject Classification ID

Bayesian inference (62F15) Empirical decision procedures; empirical Bayes procedures (62C12)

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Uses Software

• fastSTRUCTURE

Cites Work

• Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
• On Bayesian supremum norm contraction rates
• Bayesian linear regression with sparse priors
• On adaptive posterior concentration rates
• Rates of contraction of posterior distributions based on Gaussian process priors
• On rates of convergence for posterior distributions in infinite-dimensional models
• Convergence rates of posterior distributions for non iid observations
• Consistency of variational Bayes inference for estimation and model selection in mixtures
• Convergence rates of posterior distributions.
• Rates of convergence of posterior distributions.
• Lower bounds for posterior rates with Gaussian process priors
• Adaptive Bayesian density estimation with location-scale mixtures
• The consistency of posterior distributions in nonparametric problems
• Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator
• \(\alpha\)-variational inference with statistical guarantees
• Concentration of tempered posteriors and of their variational approximations
• Simultaneous analysis of Lasso and Dantzig selector
• Convergence of estimates under dimensionality restrictions
• Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies
• Posterior concentration rates for infinite dimensional exponential families
• On Bayesian Consistency
• Rényi Divergence and Kullback-Leibler Divergence
• 10.1162/jmlr.2003.3.4-5.993
• Frequentist Consistency of Variational Bayes
• Adaptive density estimation for clustering with Gaussian mixtures
• On Bayes procedures
• Rate exact Bayesian adaptation with modified block priors

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