Efficient Implementation of the AI-REML Iteration for Variance Component QTL Analysis

TL;DR

This paper introduces a computationally efficient AI-REML algorithm for QTL mapping that leverages low-rank matrix representations to significantly reduce computation time in variance component analysis.

Contribution

The authors develop a novel AI-REML implementation that uses low-rank matrix approximations and the Woodbury formula to accelerate QTL analysis.

Findings

Almost twice faster AI-REML with exact low-rank IBD matrix

Significant efficiency gains with spectral decomposition approximation

Applicable to large-scale genetic data analysis

Abstract

Regions in the genome that affect complex traits, quantitative trait loci (QTL), can be identified using statistical analysis of genetic and phenotypic data. When restricted maximum-likelihood (REML) models are used, the mapping procedure is normally computationally demanding. We develop a new efficient computational scheme for QTL mapping using variance component analysis and the AI-REML algorithm. The algorithm uses an exact or approximative low-rank representation of the identity-by-descent matrix, which combined with the Woodbury formula for matrix inversion results in that the computations in the AI-REML iteration body can be performed more efficiently. For cases where an exact low-rank representation of the IBD matrix is available a-priori, the improved AI-REML algorithm normally runs almost twice as fast compared to the standard version. When an exact low-rank representation is not available, a truncated spectral decomposition is used to determine a low-rank approximation. We show that also in this case, the computational efficiency of the AI-REML scheme can often be significantly improved.