Convergence of latent mixing measures in finite and infinite mixture models

DOI10.1214/12-AOS1065zbMath1347.62117arXiv1109.3250OpenAlexW3105981035MaRDI QIDQ1952455

XuanLong Nguyen

Publication date: 30 May 2013

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

Full work available at URL: https://arxiv.org/abs/1109.3250

zbMATH Keywords

Wasserstein metricrates of convergenceBayesian nonparametricsDirichlet processeshierarchical modelstransportation distances\(f\)-divergencemixture distributions

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Nonparametric estimation (62G05) Bayesian inference (62F15)

Related Items (52)

Discussion of “Confidence Intervals for Nonparametric Empirical Bayes Analysis” by Ignatiadis and Wager ⋮ Supermix: sparse regularization for mixtures ⋮ On emergence and complexity of ergodic decompositions ⋮ Borrowing strengh in hierarchical Bayes: posterior concentration of the Dirichlet base measure ⋮ Minimax confidence intervals for the sliced Wasserstein distance ⋮ Convergence of an iterative algorithm to the nonparametric MLE of a mixing distribution ⋮ The joy of proofs in statistical research ⋮ Mixture Models With a Prior on the Number of Components ⋮ Bayes and maximum likelihood for \(L^1\)-Wasserstein deconvolution of Laplace mixtures ⋮ Asymptotic accuracy of Bayesian estimation for a single latent variable ⋮ Parameter recovery in two-component contamination mixtures: the \(L^2\) strategy ⋮ Bayesian estimation of multidimensional latent variables and its asymptotic accuracy ⋮ Semi-discrete optimal transport: hardness, regularization and numerical solution ⋮ Uniform consistency in nonparametric mixture models ⋮ Optimal estimation of high-dimensional Gaussian location mixtures ⋮ Adaptive Bayesian density estimation in \(L^p\)-metrics with Pitman-Yor or normalized inverse-Gaussian process kernel mixtures ⋮ Bayesian adaptation ⋮ Fisher-Pitman Permutation Tests Based on Nonparametric Poisson Mixtures with Application to Single Cell Genomics ⋮ Revisiting consistency of a recursive estimator of mixing distributions ⋮ Consistency of mixture models with a prior on the number of components ⋮ Approximation of Bayesian models for time-to-event data ⋮ Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective ⋮ Optimal Bayesian estimation of Gaussian mixtures with growing number of components ⋮ Convergence rates of latent topic models under relaxed identifiability conditions ⋮ Bayesian nonparametric modeling for functional analysis of variance ⋮ Optimal estimation of Gaussian mixtures via denoised method of moments ⋮ Identifiability of nonparametric mixture models and Bayes optimal clustering ⋮ Posterior asymptotics in Wasserstein metrics on the real line ⋮ Bayesian consistency for a nonparametric stationary Markov model ⋮ On posterior contraction of parameters and interpretability in Bayesian mixture modeling ⋮ Strong identifiability and optimal minimax rates for finite mixture estimation ⋮ Singularity, misspecification and the convergence rate of EM ⋮ Consistency of the penalized MLE for two-parameter gamma mixture models ⋮ Wasserstein upper bounds of the total variation for smooth densities ⋮ Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications ⋮ On strong identifiability and convergence rates of parameter estimation in finite mixtures ⋮ Latent nested nonparametric priors (with discussion) ⋮ Statistical convergence of the EM algorithm on Gaussian mixture models ⋮ Robust estimation of mixing measures in finite mixture models ⋮ Quantifying Distributional Model Risk via Optimal Transport ⋮ Measuring dependence in the Wasserstein distance for Bayesian nonparametric models ⋮ Penalization of Barycenters in the Wasserstein Space ⋮ Estimating the number of components in finite mixture models via the group-sort-fuse procedure ⋮ A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models ⋮ Convergence of de Finetti's mixing measure in latent structure models for observed exchangeable sequences ⋮ Unnamed Item ⋮ Posterior contraction of the population polytope in finite admixture models ⋮ Is infinity that far? A Bayesian nonparametric perspective of finite mixture models ⋮ Variable selection in finite mixture of generalized estimating equations ⋮ Singularity Structures and Impacts on Parameter Estimation in Finite Mixtures of Distributions ⋮ Asymptotic accuracy of Bayes estimation for latent variables with redundancy ⋮ Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic Behaviour of the Posterior Distribution in Overfitted Mixture Models
• On the optimal rates of convergence for nonparametric deconvolution problems
• Posterior convergence rates of Dirichlet mixtures at smooth densities
• On rates of convergence for posterior distributions in infinite-dimensional models
• Convergence rates of posterior distributions for non iid observations
• Asymptotic methods in statistical decision theory
• Some asymptotic theory for the bootstrap
• Tests of goodness of fit based on the \(L_2\)-Wasserstein distance
• New approaches to Bayesian consistency
• Posterior consistency of Dirichlet mixtures in density estimation
• Fourier methods for estimating mixing densities and distributions
• Convergence rates of posterior distributions.
• Rates of convergence for the Gaussian mixture sieve.
• Rates of convergence of posterior distributions.
• Optimal rate of convergence for finite mixture models
• The consistency of posterior distributions in nonparametric problems
• A Bayesian analysis of some nonparametric problems
• Inference of global clusters from locally distributed data
• Hybrid Dirichlet Mixture Models for Functional Data
• The Nested Dirichlet Process
• On the Mixture of Distributions
• Hierarchical Dirichlet Processes
• Bayesian Nonparametrics
• Optimal Rates of Convergence for Deconvolving a Density
• Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions
• Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization
• Polynomial Learning of Distribution Families
• Identifiability of Mixtures
• A Note on Asymptotic Joint Normality
• Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing
• Optimal Transport

This page was built for publication: Convergence of latent mixing measures in finite and infinite mixture models