Bayesian Sparse Spiked Covariance Model with a Continuous Matrix Shrinkage Prior

We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The matrix is reparameterized terms of the latent factor model, where loading equipped novel spike-and-slab LASSO prior, which continuous shrinkage prior modeling matrices. establish rate-optimal posterior contraction respect to spectral norm as well that principal subspace projection loss. also study rate two-to-infinity loss, loss function measuring distance between subspaces able capture entrywise eigenvector perturbations. show tighter than routinely used under certain low-rank and bounded coherence conditions. In addition, point estimator proposed risk bound numerical performance assessed through synthetic examples analysis real-world face data example.