Bayesian computation of high-dimensional linear regression models with popular Gaussian scale mixture prior distributions using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the heavy computational cost that grows in the order of $p^3$, with $p$ as the number of features. Although a few recently developed algorithms allow computational efficiency in presence of a small to moderately large sample size, the computational issues are considerably less explored when sample size $n$ is also large, except for a few recent articles. In this article we propose a sketching approach to compress the $n$ original samples by a random linear transformation to $m< [abs][pdf][bib] © JMLR 2025. (edit, beta) Mastodon