Publication
Towards solving massive regression problems
Book Contribution - Book Chapter Conference Contribution
Indirect measurements of physical parameters of interest often require a mathematical model in which these parameters are estimated accordingly to the gathered measurements. Within the Least Squares estimation, the parameters are estimated through a regression problem. The presence of dynamics, multiple sensors and high sampling rates lead to high dimensional regression matrices. This paper deals with solving such massive regression problems efficiently. We revisit Renaut's Least Squares Multisplitting (LSMS) technique aimed at solving the ordinary least squares problem in parallel. The LSMS decomposes the design matrix column-wise into several (possibly overlapping) blocks. The global least squares solution is subsequently replaced by an equivalent set of local least squares problems which are to be solved in parallel. At every iteration step the local solutions are recombined using an appropriate weighting scheme. This allows for a scalable and highly parallel implementation aimed at distributed systems. We study how to decompose the global estimation problem in smaller subproblems and quantify the effects of various possible partitions. The method is illustrated with dedicated numerical simulations and a toy application in the area of sensor fusion.