A1366
Title: Efficient Bayesian inference on sparse and low-rank covariance matrices via projection
Authors: Maoran Xu - Indiana University (United States) [presenting]
Abstract: In covariance estimation for high-dimensional data, sparsity and low-rank assumptions are commonly used to reduce dimensionality. However, in a Bayesian paradigm, it is challenging to conduct posterior computation under priors that simultaneously impose sparsity and low-rank (SLR) structure. To bypass the usual challenges inherent in computation for orthogonal and sparse matrix factorizations, a novel transformation-based approach is proposed. A normal-inverse-Gamma prior is projected from to the SLR space by thresholding the row-norm and trace norm, leading to a projected SLR (PSLR) prior. Remarkably, it is shown that it is possible to conduct posterior computation under the PSLR prior by sampling from the conjugate normal-inverse-Gamma posterior and projecting the draws. This dramatically simplifies computation. The resulting posterior distribution is shown to satisfy frequentist optimality properties, including adaptive posterior contraction rates. The approach is evaluated in simulation studies and applied to a gene expression data set.
