Fast calculation of restricted maximum likelihood methods for unstructured high-throughput data

Linear mixed models are often used for analysing unbalanced data with certain missing values in a broad range of applications. The restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance parameters. The restricted log-likelihood function involves log determinants of a complicated co-variance matrix which are computational prohibitive. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the observed or the Fisher information matrix. Standard approaches to compute the observed and Fisher information matrix are computationally prohibitive. Customized algorithms are of highly demand to keep the restricted log-likelihood method scalable for increasing high-throughput unbalanced data sets. In this paper, we explore how to leverage an information splitting technique and dedicate matrix transform to significantly reduce computations. Together with a fill-in reducing multi-frontal sparse direct solvers, this approach improves performance of the computation process.