SL_REML

SL_REML estimates genomic variance components in linear mixed-effects models using stochastic Lanczos-based REML algorithms to accelerate residual maximum likelihood estimation for genome-wide association studies.

Key Features:

• Novel Algorithms: Implements stochastic Lanczos derivative-free REML (SLDF_REML) and Lanczos first-order Monte Carlo REML (L_FOMC_REML) to address REML estimation challenges.
• Iterative Matrix Operations: Requires a single round of iterative matrix operations followed by repeated evaluations using vector operations.
• Precomputed Genomic Relatedness Matrices (GRMs): SLDF_REML can utilize precomputed GRMs to further expedite computation.
• Performance: Numerical experiments report matching or exceeding the speed, accuracy, and flexibility of existing compiled-language software packages when implemented in interpreted languages.
• Compatibility: Algorithms are suitable for integration into existing GWAS LMM software implementations.

Scientific Applications:

• Genome-Wide Association Studies (GWAS): Facilitates efficient variance component estimation to support large-scale genetic association analyses.
• Linear Mixed-Effects Models (LMM): Enables REML-based estimation of variance components in LMMs that account for fixed and random effects in genetic data.

Methodology:

Uses Krylov subspace shift-invariance and stochastic Lanczos techniques (SLDF_REML and L_FOMC_REML); replaces direct matrix operations with iterative methods, performs a single round of iterative matrix operations followed by vector-based evaluations, employs loose tolerances during REML optimization to reduce iterations, and can use precomputed GRMs for SLDF_REML.