Stochastic Lanczos estimation of genomic variance components for linear mixed-effects models

BMC Bioinformatics
Richard Border, S. Becker

Abstract

Linear mixed-effects models (LMM) are a leading method in conducting genome-wide association studies (GWAS) but require residual maximum likelihood (REML) estimation of variance components, which is computationally demanding. Previous work has reduced the computational burden of variance component estimation by replacing direct matrix operations with iterative and stochastic methods and by employing loose tolerances to limit the number of iterations in the REML optimization procedure. Here, we introduce two novel algorithms, stochastic Lanczos derivative-free REML (SLDF_REML) and Lanczos first-order Monte Carlo REML (L_FOMC_REML), that exploit problem structure via the principle of Krylov subspace shift-invariance to speed computation beyond existing methods. Both novel algorithms only require a single round of computation involving iterative matrix operations, after which their respective objectives can be repeatedly evaluated using vector operations. Further, in contrast to existing stochastic methods, SLDF_REML can exploit precomputed genomic relatedness matrices (GRMs), when available, to further speed computation. Results of numerical experiments are congruent with theory and demonstrate that interpreted-language implement...Continue Reading

References

Dec 21, 2010·American Journal of Human Genetics·Jian YangPeter M Visscher
Sep 6, 2011·Nature Methods·Christoph LippertDavid Heckerman
Jun 19, 2012·Nature Genetics·Xiang Zhou, Matthew Stephens
Jul 23, 2013·PLoS Genetics·Gustavo de Los CamposDaniel Sorensen
Jan 30, 2014·Nature Genetics·Jian YangAlkes L Price
Jun 13, 2018·Nature Genetics·Po-Ru LohAlkes L Price
Apr 12, 2019·BioRxiv : the Preprint Server for Biology·Richard Border, S. Becker

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Methods Mentioned

BETA
genotyping

Software Mentioned

FaST
LMM
ldots
Seed
Python
NumPy
BOLT
GEMMA
GCTA
FOMC

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