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On the convergence rate of sparse grid least squares regression

: Bohn, B.

Fulltext ()

Garcke, J.:
Sparse Grids and Applications - Miami 2016
Cham: Springer International Publishing, 2018 (Lecture notes in computational science and engineering 123)
ISBN: 978-3-319-75426-0
ISBN: 978-3-319-75425-3
Workshop on Sparse Grids and Applications (SGA) <4, 2016, Miami/Fla.>
Conference Paper, Electronic Publication
Fraunhofer SCAI ()

While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, error decay behavior and appropriate couplings between the dataset size and the grid size has not been provided yet. In this paper, we will present a framework which will allow us to close this gap and rigorously derive upper bounds on the expected error for sparse grid least squares regression. Furthermore, we will verify that our theoretical convergence results also match the observed rates in numerical experiments.