\(\alpha\)-variational inference with statistical guarantees

DOI10.1214/19-AOS1827zbMath1450.62031arXiv1710.03266OpenAlexW3029292097MaRDI QIDQ2196198

Yun Yang, Debdeep Pati, Anirban Bhattacharya

Publication date: 28 August 2020

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

Full work available at URL: https://arxiv.org/abs/1710.03266

zbMATH Keywords

Bayes risklatent variable modelsvariational inferenceRényi divergenceevidence lower bound

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (15)

Variational Inference for Latent Space Models for Dynamic Networks ⋮ The computational asymptotics of Gaussian variational inference and the Laplace approximation ⋮ Comprehensive study of variational Bayes classification for dense deep neural networks ⋮ Statistical foundation of variational Bayes neural networks ⋮ On Negative Transfer and Structure of Latent Functions in Multioutput Gaussian Processes ⋮ Unnamed Item ⋮ User-friendly Introduction to PAC-Bayes Bounds ⋮ Variational Bayes in State Space Models: Inferential and Predictive Accuracy ⋮ Local convexity of the TAP free energy and AMP convergence for \(\mathbb{Z}_2\)-synchronization ⋮ Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression ⋮ Adaptive variational Bayes: optimality, computation and applications ⋮ Variational Bayes for High-Dimensional Linear Regression With Sparse Priors ⋮ Conditionally structured variational Gaussian approximation with importance weights ⋮ Convergence rates of variational posterior distributions ⋮ Unnamed Item

Uses Software

• Adam
• PRMLT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gibbs posterior for variable selection in high-dimensional classification and data mining
• Convergence rates of posterior distributions for non iid observations
• Bayesian fractional posteriors
• Convergence rates of posterior distributions.
• An introduction to variational methods for graphical models
• Simultaneous analysis of Lasso and Dantzig selector
• A variational Bayes approach to variable selection
• Variational Bayesian inference with Gaussian-mixture approximations
• Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies
• On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models
• On the properties of variational approximations of Gibbs posteriors
• Rényi Divergence and Kullback-Leibler Divergence
• Approximate Bayesian inference for simple mixtures
• Sampling-Based Approaches to Calculating Marginal Densities
• Graphical Models, Exponential Families, and Variational Inference
• Asymptotic Statistics
• 10.1162/jmlr.2003.3.4-5.993
• A General Framework for Updating Belief Distributions
• Monte Carlo sampling methods using Markov chains and their applications
• Convergence properties of a general algorithm for calculating variational Bayesian estimates for a normal mixture model

This page was built for publication: \(\alpha\)-variational inference with statistical guarantees