Posterior contraction in sparse Bayesian factor models for massive covariance matrices
超大协方差矩阵稀疏贝叶斯因子模型的后验收缩
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size. Under relevant sparsity assumptions on the true covariance matrix, we show that commonly-used point mass mixture…