Speaker: 朱圣鑫，西交利物浦大学
Date: 2019/04/10, Wednesday, 10:00-11:00
Venue: 数学楼307教室
Abstract: Linear mixed models are frequently used for analyzing heterogeneous data 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. An efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the first derivatives and the second derivatives of the restricted log-likelihood function, i.e., the observed information. Standard approaches to compute the observed information and its expectation, the Fisher information, is computationally prohibitive for linear mixed models with thousands random and fixed effects. Customized algorithms are of highly demand to keep mixed models analysis scalable for increasing high-throughput heterogeneous data sets. In this paper, we will explain why the multi-frontal solver is preferred for such a class of problems, we explore how to leverage an averaged information splitting technique and dedicate matrix transform to significantly reduce computations, and how to use the multi-frontal solvers on linear systems with multiple right-hand sides to accelerate computing. This research is stimulated by a knowledge transfer project by EPSRC, VSN International Ltd and the University of Oxford.