Prior-Preconditioned Conjugate Gradient Method for Accelerated Gibbs Sampling in Large n, Large p'' Bayesian Sparse Regression

• 成果类型: Article
• 署名作者: Nishimura, Akihiko; Suchard, Marc A.
• 署名单位: Johns Hopkins University; University of California System; University of California Los Angeles
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2057859
• 发表日期: 2023
• 页码: 2468-2481
• 关键词: VARIABLE SELECTION; horseshoe; inference; Iterations; EQUATIONS; models

摘要

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of 10(5)-10(6) and of 10(4) -10(5). Despite the large sample size, data rarely provide sufficient information to reliably estimate such a large number of parameters. Sparse regression techniques provide potential solutions, one notable approach being the Bayesian method based on shrinkage priors. In the large n and large psetting, however, the required posterior computation encounters a bottleneck at repeated sampling from a high-dimensional Gaussian distribution, whose precision matrix Phi is expensive to compute and factorize. In this article, we present a novel algorithm to speed up this bottleneck based on the following observation: We can cheaply generate a random vector b such that the solution to the linear system Phi beta = b has the desired Gaussian distribution. We can then solve the linear system by the conjugate gradient (CG) algorithm through matrix-vector multiplications by Phi; this involves no explicit factorization or calculation of Phi itself. Rapid convergence of CG in this context is guaranteed by the theory of prior-preconditioning we develop. We apply our algorithm to a clinically relevant large-scale observational study with n = 72,489 patients and p = 22,175 clinical covariates, designed to assess the relative risk of adverse events from two alternative blood anti-coagulants. Our algorithm demonstrates an order of magnitude speed-up in posterior inference, in our case cutting the computation time from two weeks to less than a day. Supplementary materials for this article are available online.