Rate-optimal posterior contraction for sparse PCA

DOI10.1214/14-AOS1268zbMath1312.62078arXiv1312.0142MaRDI QIDQ2343963

Chao Gao, Harrison H. Zhou

Publication date: 11 May 2015

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

Full work available at URL: https://arxiv.org/abs/1312.0142

zbMATH Keywords

principal component analysisBayesian estimationposterior contraction

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Nonparametric estimation (62G05) Bayesian inference (62F15)

Related Items (19)

Wald Statistics in high-dimensional PCA ⋮ Optimal Bayesian minimax rates for unconstrained large covariance matrices ⋮ Bernstein-von Mises theorems for functionals of the covariance matrix ⋮ Estimating Large Precision Matrices via Modified Cholesky Decomposition ⋮ Bayesian inference for spectral projectors of the covariance matrix ⋮ Efficient estimation of linear functionals of principal components ⋮ Minimax estimation in sparse canonical correlation analysis ⋮ Bayesian sparse spiked covariance model with a continuous matrix shrinkage prior ⋮ Bayesian modeling of interaction between features in sparse multivariate count data with application to microbiome study ⋮ Posterior consistency of factor dimensionality in high-dimensional sparse factor models ⋮ A general framework for Bayes structured linear models ⋮ Bayesian bandwidth test and selection for high-dimensional banded precision matrices ⋮ Shrinkage priors for single-spiked covariance models ⋮ Posterior contraction rates of the phylogenetic Indian buffet processes ⋮ Minimax posterior convergence rates and model selection consistency in high-dimensional DAG models based on sparse Cholesky factors ⋮ Oracle posterior contraction rates under hierarchical priors ⋮ Adaptive Bayesian nonparametric regression using a kernel mixture of polynomials with application to partial linear models ⋮ The beta-mixture shrinkage prior for sparse covariances with near-minimax posterior convergence rate ⋮ Rate-optimal posterior contraction for sparse PCA

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