Large-Scale Regression: A Partition Analysis of the Least Squares Multisplitting

Indirect measurements of physical parameters of interest require a mathematical model in which these parameters are estimated from the gathered measurements. Within the least squares (LS) estimation, the parameters are estimated through a regression problem. The presence of dynamics, multiple sensors, and high sampling rates leads to high-dimensional regression matrices. This paper deals with solving such large-scale regression problems time efficiently. We revisit Renaut's least squares multisplitting (LSMS) technique aimed at solving the ordinary LS problem in parallel. The LSMS decomposes the design matrix column-wise into several blocks. The global LS solution is subsequently replaced by an equivalent set of local LS problems that are to be solved in parallel. We study how the user should configure the partition of the multisplitting. We propose a partition design based on a clustering analysis and prove the consistency of this approach. The method is illustrated with dedicated numerical simulations for a highly scalable LS-based problem within engineering: frequency response function (FRF) estimation in the presence of missing output samples. Finally, its practical utility is shown with a laboratory measurement application.