49: Scalable Bayesian regression with massive and high-dimensional data

Music City Center 

Recent advances in scalable MCMC methods for high-dimensional Bayesian regression have focused on addressing computational challenges associated with iterative computations with large-scale covariance matrices. While existing research heavily relies on the large-p-small-n assumption to scale down computational costs, scenarios where both n and p have not been yet explored. In this study, we propose an innovative solution to the large-p-large-n problem by integrating a randomized sketching approach into a Gibbs sampling framework. Our method leverages a random sketching matrix to approximate high-dimensional posterior distributions efficiently, enabling scalable Bayesian inference for high-dimensional and massive datasets. Our proposed approach is applicable to the variety of shrinkage priors that are widely used in high-dimensional regression. We investigated the performance of the proposed method via simulation studies.

Acceptance-rejection method

Gibbs sampling

High-dimensional Bayesian regression

Scalable Bayesian computation 

Section on Bayesian Statistical Science