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June 2019 Fast Model-Fitting of Bayesian Variable Selection Regression Using the Iterative Complex Factorization Algorithm
Quan Zhou, Yongtao Guan
Bayesian Anal. 14(2): 573-594 (June 2019). DOI: 10.1214/18-BA1120

Abstract

Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to solve a special class of linear systems, which can increase the speed of the BVSR model-fitting tenfold. The iterative method hinges on the complex factorization of the sum of two matrices and the solution path resides in the complex domain (instead of the real domain). Compared to the Gauss-Seidel method, the complex factorization converges almost instantaneously and its error is several magnitude smaller than that of the Gauss-Seidel method. More importantly, the error is always within the pre-specified precision while the Gauss-Seidel method is not. For large problems with thousands of covariates, the complex factorization is 10–100 times faster than either the Gauss-Seidel method or the direct method via the Cholesky decomposition. In BVSR, one needs to repetitively solve large penalized regression systems whose design matrices only change slightly between adjacent MCMC steps. This slight change in design matrix enables the adaptation of the iterative complex factorization method. The computational innovation will facilitate the wide-spread use of BVSR in reanalyzing genome-wide association datasets.

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Quan Zhou. Yongtao Guan. "Fast Model-Fitting of Bayesian Variable Selection Regression Using the Iterative Complex Factorization Algorithm." Bayesian Anal. 14 (2) 573 - 594, June 2019. https://doi.org/10.1214/18-BA1120

Information

Published: June 2019
First available in Project Euclid: 29 August 2018

zbMATH: 07045443
MathSciNet: MR3934098
Digital Object Identifier: 10.1214/18-BA1120

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Vol.14 • No. 2 • June 2019
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